Safety performance metrics for decision making

GEORGIA DOT RESEARCH PROJECT 18-15 FINAL REPORT
SAFETY PERFORMANCE METRICS FOR DECISION MAKING
OFFICE OF PERFORMANCE-BASED MANAGEMENT AND RESEARCH
600 WEST PEACHTREE STREET NW ATLANTA, GA 30308

TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.: FHWA-GA-21-1815

2. Government Accession No.: 3. Recipient's Catalog No.:

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4. Title and Subtitle: Safety Performance Metrics for Decision Making

5. Report Date: March 2021

6. Performing Organization Code: N/A

7. Author(s): Kari Watkins, Ph.D. (https://orcid.org/0000-0002-3824-2027); Michael Hunter, Ph.D.; Michael Rodgers, Ph.D. (https://orcid.org/0000-0001-6608-9333); David Ederer (https://orcid.org/0000-0002-6362-2099)

8. Performing Organization Report No.: 18-15

9. Performing Organization Name and Address: Georgia Institute of Technology 790 Atlantic Drive Atlanta, GA 30332-0355 Phone: (206) 250-4415 Email: kari.watkins@ce.gatech.edu

10. Work Unit No.: N/A
11. Contract or Grant No.: PI#0016324

12. Sponsoring Agency Name and Address: Georgia Department of Transportation Office of Performance-based Management and Research 600 West Peachtree St. NW Atlanta, GA 30308

13. Type of Report and Period Covered: Final; Nov. 2018 March 2021
14. Sponsoring Agency Code: N/A

15. Supplementary Notes: Conducted in cooperation with the U.S. Department of Transportation, Federal Highway Administration.

16. Abstract: This research uses probe vehicle speeds and crash reports to assess safety on road networks. It examines the relationship between the distribution of aggregated vehicle speeds and safety on arterials in Georgia. Using negative binomial models, we estimate the relationship between aggregate speeds and crash likelihood on arterials. Notably, differences in percentile speeds were more informative than individual percentile speeds alone. We propose several metrics of speed differences, each with a different application. First, we propose examining the "high-speed difference," defined as the difference between the 85th percentile speed and the median speed. A second metric, the difference between the 95th and 85th percentile speeds measures the most excessive speeders on a roadway link, noting when the highest speeds differ substantially from already high speeds. Finally, speed dispersion, defined as the difference between the 95th and 5th percentile speeds, is a measure of the overall distribution of speeds. Based on our analysis, we recommend that GDOT (1) Use these metrics as network screening tools to identify locations where potential safety countermeasures, (2) Undertake potential pilot safety studies that assess speed difference metrics over time and validate probe speed data, and (3) Use speed differences in GDOT road safety audits, safety studies, and design guidance.

17. Keywords: Metrics, Speed, Safety, Distributions, Differences, Percentile, Data

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GDOT Research Project No. 18-15 Final Report
SAFETY PERFORMANCE METRICS FOR DECISION MAKING
By Kari Watkins, Ph.D. Associate Professor School of Civil and Environmental Engineering Michael Hunter, Ph.D. Professor School of Civil and Environmental Engineering Michael Rodgers, Ph.D. Regents Researcher School of Civil and Environmental Engineering
David Ederer Graduate Research Assistant
Georgia Tech Research Corporation
Contract with Georgia Department of Transportation
In cooperation with U.S. Department of Transportation Federal Highway Administration
March 2021
The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Georgia Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.
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Symbol
in ft yd mi
in2 ft2 yd2 ac mi2
fl oz gal ft3 yd3
oz lb T
oF
fc fl
lbf lbf/in2
Symbol
mm m m km
mm2 m2 m2 ha km2
mL L m3 m3
g kg Mg (or "t")
oC
lx cd/m2
N kPa

SI* (MODERN METRIC) CONVERSION FACTORS

APPROXIMATE CONVERSIONS TO SI UNITS

When You Know

Multiply By

To Find

inches feet yards miles

LENGTH
25.4 0.305 0.914 1.61

millimeters meters meters kilometers

square inches square feet square yard acres square miles

AREA
645.2 0.093 0.836 0.405 2.59

square millimeters square meters square meters hectares square kilometers

fluid ounces gallons cubic feet cubic yards

VOLUME

29.57

milliliters

3.785

liters

0.028

cubic meters

0.765

cubic meters

NOTE: volumes greater than 1000 L shall be shown in m3

ounces pounds short tons (2000 lb)

MASS
28.35
0.454
0.907

grams kilograms megagrams (or "metric ton")

Fahrenheit

TEMPERATURE (exact degrees)

5 (F-32)/9

Celsius

or (F-32)/1.8

foot-candles foot-Lamberts

ILLUMINATION
10.76
3.426

lux candela/m2

FORCE and PRESSURE or STRESS

poundforce

4.45

newtons

poundforce per square inch

6.89

kilopascals

APPROXIMATE CONVERSIONS FROM SI UNITS

When You Know

Multiply By

To Find

LENGTH

millimeters

0.039

inches

meters

3.28

feet

meters

1.09

yards

kilometers

0.621

miles

AREA

square millimeters

0.0016

square inches

square meters

10.764

square feet

square meters

1.195

square yards

hectares

2.47

acres

square kilometers

0.386

square miles

VOLUME

milliliters

0.034

fluid ounces

liters

0.264

gallons

cubic meters

35.314

cubic feet

cubic meters

1.307

cubic yards

MASS

grams

0.035

ounces

kilograms

2.202

pounds

megagrams (or "metric ton")

1.103

short tons (2000 lb)

TEMPERATURE (exact degrees)

Celsius

1.8C+32

Fahrenheit

ILLUMINATION

lux candela/m2

0.0929 0.2919

foot-candles foot-Lamberts

FORCE and PRESSURE or STRESS

newtons

0.225

poundforce

kilopascals

0.145

poundforce per square inch

Symbol
mm m m km
mm2 m2 m2 ha km2
mL L m3 m3
g kg Mg (or "t")
oC
lx cd/m2
N kPa
Symbol
in ft yd mi
in2 ft2 yd2 ac mi2
fl oz gal ft3 yd3
oz lb T
oF
fc fl
lbf lbf/in2

* SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. (Revised March 2003)

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TABLE OF CONTENTS
TABLE OF CONTENTS ............................................................................................... IV LIST OF FIGURES ...................................................................................................... VII LIST OF TABLES .......................................................................................................... IX EXECUTIVE SUMMARY .............................................................................................. 1 CHAPTER 1. INTRODUCTION .................................................................................... 4 CHAPTER 2. LITERATURE REVIEW ........................................................................ 7
THEORIES ON SPEED AND CRASH FREQUENCY............................................ 7 Solomon's Curve ....................................................................................................... 8 Power and Exponential Models of Speed and Crashes ....................................... 10 Speed Variation and Safety.................................................................................... 13
CRASH COUNT MODELING TECHNIQUES...................................................... 17 SPEED LIMITS AND SAFETY................................................................................ 19 INFRASTRUCTURE, SPEED, AND SAFETY....................................................... 21
Horizontal Curvature ............................................................................................. 22 Lane Number and Width ....................................................................................... 22 Access Density ......................................................................................................... 23 CONGESTION AND SAFETY ................................................................................. 24 NETWORK SCREENING FOR SAFETY .............................................................. 25 FACTORS IN BICYCLE AND PEDESTRIAN CRASHES .................................. 26 Vehicle Speed and Bicycle/Pedestrian Crashes .................................................... 27 Speed and Frequency of Crashes Involving Bicyclists and Pedestrians ............ 27 Severity of Bicycle and Pedestrian Crashes.......................................................... 28 Safety in Numbers: Bicycle and Pedestrian Activity and Crash Rate ............... 31 Land Uses, Land Use Types, and Urban Form .................................................... 32 Public Assets: Transit, Schools, and Parking ....................................................... 34 SUMMARY ................................................................................................................. 35 CHAPTER 3. METHODS.............................................................................................. 37
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CRASH DATA ............................................................................................................ 37
SPEED AND ROADWAY DATA ............................................................................. 38
SPEED LIMIT DATA ................................................................................................ 40
ECOREGION DATA ................................................................................................. 40
DATA PREPARATION............................................................................................. 41
Crashes: Validating and Cross-Referencing Invalid Spatial Data with GEARS Reports.................................................................................................... 42
Processing TMCs and Speeds ................................................................................ 43 Data Conflation Methods ....................................................................................... 45
METHODS FOR STATISTICAL MODELING ..................................................... 53
CHAPTER 4. RESULTS................................................................................................ 55
GEORGIA STATE ROUTE 6 ANALYSIS.............................................................. 56
Percentile Speed Models ......................................................................................... 56 Differences in Percentile Speed Models ................................................................ 58
FULL GEORGIA DEPARTMENT OF TRANSPORTATION ARTERIAL NETWORK ................................................................................................................. 60
Percentile Speed Models ......................................................................................... 61 Differences in Percentile Speed Models ................................................................ 64
BICYCLE AND PEDESTRIAN CRASHES ............................................................ 82
Speed Percentiles and Crash Frequency............................................................... 82 Speed Differences and Crash Frequency .............................................................. 83 Covariates ................................................................................................................ 84
CHAPTER 5. CONCLUSIONS..................................................................................... 86
PROGRAM AND POLICY IMPLICATIONS ........................................................ 90
Probe Vehicle Speed Data as a Network Screening Tool .................................... 91 Network Screening .................................................................................................. 92 Pilot Safety Studies to Assess Speed Difference Metrics Over Time and
Validate Probe Speed Data .................................................................................. 94 Incorporating Speed into Design and Operations................................................ 96
CHAPTER 6. RECOMMENDATIONS ....................................................................... 98
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APPENDIX A. BEST PRACTICES FOR SPEED MANAGEMENT ON ARTERIAL ROADS........................................................................................................................... 100
Enforcement vs. Roadway Design in Speed Management ................................ 101 Active vs. Passive Speed Control Measures........................................................ 108 CONCLUSION ......................................................................................................... 109 APPENDIX B. SUPPLEMENTARY DATA TABLES AND FIGURES................. 110 ACKNOWLEDGMENTS ............................................................................................ 141 REFERENCES.............................................................................................................. 142
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LIST OF FIGURES
Figure 1. Line graph. Solomon's curve of the relationship between crash rate per 100 million vehicle miles traveled and travel speed ..................................................... 9
Figure 2. Equation. Nilsson's power model of changes in speed and crashes.................. 10 Figure 3. Equation. Exponential model of speed and crashes. ......................................... 11 Figure 4. Equation. Generalized power model for speed and crashes .............................. 12 Figure 5. Equation. Power model for speed and injuries .................................................. 12 Figure 6. Line graph. Relationship between average speed and speed variance .............. 15 Figure 7. Flowchart. Taylor's conceptual model relating road characteristics and
speed-based performance metrics to safety outcomes ................................................ 16 Figure 8. Diagram. Weighted nearest neighbor on nearby road links .............................. 19 Figure 9. Line graphs. The S-shaped severe injury and fatality risk curves modeled ...... 29 Figure 10. Map. Area-level social crash cost in Manhattan ............................................. 30 Figure 11. Scatterplot. Sublinear growth rate between pedestrian activity and
pedestrian crash counts at 247 intersections in Oakland, CA ..................................... 32 Figure 12. Diagram. Example of internal (red/blue), external (black) TMCs .................. 40 Figure 13. Flowchart. Sequence of steps in data preparation, and their necessary
inputs........................................................................................................................... 41 Figure 14. Map. Arterial roadways highlighted by 85th percentile speed on each
TMC. ........................................................................................................................... 44 Figure 15. Diagram. TMCs non-primary overlap with primary TMCs ............................ 44 Figure 16. Diagram. Illustration of Intersect process and resulting shapes, data
attribution. ................................................................................................................... 48 Figure 17. Functional form for the negative binomial model. .......................................... 53 Figure 18. Line graph. Relationship between crashes and 85th 50th speed percentile
by AADT .................................................................................................................... 67 Figure 19. Line graph. 85th percentile speeds by land use type. ...................................... 69 Figure 20. Line graph. Speed dispersion (95th-5th percentile speeds) on TMCs by
land use type. .............................................................................................................. 70 Figure 21. Line graph. Distribution of 85th percentile speeds by time of day. ................ 78 Figure 22. Line graph. Distribution of 15th percentile speeds by time of day. ................ 79 Figure 23. Chart. NACTO City Limits guidance on speed performance metrics. ............ 92 Figure 24. Diagram. Coordinated phase diagram for three consecutive intersection
signals ....................................................................................................................... 106 Figure 25. Scatterplot. TMC length and number of crashes in 2017. ............................. 122 Figure 26. Histogram. TMC lengths (miles)................................................................... 123 Figure 27. Bar chart. Crashes per TMC by AADT range. .............................................. 124 Figure 28. Scatterplot. Crashes per TMC in relation to TMC length and AADT
category..................................................................................................................... 125 Figure 29. Line graph. Distribution of 5th percentile speeds per TMC by land use. ..... 127 Figure 30. Line graph. Distribution of 15th percentile speeds per TMC by land use. ... 128 Figure 31. Line graph. Distribution of 50th percentile speeds per TMC by land use. ... 129 Figure 32. Line graph. Distribution of 85th percentile speeds per TMC by land use. ... 130 Figure 33. Line graph. Distribution of 95th percentile speeds per TMC by land use. ... 131 Figure 34. Line graph. Distribution of 5th percentile speeds per TMC by AADT......... 132
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Figure 35. Line graph. Distribution of 15th percentile speeds per TMC by AADT....... 133 Figure 36. Line graph. Distribution of 50th percentile speeds per TMC by AADT....... 134 Figure 37. Line graph. Distribution of 85th percentile speeds per TMC by AADT....... 135 Figure 38. Line graph. Distribution of 95th percentile speeds per TMC by AADT....... 136 Figure 39. Bar chart. Crashes by land use type............................................................... 137 Figure 40. Bar chart. TMC mileage by land use type..................................................... 138 Figure 41. Bar chart. Crashes by AADT category.......................................................... 139 Figure 42. Bar chart. TMC mileage by AADT category. ............................................... 140
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LIST OF TABLES
Table 1. Elvik's estimates for the power model estimating the relationship between operating speed, crashes, and injuries......................................................................... 13
Table 2. Included TMCs by functional class. ................................................................... 45 Table 3. Results of posted speed limit conflation by tolerance distance. ......................... 47 Table 4. Included TMCs by ecoregion. ............................................................................ 49 Table 5. Summary statistics for each TMC on State Route 6. .......................................... 51 Table 6. Summary statistics for each TMC. ..................................................................... 52 Table 7. Negative binomial model of percentile speeds on total annual crashes per
TMC on Georgia State Route 6. ................................................................................. 57 Table 8. Negative binomial model of speed differences on total annual crashes per
TMC. ........................................................................................................................... 59 Table 9. Negative binomial model of percentile speeds on total annual crashes per
TMC. ........................................................................................................................... 63 Table 10. Negative binomial model of speed differences on total annual crashes per
TMC. ........................................................................................................................... 66 Table 11. Crashes and TMC characteristics in urban, small urban, and rural areas. ........ 68 Table 12. Difference in percentile speed models, limited to TMCs longer than
0.025 mile. .................................................................................................................. 73 Table 13. Differences in percentile speed models, statewide crashes TMCs with
13,000 or more AADT. ............................................................................................... 75 Table 14. Differences in percentile speed models, statewide crashes TMCs with less
than 13,000 AADT...................................................................................................... 76 Table 15. Speed differences and crashes, AM Peak. ........................................................ 80 Table 16. Speed differences and crashes, Overnight. ....................................................... 81 Table 17. Speed models, statewide bicycle and pedestrian crashes. ................................ 83 Table 18. Speed difference models, statewide bicycle and pedestrian crashes. ............... 84 Table 19. Results limited to only TMCs longer than 0.025 mile.................................... 110 Table 20. Differences in percentile speed models, limited to TMCs longer than
0.025.......................................................................................................................... 111 Table 21. Morning peak speed percentiles and crashes. ................................................. 112 Table 22. Morning peak speed differences and crashes. ................................................ 113 Table 23. Midday crashes and speed percentiles. ........................................................... 114 Table 24. Midday crashes and speed differences............................................................ 115 Table 25. Evening peak speed percentiles and crashes................................................... 116 Table 26. Evening peak speed differences and crashes. ................................................. 117 Table 27. Nighttime speed percentiles and crashes. ....................................................... 118 Table 28. Nighttime speed differences and crashes........................................................ 119 Table 29. Overnight speed percentiles and crashes. ....................................................... 120 Table 30. Overnight speed differences and crashes........................................................ 121 Table 31. Correlation table of all variables in analysis (correlations greater than |0.7|
highlighted in yellow). .............................................................................................. 126
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EXECUTIVE SUMMARY
Speed is a primary risk factor for road crashes and injuries. Previous research has attempted to ascertain the relationship between individual vehicle speeds, aggregated speeds, and crash frequency on roadways. Although a large body of research links vehicle speed to crash likelihood, there remains disagreement about the precise nature of the relationship.
With the widespread and rapid adoption of cellular phones and global navigation satellite systems technology, new sources of vehicle speed data with high geographic and temporal coverage are increasingly available. These data are frequently referred to as probe vehicle speed data.
This research uses probe vehicle speeds and crash reports to assess safety on road networks. It examines the relationship between the distribution of aggregated vehicle speeds and safety on arterials in Georgia.
Using negative binomial models, we estimate the relationship between aggregate speeds and crash likelihood on arterials. Notably, differences in percentile speeds were more informative than individual percentile speeds alone. For example, models only using the 85th percentile speed yielded counterintuitive results, depending on which variables were included in the model. However, the difference between the 85th percentile and 50th percentile speeds suggests that larger differences in speeds are related to increased crash frequency on a given roadway link. Larger differences between the 95th and 85th percentiles, and 95th and 5th percentiles were also related to increased crash frequency. While differences in speed percentiles were useful for assessing where crashes are more likely to occur, other variables were also related to crash frequency, such as location in an
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urban/rural area, traffic volume, segment length, and the region of Georgia. Thus, speed metrics should be considered within similar contexts when assessing safety.
Our analysis demonstrates a promising application of the National Performance Management Research Data Set (NPMRDS) speed data using speed percentile differences to determine where more crashes may occur. The consistent positive relationship across different iterations of models suggests that speed differences may be a useful operational metric. Conversely, examining individual percentiles alone yielded results that were counterintuitive and changed depending on which percentile values were included in models.
We propose several metrics of speed differences, each with a different application. First, we propose examining the "high-speed difference," defined as the difference between the 85th percentile speed and the median speed. A second metric we found to be related to increased expected crash frequency on a roadway link is the difference between the 95th and 85th percentile speeds. Unlike the high-speed difference, this difference is a metric of the most excessive speeders on a roadway link; it notes when the highest speeds differ substantially from already high speeds. A third metric that we found to be significantly related to crash frequency was the speed dispersion, defined as the difference between the 95th and 5th percentile speeds. The speed dispersion is a measure of the overall distribution of speeds. With a wider distribution of overall speeds, crashes are expected to occur at an increased rate.
Arterials serve multiple purposes, and limiting the highest speeds and speed differentials on arterials may limit the number of crashes and injuries. This research suggests that probe vehicle speeds may provide a useful tool for investigating potential safety problems in the
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future. Further, speed differences, especially those at the higher end of the speed distribution, are a promising means of measuring the speed distribution as it relates to safety. Based on the analysis, three recommendations were identified:
Use probe vehicle speed data and, specifically, differences in high end speeds as a network screening tool to identify locations where interventions are needed.
Undertake a series of pilot safety studies that assess speed difference metrics over time and validate probe speed data against another speed data source.
Use speed differences in GDOT road safety audits, safety studies, and design guidance.
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CHAPTER 1. INTRODUCTION
Road traffic crashes are one of the leading causes of death in the United States, with more than 35,000 deaths every year and over 100,000 injuries (Webb 2020). To prevent road traffic injuries and deaths, it is important to understand the causes for crashes, and implement countermeasures to address risk factors related to crashing.
Speed is a primary risk factor for road crashes and injuries. Previous research has attempted to ascertain the relationship between individual vehicle speeds, aggregated speeds, and crash frequency on roadways. Although a large body of research links vehicle speeds to safety outcomes, disagreement remains about the nature of the relationship between vehicle speeds and safety. Due to the cost and labor-intensive nature of speed data collection, speed studies have traditionally been limited to studies of specific corridors, or instrumented vehicles over a limited time period. With the widespread and rapid adoption of cellular phones and global positioning systems (GPS) technology, new sources of vehicle speed data with high geographic and temporal coverage are increasingly available. These data are typically reported for a sample of vehicles, yielding probe vehicle speed estimates on roadway links. To date, probe vehicle speed data have been used to estimate travel times and congestion levels, but only sparingly to assess safety. An opportunity exists to develop network-level safety performance metrics that can be assessed in near real time.
This research focuses on using probe vehicle speeds and crash injury reports to assess safety on road networks and in safety projects. Because probe vehicle speeds are collected at all times of day, these data provide a more complete understanding of the distribution of
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speeds on specific roadway links. This research is specifically intended to examine the relationship between the distribution of aggregated vehicle speeds and safety.
Recently, probe vehicle speed data have been used to estimate speed on roadway networks. Probe vehicle speeds were initially recorded in a fixed sample of vehicles operated by professional drivers (e.g., taxi and freight operators) or people opting into a study that would place a recorder into their vehicle. Now, probe vehicle speed data are mined from cell phones. As communications technology improves and cell phones become more prevalent, these data are available on an increasingly large roadway network. These data are mined by companies that aggregate cell phone location data from users and calculate speed based on roadway location. These data are then used to calculate vehicle speeds on a highly disaggregated roadway network. These data are now widely available to government agencies. The United States Department of Transportation (USDOT) provides probe vehicle speed data to State and City departments of transportation and metropolitan planning organizations (MPOs) through the National Performance Management Research Data Set (NPMRDS). In addition, transportation network companies (TNCs), such as Uber and Lyft, collect data on vehicles that are serving their customers at any given time. TNCs may act as probes for vehicle speeds on roadway segments in cities that have a large fleet of TNCs operating. Uber created the Uber Movement platform to provide cities with vehicle speeds and travel times on urban roadway networks.
Network-level speed data present a new opportunity for transportation safety research and practice. Much of the research on speed and safety at the network level has been conducted on highways. While highways experience high daily volumes, many crashes occur off the highway network, and frequently on arterials. Increased network coverage means that
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vehicle speed data are now available on many arterial roads. The relationship between speed and safety on arterial roads is likely different than on interstates. Arterials can present a more complex roadway environment with signalized and unsignalized intersections, a mix of road users, diverse land uses adjacent to the roadway, and lack of grade separation. It is important to understand how speed influences safety outside of grade-separated interstates, where the roadway environment and traffic are much different. Further, probe vehicle speeds are likely to become an increasingly popular data source for road safety researchers and practitioners. Understanding the different potential uses for these data will inform future research and practice. This research project had three objectives: (1) review the existing literature on operational speeds and crash frequency; (2) model the relationship between operational speeds and crash likelihood using probe vehicle speed data; and (3) propose different metrics based on probe vehicle speed data and apply it to the Georgia Department of Transportation (GDOT) off-highway network.
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CHAPTER 2. LITERATURE REVIEW
Vehicle speed is a widely studied topic in transportation safety. However, hypotheses on the relationship between speed and crashes frequently contradict one another (Shinar 1998). For example, some studies suggest that traveling at lower speeds is associated with a decreased risk of crashing (Elvik et al. 2019), while others claim that low vehicle speeds may be associated with increased risk of crashing (Solomon 1964). When studying speed, it is important to clarify whether one is interested in the nature of this relationship at the individual driving level or at the aggregated traffic level. At the individual level, increased driving speed is associated with increased braking distance and increased severity of injury should a crash occur (Elvik et al. 2019).
In this review, we focus on the relationship between aggregated operating speeds on roadways and crash frequency. This relationship has been the subject of several research studies, but its precise nature is still debated. In this chapter, we provide an overview of the research on aggregated speeds and crash frequency, as well as the statistical models used to evaluate this relationship. In addition, this review includes research on key mediating factors between operating speed and crash frequency, such as speed limits and roadway characteristics. We also include separate sections on the relationship between speed and safety for pedestrians and cyclists, i.e., vulnerable road users, as speed is an especially important factor for crashes involving these groups.
THEORIES ON SPEED AND CRASH FREQUENCY Several hypotheses have been made about the nature of the relationship between speed and crash frequency. One of the most widely cited studies on the relationship between vehicle
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speed and crash frequency in the United States was conducted by David Solomon on rural roads in 1964. Solomon's study posits that there is a U-shaped relationship where crashes are most likely to occur at the highest and lowest speeds (Solomon 1964). More recent research on the speedcrash relationship suggested that there is a power/exponential relationship between speed and likelihood of crashing (Elvik et al. 2019). The relationship between the mean travel speed (i.e., operating speed) and likelihood of injury has frequently been studied (Aarts and van Schagen 2006, Elvik 2005, Elvik 2013, Elvik et al. 2019, Nilsson 2004, and Shinar 1998). Despite the many studies on the topic of speed and safety, speed measurement has not been incorporated into regular performance management practices. The next sections primarily focus on the different theories about the relationship between aggregated vehicle speed and risk. Solomon's Curve The U-shaped curve was proposed as the prevailing relationship between speed and crash rates as early as the mid-20th century by David Solomon (1964). This model suggests that there is a traffic speed that minimizes collisions, and that large deviations from that speed tend to increase collision risk (Solomon 1964). The "Solomon's curve" presented in figure 1 is based on Solomon's analysis of two- and four-lane rural highways in the 1950s.
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Figure 1. Line graph. Solomon's curve of the relationship between crash rate per 100 million vehicle miles traveled
and travel speed (Solomon 1964).
This theoretical model has been prevalent in transportation engineering for decades and continues to be referenced today. For example, Solomon's curve is featured in the Highway Safety Manual (HSM), Federal Highway Administration (FHWA) guidance on changing speed limits, and state-level speed limit guidance (Parker 1997, AASHTO 2014, Tennessee Department of Transportation 2019). Although "A Policy on Geometric Design of Highways and Streets" does not explicitly cite Solomon, it references his thesis on deviations from speed being dangerous:
"Crashes are not related as much to speed as to the range in speeds from the highest to the lowest. Regardless of the average speed on a main rural highway, the greater a driver's deviation from this average speed, either lower or higher, the greater the probability that the driver will be involved in crashes" (AASHTO 2011, p. 2-83).
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Notably, very low-speed crashes account for less than 1 percent of the crashes in Solomon's study. The relationship between speed and safety at higher speeds in Solomon's study is far more precise. In figure 1 above, a few observations of crashes below 10 mph heavily skew the crash rate at low speeds. Most speeds in Solomon's study were above 45 mph (Solomon 1964). Although the weaknesses of Solomon's study have been pointed out, it continues to be cited today. However, it is increasingly assumed that higher speeds are associated with more and more severe crashes.
Power and Exponential Models of Speed and Crashes Using the Newtonian equations for kinetic energy, researchers developed an empirical model relating mean operating speed to the number of crashes on a typical roadway using a power model (Nilsson 2004). This model states that the increase in the number of crashes is proportional to the increase in operating speed. Nilsson's power model uses the general functional form shown in figure 2.



=





( )

Figure 2. Equation. Nilsson's power model of changes in speed and crashes.

In the equation in figure 2, Nilsson describes a relationship before and after a change in speed. Should a change in aggregate operating speed occur, Nilsson posits that the change in crashes is proportional to the ratio of the change in mean speeds. The exponent on the ratio of average speeds before and after depends on the severity of injuries being calculated. Nilsson's power model can, thus, be fitted for different crash severities and road types. The

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power model has been studied repeatedly and is frequently used as a baseline estimate for safety performance functions (Elvik 2005).
The exponential model has been suggested as more appropriate than a power model for studying the relationship between speed and safety (Hauer 2009). The exponential and power models are very similar, but they differ in one key aspect: the power model suggests that the relationship between speed and safety does not depend on the initial speed, while the exponential model does. The proposed exponential model is given in figure 3, where Y denotes crashes and v denotes speed, subscript 1 after a change in speed and subscript 0 before a change in speed.
1 = 0 ((1-0)) Figure 3. Equation. Exponential model
of speed and crashes.
In other words, the power model assumes that a speed reduction from 30 mph to 20 mph provides the same benefit as a reduction from 70 mph to 60 mph. Conversely, the exponential model suggests that the magnitude of the change in crashes after decreasing from 70 mph to 60 mph would be larger than the change after decreasing from 30 mph to 20 mph.
In response to these criticisms, Elvik (2013) updated his power model to use a continually varying coefficient depending on the severity of the injury. Elvik's updated power model of speed and safety is a set of six equations: one each for deaths, fatal and serious injuries, and all injuries, and then three for the number of crashes in each of those categories, respectively. The general form of the model remains the same, as in the equation in
11

figure 4; however, the exponent x varies from 2 to 6, depending on whether the user is estimating all crashes, injury crashes, or fatal crashes.

1 = (10)0 Figure 4. Equation. Generalized power model
for speed and crashes (Elvik 2013).
To model overall injuries, Elvik proposed adding a second term, Z, to represent the number of people injured or killed before and after a change in speed. The model, thus, becomes as the equation in figure 5.

1

=

(1) 0

0

+

102

(0

-

0 )

Figure 5. Equation. Power model for speed and injuries (Elvik 2013).

The model can, thus, be used to estimate the total change in injuries or injury crashes relative to a change in speed. Elvik's model suggests that there is a clear "doseresponse" relationship between speed and road safety. The larger the "dose" of the speed, the larger the increase in potential injuries. This updated power model is slightly different than Elvik's initial conception, with specific values for each exponent, as described in table 1. Other studies focused more on the roadway context instead of solely speed. In those cases, increases in average speeds differed depending on the class of roadway, with increases in operating speeds increasing risk more on lower roadway classifications relative to higher roadway classifications (Elvik, Christensen, and Amundsen 2004; Nilsson 2004).

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Table 1. Elvik's estimates for the power model estimating the relationship between operating speed, crashes, and injuries (Elvik 2013).
Many studies that examined the effect of average operating speed on a roadway concluded that crash rates increased as operating speeds increased (Aarts and van Schagen 2006). This relationship between speed and crashes can be described using several mathematical models, but the most prevalent are power and exponential functions (Finch et al. 1994; Nilsson 1982, 2004; Elvik et al. 2019). Speed Variation and Safety Speed variation is another measure of speed cited as a predictor of crashes on specific roadway links (Solomon 1964, Lave 1985). Speed variation is frequently assessed using the standard deviation or coefficient of variation of a speed distribution (Taylor, Lynam, and Baruya 2000). These studies suggested that if there is a large standard deviation in speeds, there is likely to be more crashes on a roadway link. However, the magnitude of the relationship between standard deviation and increased probability of crashing is difficult to quantify or interpret in real-world scenarios. Other metrics of speed variation or dispersion have been studied, such as the variance (Kweon and Kockelman 2005).
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Studies that have found a positive relationship between speed variance and crashes often found that there is a negative relationship between average speed and crashes (Lave 1985). Lave's analysis examined the relationship between speed and number of crashes on urban and rural interstates, arterials, and collectors. In each of 12 different regressions, speed variation was significantly related to increased crashes. None of the models with average speed found a significant relationship between average speed and risk of crashes. In fact, in 10 of the 12 regression models, the coefficient on average speed and crashes was negative. Similar to the proposed analysis, Lave used annual speed variation and measures of central tendency. Further, Lave's analysis concluded that changes in speed variation are symmetric across the speed distribution. Under this assumption, an increase of 1 mph in mean speed is equal to a 1-mph decrease in the 85th percentile speed in terms of expected safety outcomes. Lave's conclusion that "variance kills" rather than speed kills, and his suggestion to enforce low speeds (to reduce variance) led several other researchers to reanalyze Lave's data (Levy and Asch 1989, Fowles and Loeb 1989, and Snyder 1989). One of the main criticisms was that Lave's research did not consider the joint effect of speed and speed variance, and a singular focus on increasing average speed to decrease variance. In response to Lave's analysis, Levy and Asch (1989) used the difference between 85th percentile and mean speed, as well as an interaction between mean speed and the difference. Levy and Asch, thus, concluded that speed itself is important, but through its interaction with speed variance.
Shefer and Reitveld (1997) posited that when average speed is held constant, speed variance increases risk, and when variance is held constant, increasing speed increases risk. When both mean speed and variance increase at the same time, risk still increases, but the
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potential contribution of speed variation to risk decreases. Thus, risk still increases, but the marginal effect of the increase in average speed decreases. This argument is presented from Figure 2a of Shefer and Reitveld (1997) in figure 6.
Figure 6. Line graph. Relationship between average speed and speed variance (Shefer and Reitveld 1997, Figure 2a).
Roadway sections with large variations in speed may be indicative of high congestion and low speeds during peak hours, but low congestion and high speeds at other hours. Areas with lower traffic may have more variation in speed but simply have fewer vehicles present on the roadway. Speed variance may capture information on roadways that are built specifically for high congestion conditions, but function poorly at all other times of day. This hypothesis is supported by several studies that found that areas with high speed variances tended to have lower average speeds (Garber and Gadiraju 1989; Taylor, Lynam, and Baruya 2000). Roadways with higher average speeds also tended to have less variation
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in speeds in both studies. As with other areas of speed research, the functional class and context of the roadway are important when considering speed variance. The effect of speed variance is likely different across different functional classes of roadways. Taylor, Lynam, and Baruya (2000) proposed a theoretical relationship between speed, speed variance, and safety, noting that both speed and speed variance are related to safety outcomes and should be accounted for in an analysis or performance metric (see figure 7). Taylor's conceptual framework noted that infrastructural and traffic flow characteristics influence a driver's speed choice and, thus, influence the speed distribution (Taylor, Lynam, and Baruya 2000). In addition, Taylor also pointed out that other factors, such as weather or lighting, influence crash frequency. Notably, Taylor posited that measures of average, spread, and percentage of those exceeding the speed limit on a roadway link influence crash frequency jointly. Thus, Taylor concluded that multiple metrics should be considered together when evaluating safety through speed performance measurement.
Figure 7. Flowchart. Taylor's conceptual model relating road characteristics and speed-based performance metrics to safety outcomes (Taylor, Lynam, and Baruya 2000).
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Considerable theoretical and quantitative evidence exists to suggest that speed variance influences crash frequency, and that increasing variation in speeds is likely to result in more crashes. However, high speeds are naturally more likely to be severe should a crash occur. It is reasonable to suggest that the relationship between speed and crash frequency is likely influenced by the spread of speed as well as the overall operating speed.
CRASH COUNT MODELING TECHNIQUES Crash modeling techniques continue to develop today. Linear models have long been shown to be inadequate since crash outcomes are discrete and at least zero. As a result, Poisson and negative binomial (NB) models have long been the standard for estimating crash frequency (Lord, Washington, and Ivan 2005). The NB model is generally preferred, because the Poisson model makes a restrictive assumption that the dependent variable is not over dispersed (i.e., its variance is greater than its mean). In the case of unlikely, random events such as crashes, the NB model offers welcome freedom from that restriction (Lord, Washington, and Ivan 2005).
Crashes are relatively rare events, and depending on the unit of analysis, many observations may have zero crashes. Zero-inflated negative binomial (ZINB) models have become popular for this kind of data. These models break out observations with zero crashes from observations with at least one crash, modeling them separately (Lord, Washington, and Ivan 2005). ZINB models have shown improved fit compared to NB models in some cases, because aggregated crash data frequently come with a preponderance of zeros. However, they come with an important caveat: ZINB models assume separate models for observations with and without crashes. The distribution for observations with zero crashes suggests that there is an "unsusceptible" population. This distribution is not derived from
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the distribution of all observations (i.e., including those with crashes, or the "susceptible" population), but is an assumed distribution based on only those observations without crashes. Some researchers have considered ZINB models with some skepticism because of this assumption (Lord, Washington, and Ivan 2005).
More recently, Bayesian methods have grown more popular, and are the standard according to the Highway Safety Manual. The key advantage of Bayesian methods is their ability to account for spatial correlation in crash occurrences. Thus, Bayesian methods can account for a significant portion of the variation found in crash data (Aguero-Valverde and Jovanis 2006, Quddus 2008, Chen 2015). Several studies have compared naive models to Bayesian models and found that the latter had significantly greater explanatory power in modeling coefficients related to crash frequency (Quddus 2008; Siddiqui, Abdel-Aty, and Choi 2012). Importantly, Quddus (2008) found that when comparing naive models to Bayesian, most variable coefficients were similar, except for the coefficient for average speed. Notably, Bayesian methods have become the new standard for modeling crashes at the area level (Hauer et al. 2002).
Functionally, accounting for spatial correlation in crashes requires creating a variable for each unit that captures the crash levels of adjacent units. At its simplest, the crash behavior of adjacent neighbors is accounted for, but a weighted nearest neighbor is more common (Aguero-Valverde and Jovanis 2008). Figure 8 shows an example of weighted nearest neighbor logic for nearby road links.
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Figure 8. Diagram. Weighted nearest neighbor on nearby road links (Aguero-Valverde and Jovanis 2008).
Tasic, Elvik, and Brewer (2017) proposed the generalized additive model (GAM) for modeling crashes to account for spatial correlation in crash data. They argued that the modeling process' key advantage is being simpler and less intensive than Bayesian counterparts.
SPEED LIMITS AND SAFETY One of the primary means of speed control in the United States is the setting and enforcement of speed limits. Speed limits can ensure that drivers operate at a prudent and safe speed. The Uniform Vehicle Code (UVC), a set of model traffic laws, recommends establishing uniformity in roadway contexts by setting similar speed limits on roads that are physically similar (Forbes et al. 2012). Speed limits are both posted and statutory, i.e., municipalities set a default speed limit if the limit is not posted. Most states create engineering design guidelines to prescribe specific ranges for speed limits (e.g., 2545 mph for urban arterials), and geometric designs for specific functional classes (e.g., urban arterials may have a 2545 mph speed limit and two to four lanes) (Forbes et al. 2012). The
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posted speed limit is sometimes changed using an engineering study, expert system, or because of a "special" situation such as a school zone (Forbes et al. 2012). Outside of those special cases, there tends to be some degree of similarity between roadways with the same or similar speed limits. Many geometric design elements, such as horizontal curvature, are influenced by the intended design speed, which in turn informs the posted speed limit (Fitzpatrick et al. 2001). As many design elements are based on the design speed, the posted speed limit tends to accurately predict the operating speed on a given roadway (Fitzpatrick et al. 2001, Dixon et al. 2008, Wang et al. 2006).
The relationship between posted speed limits and safety continues to be investigated. Much of the research on speed limits is related to changes in speed limits and whether a change in crashes occurs after the speed limit is changed (Castillo-Manzano et al. 2019; Elvik 2013; Elvik et al. 2019; Heydari, Miranda-Moreno, and Liping 2014; Hu and Cicchino 2020; Kockelman et al. 2006; Silvano and Bang 2016).
Elvik and Vaa (2004) analyzed the results of 52 studies from 1966 to 1995 and concluded that a reduction in speed limit was associated with reduced numbers of fatal and injury crashes, with a larger decrease in fatal crashes. Elvik et al. (2019) revisited the topic again in 2019, reviewing 97 studies that analyzed changes in crashes and injuries related to changes in posted speed limits. Notably, Elvik's research on speed limit changes was specific to areas that changed speed limits without a change in built infrastructure (Elvik 2013; Elvik et al. 2019). A study of disaggregated speed and collision data on high-speed roads (i.e., speed limits 55 mph or above) estimated that a 10-mph increase in speed limit is related to a 3-mph increase in average operating speed (Kockelman et al. 2006). Similarly, decreases in speed do not have a one-to-one relationship with decreases in speed.
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A 2016 Swedish beforeafter study showed that a 10-km decrease in speed limit resulted in a 1.57-km decrease in speed (Silvano and Bang 2016). In addition, other studies found that the mean operating speed may not change, but the higher end of the speed distribution (e.g., 95th percentile speed, or those exceeding the speed limits by 20 mph or more) decreases after speed limits are lowered (Silvano and Bang 2016, Hu and Cicchino 2020). Differences in responses to speed limits may be related to where roads are located. NCHRP 504 notes that nearly all vehicles operating on rural roadways tend to be within 10 mph of the speed limit, while urban and suburban roadways have 510 percent of vehicles operating at speeds outside those bounds (Fitzpatrick et al. 2003). Thus, many analyses have found that average operating speeds tend to change after changes in speed limits. However, the magnitude of rate of change depends on the functional classification of the roadway, the context of the roadway, and local conditions that might influence speed.
INFRASTRUCTURE, SPEED, AND SAFETY The built environment and other vehicles on the roadway influence both the speed and the frequency of crashes. Several characteristics of the roadway and traffic flow are typically included in crash frequency studies. Intuition and significant research indicate that the interaction among drivers and between drivers and their immediate environment greatly influence the chances of a crash. Here, we briefly review some of the key factors that influence both speed and crash frequency.
In addition to speed limits and other traffic control devices, the Highway Capacity Manual (HCM) notes the speed of vehicles on urban streets is influenced by factors in the road environment (AASHTO 2014). These factors include number of lanes, lane width, shoulder width, surface type, access density, presence of cyclists and pedestrians, and land use
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(Ottesen and Krammes 2000, Fitzpatrick et al. 2001, Ewing and Dumbaugh 2009, Ben-Bassat and Shinar 2011, Marshall and Garrick 2011, Gargoum and El-Basyouny 2016).
Many design features are dictated by the speed limit and functional class of the roadway. For example, an urban arterial may be more likely to have a lower speed limit than a rural arterial, and thus fewer and narrower lanes. It is difficult to disaggregate the effect of specific features from the posted speed from the functional class (Gattis and Watts 1999). However, evidence suggests that different design elements have a marginal effect on speed, although it is generally less than speed limit or functional class.
Horizontal Curvature One of the key horizontal design criteria for influencing speed is curve radius. As the radius of a horizontal curve increases, speed increases (Poe et al. 1996, Fitzpatrick et al. 1995, Fitzpatrick et al. 1999, Fitzpatrick et al. 2001). In addition to the curve radius, the deflection angle of a horizontal curve may influence speed as much as or more so than the curve radius on suburban and urban roadways (Fitzpatrick et al. 2001, 2003). Fitzpatrick et al. (2001) posit that deflection angle may explain more variation in speeds because drivers may be more sensitive to the appearance of a curve rather than the perceived comfort of the curve.
Lane Number and Width In general, roadways with more lanes exhibit higher speeds (Zegeer, Deen, and Mayes 1981; Zegeer et al. 1988; Fitzpatrick et al. 2001; Dumbaugh and Li 2010). When more
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lanes are available, drivers may choose to drive at higher speeds, as an increased number of lanes allows drivers to sort themselves by speed (Dumbaugh and Li 2010).
Narrower lanes are associated with lower speeds (Fitzpatrick et al. 2001, Ewing and Dumbaugh 2009, Dumbaugh and Li 2010). Simulator studies suggest that lanes that are physically narrower or appear narrower because of street trees or other roadside elements exhibit slower speeds (Gattis and Watts 1999; Naderi, Kweon, and Maghelal 2008). However, as the overall width of a roadway increases, the effect of lane widths on speed decreases (Gattis and Watts 1999). The width of the roadway, whether right-of-way width or number of lanes, may also be a factor in explaining active transportation crashes. This element of the roadway may affect the bicyclist or pedestrian's ability to judge a safe crossing or turn, as well as having an influence on vehicle speeds (Ma et al. 2010). Ukkusuri et al. (2012) found that the number of lanes was positively associated with pedestrian crash frequency, and that right-of-way width was less effective at explaining crash frequency.
Access Density As the number of access points (e.g., driveways, intersections) increases on a roadway, speeds tend to decrease (Fitzpatrick et al. 2003). With more intersections and driveways, the potential for drivers to turn into or out of the stream of traffic increases. These movements tend to slow traffic down as the driver prepares to turn out of the stream of traffic or enters the stream of traffic. Thus, a disproportionate number of crashes may occur at lower speeds as the potential for conflicts increases (Fitzpatrick et al. 2003). An increase in crashes at low speeds may be a function of conflict density rather than speed itself.
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Access density is frequently related to land use, as denser commercial and residential land uses tend to increase the number of driveways and intersections and are associated with decreasing speeds (Ewing and Dumbaugh 2009; Marshall and Garrick 2011).
Traffic volume, intersection density, and roadway functional class are often included as controlling variables in studies that estimate expected crash frequency. Greater traffic volume leads to increased potential conflict, both among vehicles, and between vehicles and active transportation users (Kaplan and Prato 2015). Some of the earliest speed and safety studies did not control for traffic volume, leading to erroneous results (Baruya 1998, Dumbaugh and Rae 2009).
CONGESTION AND SAFETY Congestion, vehicle speed, crash frequency, and crash severity have a complex relationship. Intuitively, congestion and vehicle speeds are negatively correlated. Less congested roadways allow people to drive at high speeds. However, when roads are more congested, there are more vehicles on the roadway and, thus, a higher number of persons exposed to potential crashes and injuries. Research on the relationship between congestion and safety is mixed, with no accepted relationship (Shefer and Rietveld 1997; Zhou and Sisiopiku 1997; Kononov, Bailey, and Allery 2008; Wang, Quddus, and Ison 2013; Albalate and Fageda 2019; Retallack and Ostendorf 2020). Some research suggests that congestion improves safety by decreasing severe crashes (Shefer and Rietveld 1997), while other research notes that safety decreases with increasing congestion (Kononov, Bailey, and Allery 2008). Similar to the speed and safety relationship, it has been hypothesized that there is a "U-shaped" relationship, where the likelihood of crashes is highest at low and high congestion, with relatively fewer crashes around average congestion (Zhou and
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Sisiopiku 1997), while other evidence suggests that there is no relationship between the level of congestion and safety (Wang, Quddus, and Ison 2009; Quddus, Wang, and Ison 2010).
There is general agreement that increased congestion is related to lower speeds, and lower risk of fatal crashes exists during the congested traffic state (Zhou and Sisiopiku 1997, Ivan et al. 2000, Martin 2002). However, most of these analyses of congestion are conducted on highways, and the relationship between congestion and safety on urban and rural arterials is less clear. Congested roadways, by definition, have a high number of vehicles for the allotted space. However, congested roadways also move more slowly. Thus, it is difficult to state whether congestion itself influences crash risk.
NETWORK SCREENING FOR SAFETY In transportation, the process of analyzing a particular roadway and identifying where dangerous areas are located is referred to as "network screening" (Hauer et al. 2002). The simplest and most common form of network screening is "hotspotting," where the locations with the most crashes over a defined period of space and time are identified and prioritized for safety improvements (Montella 2010). There are several methods of hotspotting, including comparing crash frequencies, crash rate per vehicle volume, and empirical Bayes estimates (Cheng and Washington 2008, Montella 2010). Hotspotting is widely used amongst state and local departments of transportation to prioritize safety investments (Persaud 2001, Elvik 2007, Montella 2010). Crash data are regularly collected and available, making these estimates relatively easy to calculate. However, hotspotting identifies risk after crashes have occurred. Many surrogate safety measures have been proposed to proactively identify risk or supplement hotspotting methods (Moreno and
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Garca 2013; Laureshyn et al. 2017; Tarko 2012, 2018). Surrogate safety metrics tend to be used to evaluate specific intersections (e.g., those with cameras to record traffic) or evaluate projects before and after implementation (Tarko 2012, 2018).
In addition to full network screening, speed data may be used to evaluate particular roadway links or segments to suggest revision in infrastructure or speed limits. For example, the FHWA's USLIMITS2 web-based tool and the National Association of City Transportation Officials' (NACTO) City Limits guidance both use several metrics of speed in addition to infrastructure characteristics (FHWA 2019, NACTO 2020). The FHWA's "Methods and Practices for Setting Speed Limits" informational report reviews several speed study methodologies and notes that several percentile speeds should be collected, and that "the safest conditions occur when all vehicles at a site are traveling at about the same speed" (Forbes et al. 2012).
Safety performance metrics are most useful when they can be applied and analyzed to determine where intervention is needed. In addition to defining the relationship between a risk factor and an outcome, it is important to put the performance metric into use via a regularly reported program.
FACTORS IN BICYCLE AND PEDESTRIAN CRASHES Vehicle speed is an important factor in crashes with pedestrians and cyclists, i.e., vulnerable road users. In this section, we review literature specific to the relationship between vehicle speeds and crashes involving vulnerable road users.
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Vehicle Speed and Bicycle/Pedestrian Crashes The vehicle speed and bicycle/pedestrian crash literature break out broadly into two categories, both of which are described in detail below. The first category examines crash frequency or crash rate in an attempt to understand which factors influence the likelihood of pedestrian crashes occurring. Speed is usually incidental to the modeling specification and interpretation of results in these studies, since area-level speed data have historically been difficult to obtain, and the nature of the relationship between speed and crash likelihood is not universally agreed upon.
The second line of study assumes a crash has already occurred and attempts to measure the relationship between crash characteristics and the likelihood of more severe injuries or fatalities. Speed is often critical to these studies, both because fundamental physics ensures a relationship between the two and because speed data in the event of a crash are more broadly available. Speed estimation in crash reports has been standard practice for some time, and black box recording devices in vehicles have become popular more recently.
Speed and Frequency of Crashes Involving Bicyclists and Pedestrians There is a clear gap in the literature where vehicle speed and crash frequency ought to be addressed. Several studies incorporated speed limits into their analyses (Ma et al. 2010; Zahabi et al. 2011; Siddiqui, Abdel-Aty, and Choi 2012; Chen 2015; Chen and Zhou 2016; Pirdavani et al. 2017), but few considered actual operating speed. One exception is Quddus (2008), who back-calculated average speed from congestion figures and included it in the crash frequency model.
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When included in area-level bicycle and pedestrian crash studies, speed limit is generally a positive and significant explanatory variable in crash frequency (Chen 2015; Ma et al. 2010; Siddiqui, Abdel-Aty, and Choi 2012). However, speed limit has a complex relationship with operating speed (Parker 1997) and in the American context is often tied to roadway functional class. We cannot conclude that including speed limits adequately addresses the effect of vehicle speed profiles in studies such as these.
When speed is considered at all, it is typically incorporated as a single speed benchmark that describes the overall speed level (as in the case of Quddus [2008] or studies using posted speed), not the nature of the speed distribution itself. Speed distribution is rarely addressed in pedestrian or bicycle crash literature.
Severity of Bicycle and Pedestrian Crashes Speed was commonly the primary explanatory variable in several pedestrian and bicycle injury severity studies. Pedestrian crashes were more commonly studied than bicycle crashes. These studies generally modeled the probability of more severe crash outcomes in a pedestrian crash, given a pedestrian crash had taken place.
Kroyer, Jonsson, and Varhelyi (2014) conducted a review of studies that model probability of pedestrian fatalities, finding that the most-cited studies use one of two data sets as the basis for study: one collected by Tefft (2013) and another by Rosen and Sander (2009). These studies generally model crashes using logistic regression, suggesting that the fatality risk curve is S-shaped; that is, risk of severe crash outcomes increases quickly with speeds when speeds are lower, reaches an inflection point, and slows at higher speeds. Tefft thought this inflection point occurred around 40 mph for fatality crashes (figure 9).
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Figure 9. Line graphs. The S-shaped severe injury and fatality risk curves modeled (Tefft 2013).
Kroyer, Jonsson, and Varhelyi (2014) noted that the likelihood of a crash is not as practically important as total crash risk, or likelihood and exposure. Urban settings have both lower speeds and more pedestrian exposure, so they are likely to have greater pedestrian safety benefits to speed reduction and should be considered the primary target areas to reduce vehicle speeds.
Common data sources for studies of this kind are vehicle black box devices (Tefft 2013, Song et al. 2017), crash records themselves (Oikawa et al. 2016), and crashes linked to medical records (Tarko and Azam 2011). Each comes with its own challenges. Black box devices sometimes record vehicle speed (Song et al. 2017), but some require analysis of video at impact to calculate speed (Tefft 2013). Crash records place faith on the responding officer to accurately estimate the speed of the vehicle on impact, which has been shown to be inconsistent (Oikawa et al. 2016).
In some cases, crash frequency and crash severity were modeled together. This was often achieved by separating crashes by severity and modeling crash frequency on each set of
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crashes separately. Researchers could then draw conclusions about which variables have greater or more significant impact on severe crash probability (Kaplan and Prato 2015; Noland, Quddus, and Ochieng 2008). Intuitively, vehicle speed may have a greater positive relationship with severe bicycle and pedestrian crash probability than less severe crashes (Quddus 2008), but more research is needed. Xie et al. (2017) took a unique approach to modeling crash probability weighted by severity. They converted crash severity to crash cost (i.e., the social cost incurred by an injury, debilitating injury, or fatality as reported by the National Safety Council), and modeled crash cost as the dependent variable in an independent study (figure 10).
Figure 10. Map. Area-level social crash cost in Manhattan (Xie et al. 2017).
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Safety in Numbers: Bicycle and Pedestrian Activity and Crash Rate An important line of research explores how bicycle and pedestrian activity and crash rates are related. The phenomenon has been coined "safety in numbers," and suggests that promoting active transportation trips is itself a safety measure. If more bicyclists and pedestrians are out on the streets, the thinking goes, then drivers will grow more aware of them and modify their driving behavior to account for their safety. Geyer et al. (2006) showed that pedestrian activity increases at a greater rate than pedestrian crashes, so crash rate decreases with greater pedestrian activity (figure 11). The phenomenon is common in the bicycle literature, as well (Tasic, Elvik, and Brewer 2017). Others argue that this is not the case. Some evidence suggests that congestion mitigates bicycle and pedestrian crashes by discouraging active transportation trips. Noland, Quddus, and Ochieng (2008) performed a bicycle crash beforeafter analysis of London's congestion charge and found that counts of severe bicycle injuries actually increased. The authors estimate that not just higher traffic speeds, but greater bicycle traffic caused greater exposure to injury crashes for bicyclists.
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Figure 11. Scatterplot. Sublinear growth rate between pedestrian activity and pedestrian crash counts at 247 intersections in Oakland, CA (Geyer et al. 2006).
A key concern with research on safety in numbers is the causal link between activity and safety. Specifically, underlying infrastructure design could affect both activity and safety. For instance, a roadway designed with fewer lanes and for lower vehicle speed might reduce pedestrian crashes on its own and also encourage pedestrian activity through a perception of a safer, more pleasant urban environment. While this question has yet to be completely resolved, the number of active transportation trips has been clearly identified as an important factor in crash frequency.
Land Uses, Land Use Types, and Urban Form Many researchers included surrounding land uses in their models. Considering types of land use (e.g., residential, commercial, industrial) was common, and intuitively these different uses captured details in pedestrian and bicycle travel patterns, as well as the nature of conflicts with vehicles. Frequently, industrial and commercial uses were associated with increases in pedestrian crash frequency, and residential land uses were associated with
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relatively lower crash frequency (Ukkusuri et al. 2012). Crash frequency for pedestrians tended to increase closer to the city center (Kaplan and Prato 2015).
How the studies incorporated land uses varied widely, however. While many studies incorporated simply commercial, industrial, etc., Ma et al. (2010) considered both land use type and intensity. They separated primarily residential land uses and scattered residential land uses categorically.
Some literature suggested that balance among different uses was a factor in pedestrian and bicycle crashes. Wang and Kockelman (2013) found that land use entropy, a measure of uniformity among residential, commercial, office, and industrial land uses, was negatively associated with pedestrian crash frequency. In their study, a more even (uniform) distribution of uses improved pedestrian safety conditions. Chen (2015) found that land use mix had a positive impact on bicycle crash frequency.
The planning literature added to this area of study by considering urban form as well as land use type. Cervero and Kockelman (1997) showed that the "3 Ds" (i.e., density, design, and diversity) had a meaningful impact on pedestrian and automobile trip-taking, with population density being the greatest factor in promoting pedestrian activity and reducing auto activity.
Notably, Dumbaugh and Rae (2009) examined the design of commercial space and its interaction with pedestrian safety. They separated commercial development styles, identifying pedestrian-scaled commercial areas (common in pre-World War II street corner development) as opposed to the more auto-oriented arterial commercial developments. The former focuses on smaller street-fronting development accessed from the sidewalk, while
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the latter is usually anchored by a "big box" store and often places parking between the street and the storefront. Their study found that the pedestrian-scaled commercial development was linked to a reduction in pedestrian crashes, while the arterial style commercial development was associated with an increase in pedestrian crashes. The authors pointed to differences in the nature of conflict between pedestrians and cars, as well as a road design that promoted lower speeds in the first case and higher speeds in the second.
Public Assets: Transit, Schools, and Parking Various public assets along the roadway were considered in the crash frequency literature because they tend to act as indicators of special conditions, such as concentration of active transportation users, complex environments, or concentration of children or the elderly. Most commonly, transit assets and schools were considered, but parks and parking space were also explored.
The presence of schools and parks was often studied in conjunction with pedestrian crashes (Xin et al. 2017, Zahabi et al. 2011). Pedestrians and bicyclists, especially children and teens, are attracted to these environments, so intuitively conflicts with vehicles were more common near their borders. Xin et al. (2017) found that proximity to parks and schools were significant factors in risk of a pedestrian injury in a collision.
The presence of on-street parking was frequently studied as a risk factor in bicycle and pedestrian crashes. In one bicycle study, on-street parking doubled the risk of collision on major roads (Teschke et al. 2012). In a simulated driving study, driver speed behavior was studied in relation to the presence of on-street parking. With the presence of on-street
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parking--and pedestrians accessing those vehicles--drivers generally lowered their speed. However, that compensation was not large enough to safely avoid conflicts that arose. Overall, risk of a crash increased in these environments despite driver speed reduction. The authors of that study concluded that drivers do not sufficiently compensate for the risks of complex urban environments (Edquist, Rudin-Brown, and Lenne 2012).
Transit stops and transit access were commonly included in macroscopic models of pedestrian or bicycle crash counts (Ukkusuri et al. 2012; Wang and Kockelman 2013; Chen and Zhou 2016; Xin et al. 2017; and Tasic, Elvik, and Brewer 2017). These variables were frequently used as a proxy for pedestrian--or, less commonly, bicycle--activity. Going further, researchers considered transit access to be a potential cause of conflict between active road users and vehicles. Transit stops become crossing points for people attempting to make the bus or train. However, this effect independent of pedestrian activity was not clear in the literature. Wang and Kockelman (2013) found that after controlling for pedestrian activity, bus stop density was not significantly related to pedestrian crashes.
SUMMARY A review of the literature revealed that more research is needed to understand the impact of vehicle speeds on safety. Some factors are clearly related to increased crash frequency-- traffic volume, congestion, roadway characteristics, population density, and bicycle/pedestrian activity. In addition, land use characteristics have been shown to be critical factors, including higher traffic volumes and increased intersection density. In general, these same factors are related to increases in crashes involving pedestrians and cyclists should they be present on a given roadway link. Finally, increasing speed is related to increases in crashes and is becoming more prevalent. However, there is less agreement
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on how to best measure speeds for safety performance. Until recently, most speed studies relied on a limited set of speed data from corridor-level and instrumented vehicle studies. With increasingly available operating speed data reported on surface roadways, the relationship between operating speed and crash frequency is an important area of research.
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CHAPTER 3. METHODS
The data used in this analysis came from four different data sources, as follows:
The GDOT Georgia Electronic Accident Reporting System (GEARS) crash database supplied crash data for the years 20132017; these data were processed and provided by GDOT.
The National Performance Management Research Data Set (NPMRDS n.d.) furnished probe vehicle speed data. These data were obtained, consolidated, processed, and maintained by INRIX, Inc. and were accessed for this study via a GDOT data-use license. In addition to the probe vehicle speed data, this data set includes data on roadway traffic volume, number of lanes, and functional class. INRIX began providing speed data for NPMRDS in 2017; thus, 2017 was the only calendar year with complete data for this analysis.
GDOT provided speed limit data. The U.S. Environmental Protection Agency (EPA) website offered ecoregion data,
which we downloaded directly from the website.
In the following sections, we describe these data sources in detail, and then outline the methods used to prepare the final data set. After describing the data and the processes for data preparation and conflation, we discuss the modeling method and why different control variables were included in the analysis.
CRASH DATA The GEARS crash database is an exhaustive collection of crash records submitted in the state of Georgia. This database is web-hosted, and an end user can query the database to
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access crash records by date, time, jurisdiction, manner of collision, crash severity, and other key information provided on the crash record.
GDOT also creates and maintains a spatial dataset of crashes, which has been preprocessed for spatial analysis. The spatial dataset was the primary crash resource used in this analysis, but direct data pulls from GEARS were used to backfill and verify the preprocessed data set.
SPEED AND ROADWAY DATA Roadways and vehicle speeds came from the probe vehicle speed data in the NPMRDS. These data were accessed via the Regional Integrated Transportation Information System (RITIS) platform. Speeds are available as a 5-minute harmonic average for each monitored road segment in the traffic message channel (TMC) system. End users can specify the road segments of interest and the time boundaries to receive speed data and request a download. The data are delivered in a comma-separated value (.csv) file, where one row represents vehicle average speed for a TMC/5-minute interval. The RITIS platform provides a spatial data set of all TMCs for which speed data are collected--a global TMC shapefile--for each U.S. state. These data also contain roadway attributes, such as lane count, annual average daily traffic (AADT), functional class, etc. TMCs are represented as lines.
There is no imputation of speeds within the data set. NPMRDS is built from data sources generated by freight and passenger vehicles. In this analysis, only speeds of passenger vehicles were used. The driving behavior and speed of freight vehicles differs substantially from passenger vehicles due to the extensive driver training completed by freight operators, as well as large differences in the vehicle itself. Future analysis may incorporate freight
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vehicle speeds, as well as speed differences between freight and passenger traffic, but are outside the scope of this analysis.
The NPMRDS speed data were created using a path-processing algorithm. The pathprocessing algorithm was meant to limit biases that may result from variable reporting frequencies (e.g., one source may update every second, while others every minute) and slow vehicles providing more data points (e.g., if a vehicle takes longer to traverse a TMC, it will report more frequently). The path-processing algorithm also normalized the data reports across a fixed period. Speeds that were recorded as less than 3 mph or greater than 100 mph were removed from the dataset.
Speeds were validated regularly against data generated by BluetoothTM and Wi-Fi readers by the University of Maryland's Center for Advanced Transportation Technology (CATT) lab. Validation studies are posted quarterly on different roadway segments to ensure accuracy (Eastern Transportation Coalition 2000). Non-interstate data were checked to be within 10 mph average absolute speed error, and 5 mph of the speed error bias. The average absolute speed error was simply the average of the absolute deviations from the ground truth recorded using BluetoothTM or Wi-Fi data. The speed error bias was simply the average error (not the absolute value). These validations were typically carried out on the mean speed, as well as relative to the 1.96 standard error around the mean (SEM band).
TMCs were defined as either internal or external. External TMCs are stretches of roadway between major intersections or junctions, while internal TMCs are the short segments that intersect or fly over intersecting roads. Internal TMCs mark a transition point on major
39

roadways and freeways around which large portions of traffic may enter or exit the roadway (see figure 12 for an illustration).
Figure 12. Diagram. Example of internal (red/blue), external (black) TMCs (Source: NPMRDS Analytics).
SPEED LIMIT DATA Speed limit data were provided by GDOT in the form of a Keyhole Markup Language Zipped (.kmz) file, which is a Google Earth spatial data format. The data set contains a network of Georgia roadways represented as lines, and each line contains the road segment's speed limit attribute. In this analysis, speed limits were included as ordinal variables for each speed limit in the dataset. Each TMC was assigned a speed limit. This process is described in detail in the "Conflating Speed Limits to TMC" section below. ECOREGION DATA Data on ecoregions in the continental United States are publicly available from the Environmental Protection Agency. Land within each ecoregion shares important climatological and ecosystem characteristics (EPA 2018). Many climate and ecosystem characteristics affect driver behavior, as well as the physical geometry of the roadway. For example, fog patterns can vary substantially across Georgia, which affects driving sight distance. Similarly, rainfall can vary a great deal between different regions, which affects braking distance. These factors, thus, influence speed distributions as well as crash
40

frequency. While precise estimates of these factors are difficult to include for every TMC, we assumed that these conditions are similar within each ecoregion but differ between them. Ecoregions are represented using GIS data, and TMCs were identified as being part of an ecoregion if they fell within the boundaries defined by the EPA. DATA PREPARATION Since several sources of data were used to develop models of operating speeds and crashes, a series of steps was used to conflate these data together. Figure 13 is meant as a visual overview of the different sources of data and conflation steps, which are described in detail in this section.
Figure 13. Flowchart. Sequence of steps in data preparation, and their necessary inputs.
41

Crashes: Validating and Cross-Referencing Invalid Spatial Data with GEARS Reports The GDOT spatial crashes data set contains 412,035 crashes in the year 2017. Within the full crashes spatial data set, about 5 percent (24,000) of crashes were identified as having invalid spatial data. That is, the spatial positions of the crash obtained from the "spatial dataset" were outside the boundaries of Georgia or did not correspond to a valid spatial location. In cases where the indicated spatial locations of the crash were invalid, we crossreferenced the location of the crash from the GEARS database to identify the actual crash location.
As a quality assurance measure, we attempted to recover and validate the location of these data. All 2017 crash records were pulled from the GEARS online database, which contains latitude and longitude attributes. These records were joined to the invalid spatial data by crash ID, a unique identifier in the GEARS crash record. Roughly 19,000 of the 24,000 invalid points successfully joined with their GEARS record based on the crash ID. Latitude and longitude text from the GEARS record was read as spatial data and mapped. Of the 19,000 points, 11,000 were successfully mapped inside the state of Georgia. To confirm the accuracy of the new data, 100 of these 11,000 points were randomly selected for manual verification, and the location described in the crash record itself was compared to the mapped location. For example, if a crash record identified the crash location as 235 Memorial Drive Southeast, the spatial location was checked to determine if the mapped location matched the location identified in the text. All 100 points matched correctly, so all 11,000 of these corrected locations were used in the data set. Overall, the backfilled dataset contained about 399,000 of the initial 421,035 crashes (94.5 percent) in
42

the GDOT crash dataset. These crash data were then mapped onto the TMC network evaluated, resulting in 80,927 crashes analyzed in this research. The process for conflating the number of crashes per TMC is described below in the "Data Conflation Methods" section. Processing TMCs and Speeds To create a spatial data set of TMC road links containing 2017 speed summaries, speed data were summarized by TMC and combined with the spatial data. Figure 14 shows the included TMCs and their relative 85th percentile speeds. TMCs were considered for inclusion if probe vehicle speeds were collected in 2017 and had more than 1,000 speed observations in a given year. Finally, only primary TMCs were included, since TMCs not identified as primary are spatially redundant with primary TMCs (see figure 15). In this analysis, 7,050 TMCs were included, with nearly 93 percent of TMCs located on arterial roadways (table 2).
43

Figure 14. Map. Arterial roadways highlighted by 85th percentile speed on each TMC.
Figure 15. Diagram. TMCs non-primary overlap with primary TMCs (NPMRDS Analytics). 44

Table 2. Included TMCs by functional class.

Functional Class Major Arterial Minor Arterial Major Collector Minor Collector Local Total

Count 6,318
640 74 0 18 7,050

Data Conflation Methods As noted previously, the different data sources in this analysis required a conflation process so they could be evaluated on the same scale. Figure 13 above shows a flowchart of steps in data preparation and the inputs needed to complete those steps. All data preparation was completed in R statistical software and/or ArcMapTM for spatial data.
Conflating Crashes to TMCs Since the unit of analysis in this study is the TMC, crashes were associated with TMCs and summarized to describe the number of crashes on each TMC in 2017. Location in space was the primary characteristic used to associate crashes with TMCs, but the "OnStreet" location in the crash record, and vehicle direction attributes of both the crash record and TMCs were used to complete and validate the matching process between crash and TMC. This spatial conflation was completed entirely in R statistical software.
First, crash points less than 50 ft from any TMC line were considered to have taken place on a TMC and were included. Crashes within 50 ft but identified as taking place on an

45

interstate within their crash record (often "flying over" a non-interstate TMC) were excluded.
At this point, crashes were associated with the TMC located closest to the crash. However, there were 228 cases where a single crash was associated with multiple TMCs by minimum distance. Most commonly, a crash point was located near two overlapping TMCs with opposite directions of travel, but in some cases a crash was located at the intersection of two TMCs. The direction of "vehicle one" was considered first, then "vehicle two." Of the 228 crash records associated with more than one TMC, 124 were resolved this way. If there was no match based on vehicle direction, the TMC was chosen randomly. The direction of travel within the crash record was used to determine which TMC the crash occurred on, and the TMCcrash pair with matching vehicle direction was kept. For example, a crash might be equidistant from two TMCs that operate in opposite directions. If the vehicle in the crash record was identified as traveling eastbound, it would be assigned to the eastbound TMC. After this process was completed, 113 records remained. These were resolved by random choice. After this process, each included crash was associated with exactly one TMC.
Conflating Speed Limits to TMC As mentioned previously, GDOT provided posted speed limit (PSL) data in the form of polylines for the Georgia roadway network. Since no unique identifier was present to link between the TMC dataset and GDOT's speed limit dataset, the two data sets overlapped incompletely in space. Thus, a spatial association was required to attribute speed limit data to TMCs. This process is often referred to as spatial conflation. The spatial components
46

were completed using ESRI ArcGISTM software, and the data management components were completed in R statistical software. The first step in the conflation process was to align the vertices of the two sets of polylines in space. A frequent challenge with line-to-line conflation is the imperfect overlap of two lines in space, even though the lines are meant to represent the same physical object. ESRI's IntegrateTM tool was used to align vertices of the TMC data and the speed limit data within a certain tolerance distance. Choosing an appropriate tolerance required careful consideration of the benefits and drawbacks of setting tolerances of different sizes; too small, and vertices meant to represent the same object would not align, but too large, and vertices that represent different places would erroneously align. Thus, the smallest acceptable tolerance should be chosen. Table 3 shows conflation results at different tolerance levels. The difference in number of TMCs associated with a speed limit changes marginally between 35 ft and 50 ft; thus, 35 ft was chosen.
Table 3. Results of posted speed limit conflation by tolerance distance.
From here, the overlap between TMCs and speed limit polylines could be evaluated. TMC boundaries typically occur at changes in the roadway environment. Thus, changes in speed limits typically coincide with a change in TMC. However, the boundaries in different data sets were created for different purposes, and road segments in the two data sets have
47

different start and end points. ESRI's IntersectTM tool was used to divide unique pairs of overlapping TMC/speed limit polylines into unique observations. The attributes of both data sets were combined in the resulting data. Figure 16 shows an illustration of this process.
Figure 16. Diagram. Illustration of Intersect process and resulting shapes, data attribution.
As shown in figure 16, it was possible for multiple geometries in the output data set to have the same TMC ID. To get to a one-to-one relationship between TMCs and associated speed limit, the intersecting geometries were evaluated by TMC ID, and the posted speed limit of the geometry with the greatest length was selected. If a TMC had more than one speed limit assigned, the majority of the TMC length (95 percent or more) would be covered by one speed limit. After conflation, 86 percent of included TMCs were given a speed limit attribute, but 96 percent of TMC length was preserved (table 3). These figures, and visual confirmation, indicated that conflation with PSL data was more successful in rural areas than urban areas, where TMCs are longer and there tends to be less variation in the roadway environment. The primary reason for the incomplete conflation is lack of speed limit data in some areas of the network, but attempts to integrate geometries which were outside the tolerance range
48

is another possible source of error. All TMCs that did not match to a speed limit through this process were manually assigned a speed limit by manually driving on the missing roadway links or confirming in Google Street View.

Conflating Ecoregions to TMCs Climate, topography, altitude, and other factors are important for crash risk, and they vary in terms of rainfall, sunlight, and fog patterns, which affect visibility and pavement conditions (Taylor, Lynam, and Baruya 2000). These factors are likely related to an individual's choice of speed, the overall speed distribution, and the risk of crashing. In an effort to control for these factors, ecoregion information was added to the TMCs. Ecoregions are represented by large polygons.

There are five ecoregions in the state of Georgia, and all of Georgia falls into exactly one of these ecoregions. TMCs were assigned ecoregions through a spatial join process. First, the center point, or centroid, of each TMC was found. Then, a TMC was given the ecoregion attributes if its centroid falls within that ecoregion. Table 4 shows the count of TMCs by Georgia ecoregion.

Table 4. Included TMCs by ecoregion.

Ecoregion Blue Ridge Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain Total

Count 166
3,224 439
2,424 797
7,050

49

With ecoregions included, the data set used for the full analysis was assembled. Table 5 shows the TMC-level summary of each variable of interest. Crashes were present on most TMCs: 5,731 of 7,050 TMCs, or about 82 percent were associated with at least one crash. Other road characteristics vary widely among TMCs. TMC length varies by several orders of magnitude, from a few thousandths of a mile to over 12 miles. AADT ranges from under 1,000 vehicles daily to over 100,000, and speed percentiles range by 6070 mph. A broad variety of road types and contexts are present in the data set. For the single corridor analysis on Georgia State Route 6, the summary statistics are presented in table 6. Less variation exists in this subset of TMCs. Additional supplementary analyses were completed for only TMCs longer than 0.025 mile, those with more than 13,000 AADT, those with less than 13,000 AADT, and during time periods corresponding to peak and off-peak commuting hours. For the analysis limited to specific times of day, only TMCs with 1,000 speed observations during the specified time were maintained in the analysis.
50

Table 5. Summary statistics for each TMC on State Route 6.

TMC Length (miles)
Crashes
AADT (veh/day)
Speed Limit (mph)
Speed (mph) 15th Percentile
Median 85th Percentile Low Speed Diff. (Median-15th) High Speed Diff. (85th-Median)

Median 0.579 5 29,900 55
29 43 53 11
9

Min 0.006
0 1,420
35
7 17 34 5
4

Max
7.6 60 71,600 65

Std. Deviation
1.32
13
16,874


62

13.8

67

11.9

72

9.38



4.01

23

3.27

51

TMC Length (miles)
Crashes
Injuries
Fatalities
Speed (mph)
Posted Speed Limit 85th Percentile
Median
15th Percentile
High Speed Diff. (85th-Median) Low Speed Diff. (Median-15th)
AADT (veh/day)
Number of Through Lanes

Table 6. Summary statistics for each TMC.

Mean Median

Min

Max

1.556 11.48 4.49 0.046

0.711 4
1.00 45

0.004 0 0 0

12.23 289 76 9

Std. Deviation
2.13
18.9 7.37 0.281

48.00 48.81 40.13 29.99 8.68
10.13 17,800 3.59

45 48 39 27 8
10 14,641
4

20

70

9.38

17

87

12.01

9

68

14.10

4

64

15.54

2

45

3.35

2

36

3.77

531

119,000 13,604

1

8

1.13

52

METHODS FOR STATISTICAL MODELING Negative binomial regressions were used to assess the relationship between relevant roadway features, speed, and crash counts. Negative binomial models are appropriate for modeling crash counts, as crash counts are a nonzero distribution where rates over space or time are quantified. Conventional ordinary least squares regression models are inappropriate for modeling the number of crashes where outcomes are strictly zero or above. Thus, count models were tested and used in this analysis. Typically, Poisson and NB (also known as the Poissongamma) models are used to model crash risk. Both were tested in an initial case study on Georgia Route 6 and then applied to the full arterial network. Unlike Poisson models, the negative binomial accounts for when the variance is larger than the mean, a phenomenon known as overdispersion. The variance of crashes at a particular TNC in this analysis substantially exceeds the mean number of crashes, violating a key assumption of the Poisson distribution. NB regression has been used in numerous studies of crash counts (Lord and Mannering 2010).

NB models are a generalization of Poisson that differs by adding a parameter to account for overdispersion. The NB mean value is Poisson distributed. In this analysis we assumed that the number of crashes at the ith TMC having a mean value of yi crashes per year is given by the equation in figure 17.

() =

(- ) !

Figure 17. Functional form for the negative binomial model.

The Poisson parameter, lambda, is given by the following, = ( + ). The error term, (), differentiates the negative binomial from the Poisson distribution, as it is

53

gamma distributed with mean 1 and variance equal to (the overdispersion parameter). This allows the mean to differ from the variance. is a vector of unknown coefficients that are estimated from the model, while Xi is a vector of the explanatory variables observed at the TMC level, which include annual percentile speeds, differences in annual percentile speeds, the posted speed limit (factor with levels for each speed limit on the corridor), number of lanes (factor), categories for different levels of AADT, and the length of the TMC in miles, as well as metrics for short TMCs.
54

CHAPTER 4. RESULTS
The primary purpose of this research was to investigate the relationship between annual operating speeds on arterial roadway segments and determine whether and how operating speed data could be used for safety performance measurement. To assess these relationships, we used negative binomial models with the number of annual crashes per year as the outcome variable, with various measures of operating speed as the independent variable of interest.
Due to the large size of the speed data set, and the multiple data sources that needed to be conflated to the roadway network, we first tested the conflation and statistical modeling process on one corridor: Georgia State Route 6, which spans from the Atlanta Airport at Interstate 85 to the Alabama state line. We present these results first, followed by the analysis of the full roadway network.
In the initial case study of Route 6, we include estimates of traffic volumes, number of lanes, and length of TMC as control variables. We added further covariates in models of the full network and changed the specification of some covariates to adjust for the larger variation in roadway types and contexts. We included the same set of covariates in all models of the full network, including measures for traffic volume, land use context, geographic region, and length of the roadway segment. The specifications for the State Route 6 analysis are specified slightly differently than those presented for the full network. NB coefficients for continuous variables are interpreted as changes in the log count of the outcome variable. Thus, the signs of coefficients are similar to those in linear regression,
55

but calculating expected changes requires exponentiating the coefficients to determine expected counts from models.
Because the purpose of the research was to create performance metrics based on speed, we also modeled the relationship between operating speed and crashes on subsets of the data to determine whether the relationships were the same in different scenarios. For example, we segmented the speed and crash data to specific hours of the day to examine whether the speedcrash relationship differs between peak hours with congested roadways and off-peak hours when traffic may be at free flow. In the following sections, we present the results of these analyses. First, we present the results for percentile speeds, then differences in percentile speeds.
GEORGIA STATE ROUTE 6 ANALYSIS In this section we present two sets of models--those with individual percentile speeds as independent variables, and those with differences in percentile speeds as independent variables.
Percentile Speed Models The coefficients on the annual 15th percentile speed were consistently negative and small in magnitude, suggesting that as the 15th percentile speed increases, the number of annual crashes on a specific TMC would decrease slightly, on average. This result was consistent across all models, regardless of other variables included in the model. Similarly, the coefficient on the median speed was negative in all but the one model that also included 15th percentile speed (table 7, column 4). Again, this suggests increases in median speed would be associated with decreases in crashes.
56

Table 7. Negative binomial model of percentile speeds on total annual crashes per TMC on Georgia State Route 6.

Intercept
15th Percentile Speed
Median Speed
85th Percentile Speed Ln(AADT)

(1) Total Crashes
-7.07

(2) Total Crashes
-11.3***

(3) Total Crashes
-8.30***

(4) Total Crashes
-8.99***

(5) Total Crashes
-10.2***

(6) Total Crashes
-11.5***

(7) Total Crashes
-7.77***

(8) Total Crashes
-8.36***

-0.032 -0.020 -0.043*** -0.058* -0.063***







-0.084 -0.119



0.019



-0.159*** -0.041***



0.085

0.129*





0.033 0.154***



-0.039**

0.848*** 1.16*** 1.10*** 1.13*** 1.17*** 1.158*** 1.10*** 1.19***

Lanes

0.160



TMC Length (miles)

0.535*** 0.480***

Observations

149

149

Akaike Information Criterion

870.9

892.1

2*(LL)

-852.9 -878.1

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

0.486***
149 894.0 -884.0

0.498***
149 895.4 -883.4

0.504***
149 893.5 -881.5

0.461***
149 890.7 -878.6

0.427***
149 900.8 -890.8

0.389***
149 -909.0 -899.0

57

Coefficients on the 85th percentile speeds yielded results that were inconsistent and varied depending on which other percentile speed covariates were included. For example, in models with only the 85th percentile and median speeds, respectively, the percentile speed coefficients were negative and similar in magnitude (table 7, columns 7 and 8), suggesting a small decrease in expected crashes when either percentile speed increased. However, the coefficients on the 85th percentile speed and median speed were similar magnitude but opposite in direction (table 7, column 6) when both were included in the model. This suggests that including only one percentile speed in a model of crash counts may not capture the full effect of speed changes. Further, percentile speeds were highly correlated with each other. A change in an individual percentile speed is, thus, difficult to interpret. Therefore, we included differences in percentile speeds to better assess whether changes in the speed distribution influenced the expected number of crashes. These results are discussed in the next section, "Differences in Percentile Speed Models."
Control variables for traffic volume, i.e., ln(AADT), and segment length in miles were significant and positively correlated with increased crashes. This correlation is to be expected, and both variables increase exposure for any particular vehicle.
Differences in Percentile Speed Models Based on the important interactions between the percentile speeds, additional models were run using differences in percentile speeds instead. Differences in percentiles speeds were significant, positive, and larger in magnitude than individual percentile speeds. When modeled separately, both the 85th percentile-median difference and median-15th percentile difference are significant and positive, albeit with different magnitudes. Models
58

assessing the lower portion of the speed distribution (difference between median and 15th percentile speed) alone suggest a small change in the expected number of crashes, as the median is larger relative to the 15th percentile (table 8, column 4). Models only considering the higher portion of the distribution (difference between 85th percentile and median speeds) suggest a stronger relationship with the expected number of crashes (table 8, column 3).

Table 8. Negative binomial model of speed differences on total annual crashes per TMC.

Intercept
85th Percentile Speed-Median
Median-15th Percentile Speed

(1) Total Crashes -11.5***
0.164**

(2) Total Crashes -12.3***
0.158***

(3) Total Crashes -12.1***
0.166**

(4) Total Crashes
-14.5***

0.011

0.013

0.069**

Ln(AADT)

1.11*** 1.20*** 1.18*** 1.52***

4 Total Lanes

0.051

6 Total Lanes

-0.034

TMC Length (miles)

0.483*** 0.470*** 0.459*** 0.412***

Observations

149

149

Akaike Information Criterion

870.7

890.6

2*(LL)

-854.7

-878.6

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

149 888.8 -878.8

149 910.2 -900.2

59

When both differences are included in the same model, the higher speed difference is significant and larger in magnitude than the lower speed difference (table 8, column 2). The coefficient on low-speed difference is not significantly different from zero in this model, suggesting that the high-speed difference might be a better means of predicting the expected crash counts per TMC. In all models examining the relationship between speed differences and expected crashes per TMC, the control variables for traffic volume and segment length were positive and significant, as expected. The total number of lanes, and speed limits were not significant in any models in this analysis. The speed limit control variables were close to zero. In this case study, there was no variation in functional class, and relatively little variation in posted speed limit and number of lanes. It is possible that with a larger sample of roadways, there would be more variation in crashes and speeds across different geometries and posted speed limits, and a quantifiable relationship would be detected.
As the difference between 85th percentile and median speed increases, the expected number of crashes increases at a higher rate when AADT is higher (based on model results in table 8, column 3). For example, as the difference between 85th percentile and median speed increases from 5 to 10 on a TMC with 30,000 vehicles, the expected number of crashes increases from approximately four crashes to nine crashes per year.
FULL GEORGIA DEPARTMENT OF TRANSPORTATION ARTERIAL NETWORK The GDOT arterial network in this analysis consists of 10,971 lane miles of roadways, 7,272 signalized intersections, and 7,050 TMCs. All seven GDOT districts are represented in this analysis, which includes large metropolitan areas, small cities and towns, and
60

sparsely populated rural areas. Posted speed limits range from 25 mph to 70 mph, and AADT ranges from 530 to 119,000 vehicles per day. In 2017, 80,927 crashes were identified on this roadway network.
In each of the models, we include the same set of covariates: ordinal variables for AADT, a variable controlling for especially short TMCs (i.e., 0.025 mile or shorter), the length of each TMC in miles, a categorical variable corresponding to the ecoregion where the TMC is located, and a categorial variable for whether the TMC is located in an urban, small urban, or rural area. Numerous models were fit to determine the proper means of assessing covariates. Model results with additional covariates and specifications are available in Appendix B.
Percentile Speed Models In all models, speed percentiles and differences were significantly related to the expected number of crashes per TMC. However, specific percentile speeds did not influence the predicted number of crash outcomes in the same way as differences between percentile speeds.
Models were run using 5th percentile speed, 15th percentile speed, median speed, 85th percentile speed, and 95th percentile speed with the same set of covariates. The relationship between crashes and speed percentiles was initially modeled with each of the percentile speeds listed above as the only metric of speed. In all models (table 9, columns 15), the coefficient was negative, significant, and ranged from 0.044 to 0.046. After modeling the individual percentile speeds, different combinations of percentile speeds were tested. Unlike models using only one percentile speed, combinations of percentile speeds yielded
61

results that were inconsistent. The respective signs and magnitudes of coefficients changes depending on the combinations of percentile speeds included in the model. Coefficients on the 85th percentile speeds yielded results that were inconsistent and varied depending on which other percentile speed covariates were included. For example, in models with only the 85th percentile and median speeds, respectively, the percentile speed coefficients were negative and similar in magnitude (table 9, columns 7 and 8), suggesting a small decrease in expected crashes when either percentile speed increased. However, the coefficients on the 85th percentile speed and median speed were similar magnitude but opposite in direction (table 9, column 6) when both were included in the model. In further models with varying combinations of percentile speeds as explanatory variables, the coefficients on median and 85th percentile speed were significant in combination with one another and alone. The 85th percentile and median speed were not statistically significant (p < 0.10) when modeled pairwise with 15th percentile speed (table 9, column 6). This suggests that including only one percentile speed in a model of crash counts may not capture the full effect of speed changes. We, thus, included differences in percentile speed values to better assess whether changes in the speed distribution influenced the expected number of crashes. These results are discussed in the next section, "Differences in Percentile Speed Models."
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Table 9. Negative binomial model of percentile speeds on total annual crashes per TMC.

Dependent Variable

Crashes

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Constant

2.469*** 2.817*** 3.470*** 4.040*** 4.150*** 3.074*** 2.956*** 2.874***

Percentile Speeds

5th

-0.045***

-0.028*** -0.068***

15th

-0.044***

-0.031***

0.074***

50th

-0.045***

-0.014 -0.021*** -0.077***

85th

-0.046***

-0.001

0.021

95th

-0.043***

0.0001 0.001

Traffic Volume

3049,999 AADT 0.548*** 0.540*** 0.559*** 0.602*** 0.613*** 0.547*** 0.551*** 0.552***

50,000 AADT 0.692*** 0.635*** 0.596*** 0.658*** 0.737*** 0.620*** 0.641*** 0.632***

TMC Length

Short TMC

-1.095*** -1.093*** -0.996*** -0.930*** -0.904*** -1.063*** -1.062*** -1.021***

Total TMC Length (miles)

0.348***

0.360***

0.354***

0.334***

0.317*** 0.361*** 0.359***

0.351***

Land Use Context

Urban TMC

0.537*** 0.505*** 0.471*** 0.475*** 0.510*** 0.490*** 0.499*** 0.499***

Rural TMC

-0.671*** -0.710*** -0.790*** -0.879*** -0.936*** -0.724*** -0.683*** -0.671***

Ecoregion

Piedmont

0.117 0.077 -0.021 -0.105 -0.131 0.050 0.077 0.071

Ridge and Valley -0.115 -0.162 -0.287** -0.393*** -0.448*** -0.193 -0.156 -0.165

Southeastern Plain -0.417*** -0.483*** -0.630*** -0.736*** -0.768*** -0.524*** -0.483*** -0.491***

Southern Coastal Plain

-0.353*** -0.403*** -0.527*** -0.633*** -0.668*** -0.439*** -0.409*** -0.415***

Observations Log Likelihood Akaike Inf. Crit.

7,050 -21,342 42,708

7,050 -21,346 42,717

7,050 -21,369 42,762

7,050 -21,441 42,906

7,050 7,050 7,050 -21,504 -21,339 -21,311 43,033 42,707 42,650

7,050 -21,290 42,613

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

63

Differences in Percentile Speed Models Results using percentile speeds suggested that interactions among recorded percentile speeds are important. Frequently, percentile speed coefficients were close to equal in magnitude and opposite in direction. Further, signs and magnitudes of coefficients would change depending on the different covariates that were included in the model. It is unlikely that only one speed percentile would change at a time; thus, it is critical to model overall changes in the distributions of speed. Modeling differences between percentile speeds can help account for changes in speed distributions.
Based on the important interactions between the percentile speeds, additional models were run using differences in percentile speeds instead. Differences in percentiles speeds were significant, positive, and larger in magnitude than individual percentile speeds. When modeled separately, both the 85th percentile-median difference and median-15th percentile difference are significant and positive, albeit with different magnitudes. The 0.02 coefficient on the lower portion of the speed distribution (difference between median and 15th percentile speed) modeled alone suggests a relatively weak, but statistically relationship between the expected number of crashes and an increasing difference between the median and 15th percentile speed (table 10, column 1). Conversely, models only considering the upper end of the speed distribution (either the difference between 85th percentile and median speeds, or the difference between the 95th and 85th percentile speeds) or the overall speed dispersion (95th-5th percentile) suggest a stronger relationship with the expected number of crashes (table 10, columns 24).
64

When the low-speed difference is included in the same model as estimates of differences in the upper end or the entire speed distribution (table 10, columns 58), the metrics accounting for very high speeds are significant and larger in magnitude than the lower speed difference. This result suggests that the high-speed difference might be a better means of predicting the expected crash counts per TMC. In all models examining the relationship between speed differences and expected crashes per TMC, the control variables for traffic volume and segment length were positive and significant, as expected. The binary variable for a TMC less than 0.025 mile is negative in all analyses. This is likely related to the fact that longer TMCs have more space, providing more opportunities for crashes. Urban TMCs were expected to have the highest number of crashes, followed by small urban TMCs, and rural TMCs; this was consistent in all models. Ecoregion variables were also significant. All other things being equal, TMCs in the Ridge and Valley, Southeastern Plain, and Southern Coastal Plain were expected to have fewer annual crashes than TMCs in the Piedmont and Blue Ridge regions. Results related to each of these variables are discussed in detail below. The total number of lanes and speed limits were not significant in any models in this analysis; those results are available in appendix B.
65

Table 10. Negative binomial model of speed differences on total annual crashes per TMC.

Dependent Variable

Crashes (1) (2) (3) (4) (5) (6) (7) (8)

Constant

1.89*** 1.04*** 0.99*** 1.47*** 1.13*** 1.02*** 1.05*** 1.25***

Speed Difference Metrics

Low Speed Difference (Median-15th)

0.02***

-0.02*** -0.01* -0.01** 0.02***

High Speed Difference (85th-Median)

0.10***

0.11*** 0.05*** 0.09***

Speed Dispersion (95th-5th)

0.08***

0.05***

Excessive Speed Difference (95th-85th)

0.13***

0.04*** 0.13***

Traffic Volume

3049,999 AADT

0.55*** 0.47*** 0.46*** 0.50*** 0.46*** 0.46*** 0.46*** 0.49***

50,000 AADT

0.77*** 0.61*** 0.54*** 0.58*** 0.58*** 0.54*** 0.55*** 0.60***

TMC Length

Short TMC

-1.01*** -1.10*** -1.06*** -0.98*** -1.07*** -1.07*** -1.07*** -1.02***

Total TMC Length (miles)

0.24*** 0.28*** 0.28*** 0.27*** 0.28*** 0.29*** 0.29*** 0.27***

Land Use Context

Urban TMC

0.64*** 0.61*** 0.58*** 0.58*** 0.59*** 0.58*** 0.59*** 0.60***

Rural TMC

-1.24*** -1.08*** -1.08*** -1.17*** -1.09*** -1.08*** -1.08*** -1.14***

Ecoregion

Piedmont

-0.17 -0.05 -0.07 -0.16 -0.07 -0.07 -0.07 -0.12

Ridge and Valley

-0.57*** -0.42*** -0.44*** -0.53*** -0.45*** -0.44*** -0.44*** -0.48***

Southeastern Plain

-0.80*** -0.65*** -0.68*** -0.79*** -0.68*** -0.68*** -0.68*** -0.73***

Southern Coastal Plain

-0.67*** -0.50*** -0.53*** -0.65*** -0.53*** -0.53*** -0.53*** -0.60***

Observations Log Likelihood

7,050 7,050 7,050 7,050 7,050 7,050 7,050 7,050 -21,837 -21,710 -21,695 -21,762 -21,703 -21,691 -21,695 -21,753

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

66

As the binomial coefficients are difficult to interpret, figure 18 displays the marginal effect of increasing difference between 85th percentile and median speed on expected number of crashes is displayed at varying levels of AADT (based on model results in table 10, column 3). As expected, trend lines for different volumes of traffic differ. More crashes are expected when there are higher AADT. As the difference between 85th percentile and median speed increases from 5 to 10 on a TMC with 30,000 vehicles, the expected number of crashes increase from approximately 4 crashes to 9 crashes per year.
Figure 18. Line graph. Relationship between crashes and 85th 50th speed percentile by AADT
Urban/Small Urban/Rural The land use designation was an important factor in this analysis. About 80 percent of crashes occur on urban TMCs, which account for 52 percent of TMCs in this analysis
67

(table 11). Similarly, urban TMCs account for most injuries on the TMC network. Conversely, rural TMCs account for the majority of TMC miles in this analysis (56.8 percent), despite only accounting for 28.2 percent of TMCs. Despite accounting for many of the TMC miles in this analysis, relatively few crashes happen on rural TMCs (8.7 percent). However, when crashes occur on rural TMCs, they tend to be severe. Rural TMCs accounted for about 37 percent and 38 percent of serious injuries and deaths, respectively.

Table 11. Crashes and TMC characteristics in urban, small urban, and rural areas.

Total

Crash Outcomes Crashes Injuries
Serious Injuries Deaths
TMC Characteristics
Miles TMCs

80,927 30,949 3,006
325
10,971 7,050

Urban
64,786 23,746 1,291
155
3,085 3,711

Small Urban
9,044 3,658 603
46
1,650 1,350

Rural
7,097 3,545 1,112 124
6,236 1,989

In all models (Table 10), the location of a TMC in an urban, small urban, or rural area was significantly related to an expected increase in crashes. Urban areas had the highest number of expected crashes, followed by small urban TMCs, and rural TMCs. Urban areas have the highest population and tend to have the most traffic. However, operating speeds and crash risks tend to differ across land use context.
The 85th percentile speed differs between urban, small urban, and rural areas. In figure 19, the distribution of 85th percentile speeds are displayed. Eighty-fifth percentile speeds on
68

TMCs in urban areas tend to be lower than those in small urban and rural areas. The average 85th percentile speed, demarcated by the hashed red line, on an urban TMC is 43.3 mph. Most 85th percentile speeds fall in the 3060 mph range on urban TMCs. On rural TMCs, the average 85th percentile speed is 59.4 mph, demarcated by the hashed blue line. The recorded 85th percentile speeds on rural TMCs are left skewed with a far higher proportion of speeds above 60 mph than urban and small urban TMCs. Thus, the highest speeds on rural TMCs tend to be higher than those on small urban and urban TMCs. Small urban TMCs are sometimes similar to urban TMCs, while other times resembling rural TMCs, which influences speeds. This is displayed in figure 19 where the distribution of 85th percentile speeds is bimodal, with peaks around 40 and 60 mph.
Figure 19. Line graph. 85th percentile speeds by land use type. In addition to the relatively high 85th percentile speeds on rural roads, the overall distribution of speeds on rural TMCs tends to be smaller in magnitude. In figure 20, the distribution of speed dispersions (defined as the 95th-5th percentile speed) is displayed
69

by land use type. The speed dispersion on rural TMCs tends to be relatively small. Thus, the speeds on rural TMCs tend to vary less over the course of the day and year. Operating speeds on rural TMCs, thus, tend to be relatively close over the course of the year. Conversely, the speed dispersions on urban and small urban TMCs tend to be larger, likely reflecting the range of traffic conditions on urban and small urban TMCs. Urban and small urban TMCs tend to have higher traffic volumes and more congestion.
Figure 20. Line graph. Speed dispersion (95th-5th percentile speeds) on TMCs by land use type.
Ecoregions Ecoregions were significant in all models run and are included below. Ecoregions experience different sunlight and weather patterns, and topography varies between each. Thus, different ecoregions are likely to have diverse operating speeds and risks of crashes.
70

In this analysis, the Blue Ridge region is the reference category. TMCs in the Piedmont region, the largest and most populated ecoregion in Georgia, had a positive coefficient and are expected to have a higher crash frequency than TMCs in the Blue Ridge region, all things being equal. However, none of the coefficients were significantly different than the Blue Ridge region. TMCs in Ridge and Valley, Southeastern Plain, and Southern Coastal Plain regions all had negative coefficients and were expected to have fewer annual crashes than TMCs in the Blue Ridge region, all things being equal. The magnitude and significance varied for these ecoregions depending on the covariates included. However, the coefficients on these ecoregions were consistently negative and similar in magnitude in all models.
TMC Length To check for the robustness of results, models were run only on those TMCs that were 0.025 mile or longer. This cutoff was used in Erhardt et al. 2019 to eliminate TMCs that are not representative of roadway segments in the larger network.
There are 781 TMCs that are 0.025 mile or shorter. About 68 percent or 529 are classified as urban, 18 percent or 140 as small urban, and the remaining 14 percent or 112 were classified as rural TMCs.
After running models on only those TMCs longer than 0.025 mile, the estimated coefficients changed very little. Similar to the full network, the coefficient on the lowspeed difference ranges from -0.02 to 0.02 and changes depending on which other speed difference metrics are included. Similarly, coefficients on the high-speed difference, speed dispersion, and excessive speed difference were significant, positive, and much larger in
71

magnitude than the low-speed difference. The coefficients on these metrics varied from 0.07 to 0.15, with the exception of one model where the high-speed difference was not significantly different from zero (table 12, column 6). In models of the full network, these coefficients ranged from 0.05 to 0.13 (Table 10). The control variables for AADT, overall TMC length, land use context, and ecoregion were all similar to prior models.
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Table 12. Difference in percentile speed models, limited to TMCs longer than 0.025 mile.

Constant Speed Difference Metrics Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain
Observations Log Likelihood
p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

(1) 1.96***

(2) 1.11***

Dependent Variable = Crashes

(3)

(4)

(5)

(6)

0.99*** 1.38*** 1.22*** 1.06***

(7) 1.08***

(8) 1.22***

0.02***

0.09***

0.08***

0.15***

-0.02*** 0.11***

-0.01* 0.02 0.07***

-0.01** 0.08***
0.07***

0.01** 0.15***

0.56*** 0.75***

0.47*** 0.57***

0.46*** 0.50***

0.49*** 0.46*** 0.45*** 0.53*** 0.53*** 0.48***

0.45*** 0.49***

0.48*** 0.54***

0.24*** 0.28*** 0.29*** 0.27*** 0.29*** 0.29*** 0.29*** 0.27***

0.63*** -1.28***

0.60*** -1.12***

0.58*** -1.11***

0.57*** 0.59*** 0.57*** -1.19*** -1.12*** -1.11***

0.58*** -1.11***

0.58*** -1.17***

-0.19 -0.58*** -0.82*** -0.66***
6,269 -20,037

-0.07 -0.45*** -0.68*** -0.50***
6,269 -19,935

-0.08 -0.45*** -0.69*** -0.52***
6,269 -19,910

-0.16 -0.53*** -0.79*** -0.62***

-0.10 -0.48*** -0.71*** -0.53***

-0.10 -0.46*** -0.71*** -0.53***

6,269 6,269 6,269 -19,952 -19,926 -19,908

-0.10 -0.46*** -0.71*** -0.53***
6,269 -19,913

-0.13 -0.49*** -0.75*** -0.59***
6,269 -19,948

73

AADT Categories To ensure that the estimated relationships were not influenced by the accuracy of the observed speed data reported at the TMC level, the same models were run on only those TMCs where 13,000 or more AADT per day are reported. This eliminated 3,193 TMCs from the analysis, leaving about 55 percent of the initial 7,050. Once again, the estimated coefficients on speed differences changed very little, if at all. The low-speed difference coefficients ranged from -0.030 to 0.003, while the other speed difference coefficients ranged from 0.050 to 0.130 (table 13). This is similar to the results using the full network, as well as TMCs larger than 0.025 mile (table 12). One notable difference when removing TMCs with relatively low traffic was that most ecoregion coefficients were no longer significant. We also ran this model on only those TMCs with less than 13,000 AADT. Once again, the low-speed difference was small in magnitude relative to metrics that include higher speeds, and the higher speed differences were consistently positive and ranged from 0.050 to 0.110 (table 14). Several ecoregions dropped out of this analysis as there were not enough observations within them.
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Table 13. Differences in percentile speed models, statewide crashes TMCs with 13,000 or more AADT.

Constant Speed Difference Metrics Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain
Observations Log Likelihood
p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

Dependent Variable= Crashes (1) (2) (3) (4) (5) (6) (7) (8) 1.78*** 0.61*** 0.54*** 1.04*** 0.85*** 0.72*** 0.73*** 0.99***

-0.001

0.09***

0.07***

0.13***

-0.03*** 0.11***

-0.02*** 0.03* 0.06***

-0.02*** 0.08***
0.05***

0.003 0.13***

0.50*** 0.43*** 0.42*** 0.45*** 0.43*** 0.42*** 0.42*** 0.45*** 0.75*** 0.64*** 0.58*** 0.60*** 0.59*** 0.56*** 0.57*** 0.60***

-0.81*** -0.89*** -0.87*** -0.82*** -0.85*** -0.85*** -0.85*** -0.82*** 0.40*** 0.48*** 0.48*** 0.44*** 0.48*** 0.48*** 0.48*** 0.44***

0.44*** 0.43*** 0.40*** 0.39*** 0.40*** 0.39*** 0.39*** 0.39*** -0.97*** -0.83*** -0.82*** -0.89*** -0.83*** -0.83*** -0.83*** -0.88***

0.26 -0.14 -0.05 -0.03

0.44** 0.06 0.19 0.22

0.41** 0.06 0.17 0.18

0.32* -0.03 0.05 0.05

0.40** 0.01 0.13 0.16

0.39** 0.02 0.13 0.15

0.39** 0.02 0.13 0.15

0.32* -0.03 0.06 0.06

3,857 3,857 3,857 3,857 3,857 3,857 3,857 3,857 -14,200 -14,126 -14,105 -14,135 -14,111 -14,099 -14,102 -14,135

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Table 14. Differences in percentile speed models, statewide crashes TMCs with less than 13,000 AADT.

Constant Speed Differences Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley
Observations Log Likelihood
p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

Dependent Variable = Crashes (1) (2) (3) (4) (5) (6) (7) (8) 1.44*** 0.94*** 0.95*** 1.45*** 0.91*** 0.87*** 0.88*** 1.09***

0.04***

0.10***

0.07***

0.11***

0.01 0.09***

0.01 0.06*** 0.02*

0.01 0.09***
0.02

0.04*** 0.08***

-1.02*** -1.06*** -1.00*** -0.91*** -1.07*** -1.06*** -1.06*** -1.00*** 0.21*** 0.23*** 0.24*** 0.23*** 0.23*** 0.23*** 0.23*** 0.22***

0.23*** 0.25*** 0.23*** 0.20** 0.25*** 0.25*** 0.25*** 0.22*** -0.99*** -0.88*** -0.89*** -1.00*** -0.87*** -0.87*** -0.87*** -0.93***

-0.16 -0.10 -0.13 -0.20 -0.10 -0.10 -0.10 -0.13 -0.66*** -0.54*** -0.57*** -0.67*** -0.54*** -0.54*** -0.54*** -0.60***

-0.80*** -0.77*** -0.80*** -0.89*** -0.76*** -0.76*** -0.76*** -0.78*** -0.93*** -0.86*** -0.88*** -0.96*** -0.86*** -0.85*** -0.86*** -0.89***
3,193 3,193 3,193 3,193 3,193 3,193 3,193 3,193 -7,291 -7,251 -7,258 -7,295 -7,250 -7,249 -7,250 -7,274

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Time of Day Segmentation Traffic volume changes substantially over the course of a day. Generally, most traffic occurs during peak commuting hours. The volume at any given time of time also influences the overall operating speed on a roadway and the crash risk. Speeds and speed distributions are very likely to differ depending on the hour of day. For example, slower speeds are likely during peak commuting hours in congested areas. Outside peak commuting hours, congestion may decrease, and speeds may increase. Therefore, we analyzed speeds within specific time periods to determine the modeled relationships between operating speeds and crashes on TMCs changes. In this analysis, we analyzed speeds and crashes occurring during the following time periods: AM Peak (6:009:59), Midday (10:0015:59), PM Peak (16:0019:59), Evening (20:0023:59), and Overnight (24:005:59). Figure 21 displays the distribution of 85th percentile speeds. Across all time periods, the 85th percentile speeds are bimodally distributed across TMCs with peaks around 40 mph and 60 mph. During the evening and overnight time periods, 85th percentile speeds tend to be higher than the morning peak, evening peak, and midday periods. Traffic and congestion are higher in the daytime hours, and the relative lack of vehicles on the roadway allows for individuals to drive at higher speeds should they choose to do so.
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Figure 21. Line graph. Distribution of 85th percentile speeds by time of day. Similarly, 15th percentile speeds also tend to be higher during the evening and overnight periods relative to daytime speeds (figure 22). Unlike 85th percentile speeds, the 15th percentile speeds tend to vary more within any category. The 15th percentile speeds during the overnight period are again markedly different than during other periods. With low traffic volumes, it is more likely that "free flow" conditions occur more frequently overnight compared to other times of day.
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Figure 22. Line graph. Distribution of 15th percentile speeds by time of day. Assuming TMCs during the morning peak have more congested periods than during other time periods, we modeled the relationship between speeds, speed differences, and crashes during these time periods. In table 15, the results of the AM peak model are displayed. The coefficients on higher speed differences (85th-median, 95th-5th, and 95th-85th) are notably smaller, ranging from 0.01 to 0.06. However, these metrics are still positive, significant, and larger in magnitude than the low-speed difference, which continues to range from -0.01 to 0.02. Table 16 displays results during the overnight period (24:00 5:59). Similar to the AM peak, the magnitudes of the coefficients on higher speed difference metrics are smaller than in other models, ranging from 0.01 to 0.08. The lowspeed difference remains small relative to these metrics.
79

Table 15. Speed differences and crashes, AM Peak.

Constant Speed Differences Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain
Observations Log Likelihood
p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

Dependent Variable: Crashes (1) (2) (3) (4) (5) (6) (7) (8) -0.27 -0.68*** -0.62*** -0.30* -0.65*** -0.67*** -0.66*** -0.51***

0.02***

0.06***

0.04***

0.05***

-0.01 0.06***

-0.003 0.05*** 0.01

-0.004 0.06***
0.01

0.02*** 0.05***

0.54*** 0.50*** 0.50*** 0.53*** 0.50*** 0.50*** 0.50*** 0.52*** 0.74*** 0.67*** 0.65*** 0.68*** 0.66*** 0.66*** 0.66*** 0.69***

-1.13*** -1.13*** -1.11*** -1.09*** -1.12*** -1.12*** -1.12*** -1.12*** 0.27*** 0.30*** 0.30*** 0.28*** 0.30*** 0.30*** 0.30*** 0.29***

0.73*** 0.68*** 0.68*** 0.69*** 0.68*** 0.68*** 0.68*** 0.70*** -1.13*** -1.09*** -1.10*** -1.14*** -1.09*** -1.09*** -1.09*** -1.10***

0.07 0.10 0.09 0.05 0.10 0.10 0.10 0.08 -0.36** -0.30* -0.31* -0.36** -0.31* -0.31* -0.31* -0.33* -0.63*** -0.58*** -0.59*** -0.65*** -0.59*** -0.58*** -0.58*** -0.60*** -0.46*** -0.40** -0.41** -0.47*** -0.41** -0.40** -0.40** -0.43**
7,050 7,050 7,050 7,050 7,050 7,050 7,050 7,050 -11,415 -11,379 -11,383 -11,406 -11,378 -11,378 -11,378 -11,400

80

Table 16. Speed differences and crashes, Overnight.

Dependent Variable: Crashes

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Constant Speed Differences Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain

-1.98*** -2.32*** -2.23*** -1.92*** -2.28*** -2.30*** -2.29*** -2.09***

0.02**

-0.01

0.07***

0.08***

0.05***

0.04***

-0.01 0.06** 0.02

-0.01 0.02* 0.08***
0.01 0.04***

0.21** 0.20** 0.21*** 0.23*** 0.20** 0.21** 0.20** 0.21*** 0.32** 0.25* 0.27* 0.32** 0.25* 0.25* 0.25* 0.31**

-1.74*** -1.68*** -1.68*** -1.71*** -1.67*** -1.67*** -1.67*** -1.72*** 0.27*** 0.29*** 0.29*** 0.28*** 0.29*** 0.29*** 0.29*** 0.28***

1.06*** 1.00*** 1.00*** 1.04*** 1.00*** 1.00*** 1.00*** 1.03*** -0.70*** -0.70*** -0.71*** -0.73*** -0.71*** -0.71*** -0.71*** -0.70***

0.47* 0.06 -0.01 0.40

0.48* 0.10 0.02 0.44*

0.47* 0.09 0.01 0.42

0.47* 0.06 -0.02 0.39

0.48* 0.10 0.02 0.44*

0.47* 0.10 0.02 0.44*

0.47* 0.10 0.02 0.44*

0.47* 0.07 0.00 0.40

Observations Log Likelihood

4,336 4,336 4,336 4,336 4,336 4,336 4,336 4,336 -4,932 -4,915 -4,917 -4,929 -4,915 -4,914 -4,914 -4,927

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

81

BICYCLE AND PEDESTRIAN CRASHES The results of two sets of models are presented in this section: (1) models including absolute speed percentiles (15th, 50th, and 85th), and (2) models including high- and/or lowspeed differences (85th-50th and 50th-15th). The models for bicycle and pedestrian crashes differ from those for all crashes. For example, the total number of lanes was positive and significant in models for bicycle and pedestrian crashes. In addition, roads classified as local roads tended to have fewer expected crashes. However, speed differences tended to be more useful for predicating crash counts than percentile speeds alone. Speed Percentiles and Crash Frequency Table 17 shows the results of models relating speed percentiles to crashes on Georgia TMCs. When all speeds are included (models 1 and 2), each percentile speed coefficient is negative, not significant, and close to zero. However, when models do not include all three percentile speeds, the sign and significance of each of the speed coefficients changes. When two are included (models 35), one or both speed coefficients become statistically significant. When only one percentile speed is included (models 68), its coefficient is negative and significant, with roughly the same magnitude, regardless of which speed measure is included.
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Table 17. Speed models, statewide bicycle and pedestrian crashes.

Crashes (1) (2) (3) (4) (5) (6) (7) (8)

Constant Percentile Speeds 15th Percentile 50th Percentile 85th Percentile Traffic Volume AADT TMC Length Miles TMC < 0.5 Miles Speed Limits Posted Speed (mph) Road Context Thru Lanes > 4 Small Urban Urban Area Local Road

-6.87*** -5.74*** -5.74*** -5.69*** -5.70*** -5.92*** -5.71*** -5.78***

0.00 -0.07* 0.02

0.00 -0.06* 0.01

-0.06*** 0.01

-0.03** -0.03**

-0.01 -0.05**

-0.04*** -0.05*** -0.05***

0.84*** 0.66*** 0.66*** 0.67*** 0.66*** 0.67*** 0.67*** 0.71***

0.3*** 0.32*** 0.32*** 0.31*** 0.32*** 0.31*** 0.32*** 0.30*** -1.34*** -1.34*** -1.34*** -1.30*** -1.33*** -1.34*** -1.32*** -1.23***

-0.03*** -0.03*** -0.03*** -0.03*** -0.03*** -0.04*** -0.03*** -0.03***

0.29** 0.25 0.56** 1.29**

0.29** 0.25 0.56** 1.29**

0.32** 0.23 0.55** 1.29**

0.30** 0.24 0.56** 1.29**

0.34** 0.21 0.55** 1.31**

0.29** 0.25 0.56*** 1.29**

0.31** 0.29 0.60*** 1.31**

Observations Log Likelihood

7,050 7,050 7,050 7,050 7,050 7,050 7,050 7,050 -2,599 -2,586 -2,586 -2,588 -2,586 -2,592 -2,586 -2,593

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

Speed Differences and Crash Frequency Table 18 shows the model results of the speed differences model. When the high-speed difference is included, it is positive and significant in all model specifications. This result is robust to changes in the model, such as the inclusion of the low-speed difference or controlling variables (models 12, 4). The low-speed difference has a negative relationship with crashes that is much smaller in magnitude than the high-speed difference. In addition, when the high-speed difference is removed from the model, the low-speed difference is close to zero and not significant (models 1 and 4).

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Table 18. Speed difference models, statewide bicycle and pedestrian crashes.

Dependent Variable

Crashes (1) (2) (3) (4)

Constant

-7.83*** -6.92*** -7.02*** -6.90***

Speed Differences

High Speed Difference 0.09*** 0.07***

0.09***

Low Speed Difference -0.03

0.00 -0.03*

Traffic Volume

AADT

0.90*** 0.73*** 0.80*** 0.73***

TMC Length

Miles

0.27*** 0.30*** 0.28*** 0.30***

TMC < 0.5 Miles

-1.31*** -1.30*** -1.17*** -1.29***

Posted Speed Limit

Posted Speed (mph) -0.08*** -0.08*** -0.08*** -0.07***

Road Context

Thru Lanes > 4

0.31** 0.36*** 0.40*** 0.33**

Small Urban Area

0.33 0.40* 0.36*

Urban Area

0.69*** 0.76*** 0.71***

Local Road

1.40** 1.43** 1.40**

Observations Log Likelihood

7,050 7,050 7,050 7,050 -2,620 -2,609 -2,620 -2,607

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

Covariates

For all models of speed percentile and speed difference, the natural logarithm of AADT, segment length, short TMC flag, TMCs on local roads, and having more than four through lanes and being located in an urban area are positive and significant. The magnitude of

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AADT decreases when lane number, urban area, and functional class covariates are included. Posted speed limit is negative and significant in all cases. The coefficients for posted speed, segment length, short TMCs, TMCs on local roads, and greater than four through lanes do not change substantially based on which variables are included.
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CHAPTER 5. CONCLUSIONS
Assessing safety performance on roadway networks is difficult. Most transportation agencies and organizations use "hotspotting" to identify areas where an inordinate number of crashes occur. Crash data, while not perfect, are regularly collected and mostly accurate. Areas with extraordinarily high frequency or extraordinarily high crash severity are almost certainly more dangerous than area with neither high frequency nor severity of crashes. However, there are gaps in the safety picture that crash data present due to the random occurrence of crashes, underreporting of crashes for certain roadway users, and many other factors. Therefore, it is important to use other sources of data to better understand some of the factors that have been shown to influence crashes, such as speed.
Until very recently, few transportation organizations had access to regularly collected network-level vehicle speed data. Through the NPMRDS, Georgia DOT can monitor speeds on their roadway networks, and by extension safety on those networks. This is especially relevant on nonhighway road networks, where there is a greater variety of road users and contexts--a high number of intersections, interactions with pedestrians and cyclists, and potentially high differentials in vehicle speeds. However, there has been relatively little research on how to analyze regularly collected vehicle speed data on the network level to analyze safety outcomes. In addition, the NPMRDS speed data are very numerous and difficult to manipulate. While it is a potentially useful data source, it is necessary to reduce the data in a meaningful way for practitioners.
Our analysis demonstrates a promising application of the NPMRDS speed data using speed percentile differences to approximate roadway risk. In each model run, the speed percentile
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values were significantly related to the expected number of crash outcomes. This was the case on the full network as well as when segmenting the data based on factors that might influence speed distributions and crash risk: traffic volume, time of day, TMC length, and only considering pedestrian and bicycle crashes. The consistent positive relationship across different iterations of models suggests that speed differences may be a useful operational metric. Conversely, examining individual percentiles alone yielded results that were counterintuitive and changed depending on which percentile values were included in models. Using only one percentile value is unlikely to inform practitioners about the overall safety on a particular roadway link. Several studies have noted that speed variation might be an appropriate indicator of risk on roadways (Solomon 1964, Lave 1985, and Kweon and Kockelman 2005). Newly available information in the NPMRDS provides extensive and timely data that can be used to calculate the dispersion of speed on road sections.
Typically, speed dispersion is measured using the standard deviation of speeds on a road network. This is a reasonable estimate of the dispersion of speeds; however, it suffers from several limitations. Standard deviation treats differences in high speeds the same as differences in lower speeds. It is likely that the higher speeds have a different influence on crash risk than lower speeds. Further, it is difficult for practitioners to understand what a one-unit increase in standard deviation means in practice. Rather than using these metrics of speed dispersion, we propose using a measure of speed difference. Our research assessed several options for measuring speed differences, each with a different application. First, we propose examining the "high-speed difference," defined as the difference between the 85th percentile speed and the median speed. A second metric found to be related to increased expected crash frequency on a roadway link is the difference between the 95th
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and 85th percentile speeds. Unlike the high-speed difference, the difference between the 95th and 85th percentile speeds is a metric of the most excessive speeders on a roadway link. This speed metric does not characterize the speed of the typical road users but notes when the highest speeds differ substantially from already high speeds.
In this research, both the high and excessive speed differences were significantly related to the frequency of crashes on the surface roadway network in Georgia. Importantly, the coefficients on speed difference have a practical interpretation. As the difference between 85th percentile speed and median speed, or the difference between the 95th and 85th percentile speed increases, the expected number of crashes per segment increases. Models including only one percentile speed yielded coefficients that were confusing (e.g., increasing percentiles at different levels could either increase or decrease the expected number of crashes). In addition, a change in only one percentile value may yield little information about overall speeds on the roadway section.
A third metric that was significantly related to crash frequency was the speed dispersion, defined as the difference between the 95th and 5th percentile speeds. The speed dispersion is a measure of the overall distribution of speeds. When there is a wider distribution of overall speeds, crashes are expected to occur. However, the speed dispersion is highly correlated with both the high-speed difference (85th percentile median) at 0.91 and the excessive speed difference (95th percentile 85th percentile) at 0.87. While the speed dispersion is correlated with the low-speed difference (median 15th percentile), the correlation is weaker (0.44). The speed dispersion is most likely largest when high speeds are higher, rather than lower speeds being lower. Thus, using the overall speed dispersion,
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like the standard deviation of speeds, should be done in combination with metrics at the upper end of the speed distribution.
Understanding how the top-end speeds deviate could be more useful than simply understanding the median or average speed. For example, a congested roadway might exhibit a mean speed close to the posted speed limit because of high congestion at peak times (very low speeds), and very high speeds at free flow. Measuring the difference between speeds at the high end of the distribution would capture this effect in a way that a simple average or median would not. Further, different roadways are likely to exhibit different characteristics. Some roadways are meant to operate at higher speeds. Noting the median or average speed is higher is not necessarily indicative of a more dangerous road. However, noting that the top end of the speed distribution is disproportionally higher than other observed speeds on the roadway might suggest safety issues.
This research is the first to conflate speed, crash, and roadway attribute data in Georgia to test relationships between expected crashes and speeds; however, it has limitations. The availability of crash data, speed, and covariate data was limited to 2017. Future research should consider multiple years of data in order to test whether the estimated relationships between speed differences and crash frequency hold over time. Another limitation is that the outcome variable is "crashes," and distinguishing between severe and less severe crashes is difficult. When modeling reported injuries, the results do not change. High-end speed differences remain an important metric for determining where injuries occur, as the expected number of crashes per TMC and the expected number of injuries per TMC is highly correlated. However, estimating the severity of injury using speed differences is difficult. Fatal crashes account for less than 0.01 percent of crashes in this dataset, and it is
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difficult to model any expected relationship when so few TMCs experience crashes in a given year. Further, injuries and injury severity are assessed by police and reported in the crash record. While it is the best data available, reporting between agencies and even individual officers may be inconsistent across all years of crash data provided. Improved data collection is necessary to assess injury severity as it relates to crashes at the network level. Despite these limitations, understanding where crashes and reported injuries are most likely to occur is an important step in identifying higher risk roadways and improving safety for all road users. Establishing safety performance metrics beyond crash counts is an important step in building a safer roadway system.
Safety performance metrics are limited by available data and tools to analyze it. With widely available speed data, it is possible to create improved, easy-to-interpret performance metrics for practitioners to apply on roadway networks. Crash reporting suffers from a substantial lag between the event and reporting, while regularly reported probe vehicle speed data are available to the Georgia Department of Transportation for an extensive network of roadways in close to real time. Creating safety performance metrics that can predict where crashes are most likely to occur is necessary to save lives and to allocate limited resources efficiently.
PROGRAM AND POLICY IMPLICATIONS The statistical models developed in this research are useful only if they can be applied to real-world scenarios. In the following sections, we review potential applications of these metrics, and outline some key means of addressing safety problems once they are identified.
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Probe Vehicle Speed Data as a Network Screening Tool State and local governments are increasingly monitoring speeds on roadways as part of their safety performance evaluations. While this research was being conducted, the National Association of City Transportation Officials released its City Limits guidance and suggests using the standard deviation, median, 85th percentile, and 95th percentile speeds to assess corridor performance (City Limits 2020). Our research suggests that the percentile speeds cited in the NACTO guidance are important but should be evaluated in relation to one another. Speed differences are a relatively simple means of assessing the range of speeds experienced on a roadway, particularly at the higher end (85th-median), as well as the range seen among the highest speed vehicles (95th-85th). NACTO's guidance notes the importance of speed dispersion by including the standard deviation as a potential speed metric (see figure 23). However, the standard deviation may overweight the influence of deviations on the lower end of the speed distribution. Similar results were seen by Elvik et al., where they demonstrated that a project may not substantially change the mean speed on a particular roadway, but it very well may change the top end speeds, which are likely related to serious and fatal injuries (Elvik et al. 2019).
Thus, the locations with the greater differences in the high-speed range would likely have received the most safety benefit from treatments that address these speed differences. It is therefore critical that any speed-based safety metric be able to identify these sites separately from low-end speed variation sites. Using metrics based on the higher portion of the speed distribution can add a critical element to the analysis of a project to determine whether crashes are more likely to decrease. By robustly assessing program effectiveness, GDOT can spend limited budgets more effectively, and scale up interventions that work.
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Figure 23. Chart. NACTO City Limits guidance on speed performance metrics.
Network Screening Given the importance of speed differences in the higher speed range, a network evaluation approach can have several implications for transportation policy and practice. Typically, safety studies are not conducted until a high number of crashes occur in a particular location, an emotionally jarring event occurs, or if concerned citizens are organized around the topic. Rather than relying on information about crashes that have already occurred, GDOT can proactively monitor their transportation networks and identify locations with potential speed-related safety issues before people are seriously injured or killed on the
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roadway. In addition, crashes are relatively infrequent and can vary substantially from year to year at a specific location.
Network screening provides an additional tool for identifying high-risk areas for project prioritization and budgeting. Crash data are a reactive safety measure, i.e., safety issues are not identified until after crashes occur. Sufficient reporting of crash data can take several years. Speed-based metrics can be proactive, identifying potentially relatively high-risk areas before crashes are reported, and as a supplement to network screens based on crash reports. While speed data cannot replace crash data as a means of assessing safety, probe vehicle speed data can supplement crash-based network screening, potentially reducing the time window of crash data needed before mitigation actions may be taken.
For instance, safety performance metrics are reported quarterly at GDOT, and aggregated system-wide and regionally, including "Mileposts" performance measures on a quarterly basis (GDOT, 2018). The current publicly reported safety mileposts are quarterly crash deaths, work zone deaths, and Highway Emergency Response Operators (HERO) response times. Speed-based network screening is complementary to these metrics and could be reported internally for operations purposes. For example, a speed-based network screen could categorize roadway links having a "high," "medium," or "low" high-speed difference (85th-median). Corridors where the majority of TMCs are categorized as having higher high-speed differences may be identified for further analysis. Similarly, speed differences could be incorporated into dashboards, reports, and tools where probe speeds are already used to characterize roadway segments.
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As with any metric, speed differences alone should not be the sole measure that is used for decision making. As our statistical models demonstrate, there are many factors that contribute to increased number of crashes on a given roadway. The amount of traffic, land use context, roadway design, and geographic location are all important considerations when assessing the level of safety. However, probe speed data may be used in addition to other information to determine when speed reduction and/or speed variability reduction may result in significant safety benefits.
Pilot Safety Studies to Assess Speed Difference Metrics Over Time and Validate Probe Speed Data In addition to evaluating the roadways at the network level, probe speeds may be useful for evaluating specific safety projects. Our analysis of State Route 6 suggests that these data are useful at the corridor level in addition to the network level. When GDOT is attempting to determine whether specific safety projects are successful or needed, speed differences could contribute another data point on which to make decisions.
Beyond established programs, probe-based speed data may be used for before-and-after project safety evaluations. Safety data for project evaluation are typically limited to crash counts. Where speed assessment is included, it is commonly in a limited before-and-after period (e.g., 2 months before implementation and 2 months after implementation). However, the wealth of probe data now available vastly expands the pool and time frame of potential speed data. Probe vehicle data is passively collected when substantial vehicle volumes are present and is archived for several years. Thus, probe vehicle speed data may be considered for additional baseline, and longer term follow-up data, capturing trends in the speed differences before and after a project. While probe vehicle speeds cannot
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singlehandedly replace crash and speed studies for projects, they are a useful tool for providing more insight on the project performance.
To use the probe vehicle speed data for this type of analysis, we recommend that GDOT select a series of corridors to regularly conduct assessments of probe speed data over time. These studies should include the following:
Regularly reported crash and traffic volume data. Data about the speed limit and infrastructure on the corridors.
Ideally, the selected corridors should include areas that are generally stable in terms of traffic conditions. "Stable" corridors should be those where GDOT does not expect changes in the traffic environment that may affect the measurement of speeds or speed distributions. Factors that may affect the measurement of speeds could include a route that experiences a sudden increase in commercial truck traffic or a large new development that attracts a large volume of new vehicles and drivers. While we believe that the probe vehicle dataset described in this research is useful in its current state, it is important to monitor the data over time. Probe vehicle speed data sources can change as different vendors gather data. The quality of the data should not decrease as USDOT conducts regular validations of several vendors, but it is important to regularly check the data to understand whether measurements change how GDOT should interpret and use it.
After identifying "stable" corridors for further study, GDOT can monitor whether speed differences and other metrics identified previously indicate a speed-related safety problem. In areas where problems are identified, GDOT should exercise engineering judgment about the best means of addressing the speed problem. Determining the interventions that might
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reduce speed differences is outside the scope of this research. For reference, we have included a review of speed management techniques for arterial roadways in Appendix A. This review, while not exhaustive, suggests different treatment alternatives for potential speed-related projects. These should be considered along with FHWA's Countermeasures that Work series (FHWA 2019). After implementing countermeasures, GDOT can measure whether speed differences and crashes change in response to the intervention.
Incorporating Speed into Design and Operations In addition to using probe vehicle speeds as a data source, we recommend that GDOT consider other speed metrics in design and operations more broadly. Two specific areas that GDOT should consider adopting speed performance metrics are in road safety audits (RSAs) and the determination of a facilities design speed.
FHWA defines road safety audits as "a formal safety performance examination of an existing or future road or intersection by an independent audit team" (FHWA 2006). RSAs are conducted to determine the nature of a safety problem on a roadway (e.g., excessive speed) and identify solutions to address the safety problem. RSAs may be completed during the design phase of a project. However, speed differences are most useful for audits of existing projects, as there is not sufficient research about the relationship between specific design elements and speed differences. FHWA's guidelines for RSAs does not include collecting any speed or crash data. GDOT should consider include a speed study as part of its audit process. In addition to those metrics already considered, the speed differences outlined in this report could be used to identify whether speed is one of the issues potentially contributing to crashes in the audited area. Should speed be identified as one of
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the issues on the corridor, we have identified in Appendix A a number of speed countermeasures specific to arterials, in addition to those identified in FHWA's Countermeasures that Work (FHWA 2019). Along with incorporating speed into Road Safety Audits, GDOT should consider speeds other than the 85th percentile speed when developing designs and setting speed limits. Recent speed limit and design documents such as USLIMITS2 and City Limits suggest that the 50th percentile speed should be considered in addition to the 85th percentile speed when determining a design speed (Forbes et al. 2012, NACTO 2018). Our results suggest that considering both speed measurements is important. Thus, understanding the nature of a speed problem should involve examining the nature of the speed distribution, with a specific emphasis on the higher end of the speed distribution. The speed differences examined in this project are a useful means of analyzing portions of the speed distribution for safety studies.
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CHAPTER 6. RECOMMENDATIONS
Limiting the highest speeds and speed differentials on arterials may limit the number of crashes and injuries. This research suggests that probe vehicle speeds may provide a useful tool for investigating safety problems in the future. Further, speed differences, especially those at the higher end of the speed distribution, are a promising means of measuring the speed distribution as it relates to safety. In this report, we analyzed the relationship between probe vehicle speed metrics and crashes over one year. Based on this analysis, we recommend that GDOT consider using probe vehicle speed data and speed differences in their operations. We identified three broad recommendations:
1. Use probe vehicle speed data, specifically differences in high-end speeds, as a network screening tool to identify locations where interventions may be needed.
2. Undertake a series of pilot safety studies that assess speed difference metrics over time.
3. Use speed differences in GDOT road safety audits and design guidance. We have outlined how probe vehicle speeds may be used for network screening, beforeand-after studies, and road safety audits. Each of these recommendations will need to be tailored to GDOT's processes and operations. Probe vehicle speeds are increasingly available and already used to assess metrics such as travel time. These data may also be used to assess safety on GDOT's roadway works through network screening and project evaluation. Incorporating probe speed data into performance measurement, and using speed differences to do so, can help GDOT determine what works in assessing their
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projects, communicate with policymakers and the public, and create a safer roadway system.
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APPENDIX A. BEST PRACTICES FOR SPEED MANAGEMENT ON ARTERIAL ROADS
Speed management is the means of addressing unlawful or undesirable speeding within specific locations, corridors, or across entire road networks. According to the Federal Highway Administration, speed management programs should "address all factors that influence speeding: public awareness, user behavior, roadway design, surrounding land uses, traffic conditions, posted speed limits, and enforcement" (Bagdade et al. 2012). This review focuses most on the user behavior, roadway design, and traffic conditions aspects of speed management. Managing speeds on arterials is similar in principle to traffic calming practices, however, it poses unique challenges as it looks at controlling speeds on higher speed roads, such as collectors and arterials. The National Association of City Transportation Officials recommends target design speeds for urban arterial roads be no higher than 35 mph, while more "highway-like" arterials, where there are little to no pedestrian and bicyclist traffic, may be given higher target speeds (NACTO 2020). The collection of literature available on managing speeds on arterials is limited when compared to other research areas in transportation (e.g., traffic calming, crash safety, etc.), however several dedicated studies and previous literature reviews on best practices were found.
Techniques used to manage vehicles speeds can be divided into two main categories: enforcement and self-enforcement. Enforcement techniques are those that involve police monitoring and intervening when speed laws are broken. Common speed enforcement measures are described by the Insurance Institute for Highway Safety (IIHS 2020), and include using radar, Light Detection and Ranging (LIDAR), Visual Average Speed Computer And Recorder (VASCAR), aerial speed measurements, and human police
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monitoring (Parham and Fitzpatrick 2000). Typically, traffic control in the United States has relied on enforcement techniques to manage speeds. However, using design to create "self-enforcing" roadways is an increasingly popular topic in transportation safety (Donnell, Kersavage, and Tierney 2018). The remainder of this review will focus on design techniques to control vehicle operating speeds.
Enforcement vs. Roadway Design in Speed Management Through the end of the twentieth century, the most commonly used practices to manage speeds on arterials were predominantly enforcement-based, with rudimentary selfenforcing measures such as speed limit signs and rumble strips (Parham and Fitzpatrick 2000). Recently, there is increased interest in using design elements that exert influence on vehicle speed or on driver decision-making and can be used to compel drivers to maintain safe driving speeds. These design elements include road geometry, pavement markings, signage, and signals to prevent speeding (Donnell, Kersavage, and Tierney 2018). These techniques are sometimes referred to as "self-enforcing" roadway design. As research into speed management has progressed, self-enforcing techniques have proven to be more effective at preventing speeding than enforcement techniques, and have a greater likelihood of changing driver behavior long term (Harsha and Hedlund 2007). Self-enforcing techniques are preventative measures that either discourage or eliminate chances of speeding, whereas enforcement techniques are reactionary, addressing instances of speeding only once they occur. Changing American driving behavior requires more than the threat of a speeding ticket (Harsha and Hedlund 2007). This is not to say that speed enforcement measures are not important. On the contrary, the National Highway Traffic Safety Administration attests that effective speed management:
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"...involves a balanced program effort that includes: defining the relationship between speed, speeding, and safety; applying road design and engineering measures to obtain appropriate speeds; setting speed limits that are safe and reasonable; [and] applying enforcement efforts and appropriate technology that effectively address speeders and deter speeding" (NHTSA 2006).
Enforcement techniques are just as necessary as self-enforcing design measures. The issue is that, while an abundance of enforcement techniques is widely practiced, many roads are lacking in adequate design elements that prevent the opportunities for speeding. In the following sections, we review several design elements that can be used to encourage drivers to travel at a safer speed.
Intersection Treatments Traffic circles, roundabouts, and curb extensions at arterial intersections reduce vehicle speed. Traffic circles and roundabouts do so by deflecting vehicles around a central island. One study found roundabouts to reduce 85th-percentile speeds in intersections to between 13 and 17 mph, while speeds on adjacent roads were reduced by 10 percent (Grder, Ivan, and Du 2002). In addition, roundabouts reduce the potential conflict points between road users at intersections, decreasing the likelihood of a crash. Roundabouts are sometimes criticized for being unfriendly to pedestrians, however appropriately designed roundabouts with crossing islands improve safety for pedestrians. Curb extensions reduce speeds by restricting the amount of space given to vehicles, giving drivers a sense of crowding, and causing them to instinctively drive slower. A 2009 study from the City of Santa Clarita
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found curb extensions implemented at intersections to reduce vehicle speeds by 13 percent (Kimley-Horn and Associates 2009).
Pavement Markings Pavement markings can also be used to self-enforce drivers into managing their speed. Center line and edge line markings can be repainted to narrow travel lanes, making drivers feel more constricted in their lane and less comfortable at higher speeds. Narrowing lanes from 12 ft to 11 ft was found to decrease 85th-percentile speeds by 2 mph on rural arterials (Donnell, Kersavage, and Tierney 2018), while road diets that narrowed inner lanes to 10 ft and added bicycle lanes were found to decrease 85th-percentile speeds by 4 mph (KimleyHorn and Associates 2009). A road diet may consist of removing lanes, extending sidewalks, adding a median or on-street parking, or narrowing individual lanes. While curb extensions narrow the roadway only at intersections, road diets may be used to narrow the travel lane for vehicles over the entire length of a road. Road diets have become a common speed management measure on arterials in North America and have proven very effective (Kimley-Horn and Associates 2009). One beforeafter study conducted on a road in Victoria, British Columbia, consisted of the road being changed from four lanes to one lane per direction plus a center turn lane. This road diet variation, also known as a 4-to-3 conversion, was found to reduce average speeds by 3 mph (Kimley-Horn and Associates 2009). Other speed-managing techniques involving pavement markings include horizontal transverse markings in the travel lane, which can give drivers the illusion of high speeds and may compel them to maintain lower speeds. Converging chevron patterns on the pavement can have similar optical effects. An FHWA study from 2015 on how road factors influence operating speeds found horizontal transverse markings to reduce 85th-percentile
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speeds by 4 mph on rural arterials, while converging chevron markings reduced speeds by 3 mph (Boodlal et al. 2015).
Lane narrowing may be achieved using physical objects outside the travel lane as well, such as trees or buildings. Terminated vistas are a design technique that involves placing a large object (e.g., tree, building, sculpture) where a road bends or deviates in direction. The large object communicates to drivers that the road segment does not extend indefinitely and gives a sense of enclosure by blocking the view beyond. According to the Florida DOT Design Manual, this effect causes drivers to reduce and control their speed upon approach (FDOT 2020). Terminated vistas may be included at roundabouts, T-intersections, and median splitter islands, or as part of non-grid block configurations. A tree canopy that runs along an arterial road can also be a useful speed management tool, as it can have a similar enclosure effect as a terminated vista. Trees adjacent to the travel lane can also give drivers the illusion of speed, similar to the optical effect that transverse pavement markings and converging chevrons can have. One study found a 4 mph difference in speed on arterial segments with a tree canopy vs. segments without trees (Boodlal et al. 2015).
Signage Signage is another key element of self-enforcing roads. Informing drivers of the posted speed limit and other potential hazards is necessary for drivers to make informed, safe decisions. To better capture the attention of drivers, speed limit signs may be marked with a red border or indicator lights. Posted speed limits may also be painted on the surface of the road surrounded by red paint. The same 2015 study found that each of these measures reduced 85th-percentile speeds by 3 mph (Boodlal et al. 2015). These techniques can convey a sense of urgency to drivers, which can result in increased adherence to speed
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limits. Speed feedback signs that display the driver's current operating speed are found to be even more effective, reducing 85th-percentile speeds between 2 and 7 mph (Boodlal et al. 2015).
Coordinated Signal Timing Active speed management measures are not perfect for every arterial. One criticism of active speed management measures that use curvature and physical obstacles to eliminate speeding opportunities is that they limit the speed at which emergency response vehicles are able to travel along a segment of road (Furth et al. 2018). It is important for local jurisdictions to maintain an arterial road network that emergency response vehicles can navigate quickly and without increased delay. This presents the need for speed management measures that remove the opportunity of speeding for private vehicles yet may be bypassed by emergency vehicles. One such measure is through precise timing of traffic signals. Signal timing works by coordinating the phase cycles of consecutive traffic signals along a road segment to create a "green wave" of through traffic. Vehicles traveling at the posted speed will progress through each signal without impediment, while vehicles traveling faster than the posted speed will arrive at the next signal before it changes from the red phase to green phase. This incentivizes driving at the posted speed by resulting in fewer starts/stops and perceived delays for the individual driver (Furth et al. 2018). Meanwhile, emergency response vehicles are able to go around traffic and not be impeded by the signals. Signal timing is also a useful tool for managing speeds on straight-lined arterials with few curves to limit vehicle speed, and on arterials with high traffic volumes where road diets are not feasible (Furth et al. 2018).
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The general rule-of-thumb for using signal timing to dictate vehicle speed is to set the cycle length equal to twice the amount of time it takes to drive between adjacent intersections at the desired vehicle speed. Adjacent signals should be offset one half-cycle length from one another. For example, if it takes 20 seconds to drive from one signal to the next at the desired speed, then the cycle lengths for each signal should be 40 seconds, with the second signals entering the green phase 20 seconds after the first (Furth et al. 2018). Figure 24 shows phase diagrams for three consecutive signals timed in such a way. The black and blue arrows represent opposing directions of through traffic at the intersections and their slopes represent the operating speed that allows them to follow the "green wave" of signals.
Figure 24. Diagram. Coordinated phase diagram for three consecutive intersection signals (Furth et al. 2018).
By precisely timing adjacent traffic signals along an arterial in coordination with one another, signals can be used to limit the opportunities that incentivize speeding in vehicles, while not delaying emergency vehicles. While coordinated signal timing can influence
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operational speed, signal density also influences the flow and speed of traffic. Thus, the effectiveness of signal timing interventions is also dependent on the roadway context. In urban contexts with a high signal density, it is more effective to alter signal timing to influence speed. In rural contexts where signals may be sparse, this is a less effective measure.
Coordinated signals also prevent speeding by grouping vehicles together in platoons as they progress from one signal to the next. A 2018 study on the effects of signal timing found that speeding is related to opportunity, specifically that when drivers have open road free of other vehicles ahead of them, they tend to speed (Furth et al. 2018). By clustering vehicles together, thoughtfully timed signals can remove the opportunity for drivers to speed. As long as the lead vehicle of a platoon travels at or near the posted speed, other vehicles in the platoon are constrained to the leader's speed and will remain clustered together. Platooning is most effective at creating clusters and removing speeding opportunities when road volume is at saturation. Volumes below saturation result in less dense platoons and decrease the constraining effect that adjacent vehicles can impose on one another (Furth et al. 2018). This issue could be addressed by varying coordinated cycle lengths throughout the day to accommodate varying peak volume hours. It is also important to consider the hole that is left in a platoon when a vehicle turns off onto a branching road, giving room for the driver behind to increase their speed. A 2017 study on arterial speed management control measures looked at the effectiveness of coordinated signal timing on traffic operating speeds (Halkias et al. 2017). The study analyzed before-and-after data from three arterial corridors in San Francisco, all of which had 85th-percentile speeds that were higher than the posted speed limits. After implementation of the coordinated signal
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timings, all three corridors saw a 34 mph decrease in average speed. In addition, two of the arterials saw an increase in traffic volumes, and all three saw a reduction in emissions produced from the corridor (Halkias et al. 2017). The increase in traffic volume is a result of denser clusters of vehicles from the platooning effect, while the reduction in emissions can be attributed to vehicles spending less time idling at red lights while they are able to progress through more consecutive green signals.
Active vs. Passive Speed Control Measures Speed management measures discussed previously can be further classified into active speed measures and passive speed measures. Active measures are those that involve a physical design change to the roadway, such as extending the curb, narrowing of lanes, or the addition of a roundabout. Active measures work by physically removing an opportunity to exceed the design speed. Passive speed measures are those techniques that involve signage, signalization, and enforcement. Passive measures do not eliminate the opportunity to speed, but rather discourage the driver's decision to speed through negative and positive reinforcement (e.g., the "green wave" from timed signals) (Kimley-Horn and Associates 2009). Passive speed measures can be implemented more cheaply and quickly than active measures, due to the lack of design changes and construction required to implement them. This may make passive speed measures a more attractive option to transportation authorities for managing speeds. It is noted, however, that active speed management techniques are believed to be more effective in the long term, as passive techniques' influence on vehicle speeds may decrease over time, as drivers can become accustomed to their novelty (Kimley-Horn and Associates 2009).
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CONCLUSION The available literature on speed management practices has grown considerably since the end of the twentieth century, and it will continue growing as more and more research is conducted. It is now understood that implementing self-enforcing measures is just as important as enforcement techniques for the reduction of speeds. Arterials can be made into self-enforcing roadways through the physical design elements, such as tighter curves and roundabouts, which deflect vehicles horizontally and require vehicles to control their speeds. Lane narrowing, curb extensions, and road diets are speed reduction measures that constrain vehicles in their lane, making higher speeds uncomfortable for drivers. Terminating vistas and tree canopies are also helpful tools at controlling speeds by inducing a constraining effect. Signage along arterials may be made more effective and compelling through the addition of color or indicator lights, which draw a driver's attention. Coordinated signal timing has shown to be effective at controlling speeds by setting a speed for vehicles to match the "green wave" of signals. Coordinated signals can also influence higher vehicle saturations, which further constrains drivers to the speed of the vehicle leading a platoon. In applying these speed management practices to arterial roadways, it is necessary to consider what measures are best suited for a specific corridor. There is no onesize-fits-all solution. Daily traffic volumes, wait times, existing road geometry, and adjacent land uses should be carefully considered when determining what measures will be most effective in controlling speeds at a given location.
109

APPENDIX B SUPPLEMENTARY DATA TABLES AND FIGURES

Table 19. Results limited to only TMCs longer than 0.025 mile.

Crashes

(1)

(2) (3)

(4)

(5)

(6)

(7)

(8)

Constant Percentile Speeds 5th 15th 50th 85th 95th Traffic Volume (AADT) 3049,999 50,000

2.48*** 2.83*** 3.52*** 4.14*** 4.36*** 3.29*** 3.19*** 3.07***

-0.05***

-0.04*** -0.05***

-0.05***

-0.05***

-0.03*** 0.00 -0.01

-0.03*** -0.02***
0.00

-0.08*** 0.09*** -0.08*** 0.02 -0.00

0.55*** 0.54*** 0.57*** 0.61*** 0.65*** 0.58*** 0.53*** 0.60***

0.63*** 0.66***

0.56*** 0.57***

0.57*** 0.60***

0.57*** 0.59***

TMC Length Total (miles) Land Use Context Urban Rural Ecoregion Piedmont Ridge and Valley Southeastern Plains Southern Coastal Plain

0.35*** 0.36*** 0.36*** 0.34***

0.53*** 0.50*** 0.47*** 0.46*** -0.70*** -0.73*** -0.80*** -0.89***

0.10 -0.12

0.07 -0.03 -0.11 -0.16 -0.28** -0.38***

-0.43*** -0.49*** -0.64*** -0.74***

-0.34*** -0.38*** -0.50*** -0.60***

0.33***
0.49*** -0.93***
-0.14 -0.43*** -0.77***
-0.63***

0.36***
0.48*** -0.75***
0.03 -0.20 -0.55***
-0.44***

0.36*** 0.35***

0.49*** 0.49*** -0.71*** -0.69***

0.05 -0.17

0.04 -0.19

-0.51*** -0.53***

-0.41*** -0.42***

Observations Log Likelihood

6,269 6,269 6,269 6,269 6,269 6,269 6,269 6,269 -19,571 -19,575 -19,579 -19,630 -19,677 -19,560 -19,533 -19,506

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

110

Table 20. Differences in percentile speed models, limited to TMCs longer than 0.025.

Dependent Variable = Crashes

(1) (2) (3) (4) (5) (6) (7) (8)

Constant Speed Differences Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume (AADT) 3049,999 50,000 TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban Rural Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain

1.96*** 1.11*** 0.99*** 1.38*** 1.22*** 1.06*** 1.08*** 1.22***

0.02***

-0.02*** -0.01* -0.01** 0.01**

0.09***

0.11*** 0.02 0.08***

0.08***

0.07***

0.15***

0.07*** 0.15***

0.56*** 0.47*** 0.46*** 0.49*** 0.46*** 0.45*** 0.45*** 0.48*** 0.75*** 0.57*** 0.50*** 0.53*** 0.53*** 0.48*** 0.49*** 0.54***

0.24*** 0.28*** 0.29*** 0.27*** 0.29*** 0.29*** 0.29*** 0.27***
0.63*** 0.60*** 0.58*** 0.57*** 0.59*** 0.57*** 0.58*** 0.58*** -1.28*** -1.12*** -1.11*** -1.19*** -1.12*** -1.11*** -1.11*** -1.17***
-0.19 -0.07 -0.08 -0.16 -0.10 -0.10 -0.10 -0.13 -0.58*** -0.45*** -0.45*** -0.53*** -0.48*** -0.46*** -0.46*** -0.49*** -0.82*** -0.68*** -0.69*** -0.79*** -0.71*** -0.71*** -0.71*** -0.75*** -0.66*** -0.50*** -0.52*** -0.62*** -0.53*** -0.53*** -0.53*** -0.59***

Observations Log Likelihood

6,269 6,269 6,269 6,269 6,269 6,269 6,269 6,269 -20,037 -19,935 -19,910 -19,952 -19,926 -19,908 -19,913 -19,948

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

111

Table 21. Morning peak speed percentiles and crashes.

Dependent Variable = Crashes

(1) (2) (3) (4) (5) (6) (7) (8)

Constant Percentile Speeds 5th 15th 50th 85th 95th Traffic Volume (AADT) 3049,999 50,000 TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban Rural Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain

0.29* 0.51*** 0.96*** 1.35*** 1.48*** 0.79*** 0.72*** 0.67***

-0.03***

-0.03*** -0.06***

-0.03***

-0.03***

0.05***

-0.03***

0.01 0.00 -0.04**

-0.03***

-0.01

0.012

-0.03***

-0.01* -0.01

0.53*** 0.51*** 0.53*** 0.56*** 0.57*** 0.52*** 0.54*** 0.55*** 0.68*** 0.64*** 0.63*** 0.66*** 0.70*** 0.64*** 0.67*** 0.69***
-1.20*** -1.20*** -1.15*** -1.13*** -1.13*** -1.19*** -1.19*** -1.16*** 0.36*** 0.36*** 0.36*** 0.34*** 0.33*** 0.36*** 0.36*** 0.36***

0.62*** 0.59*** 0.57*** 0.59*** 0.61*** 0.59*** 0.60*** 0.60*** -0.82*** -0.86*** -0.91*** -0.94*** -0.97*** -0.86*** -0.82*** -0.82***

0.28* -0.03 -0.35** -0.22

0.26* -0.04 -0.39** -0.24

0.19 0.16 0.14 0.25*
-0.11 -0.17 -0.21 -0.05 -0.47*** -0.53*** -0.56*** -0.40** -0.32* -0.38** -0.41** -0.256*

0.27* -0.03 -0.38** -0.24

0.25*
-0.06 -0.39** -0.25*

Observations

7,050 7,050 7,050 7,050 7,050 7,050 7,050 7,050

Log Likelihood

-11,241 -11,252 -11,262 -11,283 -11,299 -11,249 -11,233 -11,225

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

112

Table 22. Morning peak speed differences and crashes.

Dependent Variable

Crashes (1) (2) (3) (4) (5) (6) (7) (8)

Constant Speed Differences Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume (AADT) 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain

-0.27 -0.68*** -0.62*** -0.30* -0.65*** -0.67*** -0.66*** -0.51***

0.02*** 0.06*** 0.04***

-0.01 -0.003 -0.004 0.02*** 0.06*** 0.05*** 0.06***
0.01

0.05***

0.01 0.05***

0.54*** 0.50*** 0.50*** 0.53*** 0.50*** 0.50*** 0.50*** 0.52*** 0.74*** 0.67*** 0.65*** 0.68*** 0.66*** 0.66*** 0.66*** 0.69***
-1.13*** -1.13*** -1.11*** -1.09*** -1.12*** -1.12*** -1.12*** -1.12*** 0.27*** 0.30*** 0.30*** 0.28*** 0.30*** 0.30*** 0.30*** 0.29***
0.73*** 0.68*** 0.68*** 0.69*** 0.68*** 0.68*** 0.68*** 0.70*** -1.13*** -1.09*** -1.10*** -1.14*** -1.09*** -1.09*** -1.09*** -1.10***
0.07 0.10 0.09 0.05 0.10 0.10 0.10 0.08 -0.36** -0.30* -0.31* -0.36** -0.31* -0.31* -0.31* -0.33* -0.63*** -0.58*** -0.59*** -0.65*** -0.59*** -0.58*** -0.58*** -0.60*** -0.46*** -0.40** -0.41** -0.47*** -0.41** -0.40** -0.40** -0.43**

Observations Log Likelihood

7,050 7,050 7,050 7,050 7,050 7,050 7,050 7,050 -11,415 -11,379 -11,383 -11,406 -11,378 -11,378 -11,378 -11,400

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

113

Table 23. Midday crashes and speed percentiles.

Constant Percentile Speeds 5th 15th 50th 85th 95th Traffic Volume (AADT) 3049,999 50,000 TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain
Observations Log Likelihood

Dependent Variable = Crashes (1) (2) (3) (4) (5) (6) (7) (8) 1.79*** 2.17*** 2.95*** 3.71*** 3.95*** 3.13*** 2.97*** 2.95***

-0.05***

-0.02*** -0.06***

-0.05***

-0.03***

0.06***

-0.06***

0.01 -0.02*** -0.05***

-0.06***

-0.04***

-0.02

-0.06***

-0.02*** 0.00

0.55*** 0.53*** 0.53*** 0.56*** 0.57*** 0.55*** 0.55*** 0.56*** 0.71*** 0.63*** 0.53*** 0.53*** 0.59*** 0.57*** 0.59*** 0.59***
-1.38*** -1.38*** -1.28*** -1.22** -1.23*** -1.30*** -1.31*** -1.26*** 0.36*** 0.38*** 0.37*** 0.35*** 0.33*** 0.37*** 0.37*** 0.36***
0.44*** 0.40*** 0.35*** 0.33*** 0.36*** 0.35*** 0.37*** 0.36*** -0.76*** -0.77*** -0.80*** -0.88*** -0.94*** -0.79*** -0.76*** -0.75***
-0.06 -0.08 -0.18 -0.28** -0.32** -0.16 -0.15 -0.16 -0.26* -0.29* -0.40*** -0.51*** -0.58*** -0.37** -0.34** -0.35** -0.50*** -0.55*** -0.70*** -0.82*** -0.87*** -0.67*** -0.63*** -0.65*** -0.46*** -0.50*** -0.65*** -0.77*** -0.82*** -0.63*** -0.59*** -0.61***
6,948 6,948 6,948 6,948 6,948 6,948 6,948 6,948 -15,407 -15,380 -15,342 -15,368 -15,428 -15,327 -15,315 -15,297
p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

114

Table 24. Midday crashes and speed differences.

Dependent Variable

Crashes (1) (2) (3) (4) (5) (6) (7) (8)

Constant Speed Differences Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume (AADT) 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain

1.59*** 0.76*** 0.53*** 0.77*** 0.94*** 0.75*** 0.76*** 0.87***

-0.01 0.07*** 0.06***

-0.04*** -0.03*** -0.03*** -0.01 0.10*** -0.01 0.06***
0.08***

0.13***

0.08*** 0.13***

0.54*** 0.52*** 0.50*** 0.50*** 0.49*** 0.48*** 0.48*** 0.49*** 0.76*** 0.76*** 0.71*** 0.67*** 0.67*** 0.64*** 0.64*** 0.66***
-1.23*** -1.32*** -1.29*** -1.22*** -1.27*** -1.24*** -1.24*** -1.20*** 0.23*** 0.26*** 0.27*** 0.26*** 0.27*** 0.28*** 0.28*** 0.26***
0.51*** 0.52*** 0.50*** 0.49*** 0.49*** 0.48*** 0.48*** 0.48*** -1.41*** -1.29*** -1.25*** -1.28*** -1.29*** -1.26*** -1.27*** -1.29***
-0.47*** -0.34** -0.33** -0.39*** -0.38*** -0.38*** -0.38*** -0.41*** -0.87*** -0.71*** -0.69*** -0.75*** -0.76*** -0.74*** -0.74*** -0.77*** -1.06*** -0.89*** -0.88*** -0.95*** -0.96*** -0.95*** -0.94*** -0.97*** -0.97*** -0.79*** -0.78*** -0.86*** -0.85*** -0.84*** -0.84*** -0.88***

Observations Log Likelihood

6,948 6,948 6,948 6,948 6,948 6,948 6,948 6,948 -15,904 -15,856 -15,823 -15,831 -15,826 -15,804 -15,810 -15,829

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

115

Table 25. Evening peak speed percentiles and crashes.

Dependent Variable = Crashes

(1)

(2) (3) (4) (5) (6) (7) (8)

Constant Speed Percentiles 5th 15th 50th 85th 95th Traffic Volume (AADT) 3049,999 AADT 50,000 AADT

1.30*** 1.68*** 2.36*** 3.01*** 3.22*** 2.34*** 2.18*** 2.12***

-0.05***

-0.03*** -0.07***

-0.05***

-0.04***

0.07***

-0.05***

0.01 -0.02** -0.05***

-0.05***

-0.03***

-0.01

-0.05***

-0.01** 0.00

0.51*** 0.59***

0.48*** 0.48*** 0.54*** 0.56*** 0.50*** 0.509*** 0.518*** 0.51*** 0.43*** 0.47*** 0.54*** 0.48*** 0.507*** 0.499***

TMC Length Short TMC

-1.48*** -1.48*** -1.37*** -1.31*** -1.33*** -1.42*** -1.42*** -1.36***

Total TMC Length (miles)

0.36*** 0.37*** 0.37*** 0.35*** 0.33*** 0.37*** 0.37*** 0.37***

Land Use Context Urban TMC Rural TMC

0.48*** 0.44*** 0.41*** 0.42*** 0.46*** 0.42*** 0.43*** 0.43*** -0.80*** -0.85*** -0.92*** -0.99*** -1.04*** -0.86*** -0.82*** -0.79***

Ecoregion

Piedmont Ridge and Valley Southeastern Plain

0.12 -0.06 -0.38**

0.07 -0.03 -0.11 -0.14 0.02 0.05 0.05 -0.10 -0.21 -0.31* -0.35** -0.15 -0.10 -0.11 -0.44*** -0.58*** -0.69*** -0.72*** -0.51*** -0.46*** -0.47***

Southern Coastal Plain

-0.26* -0.30* -0.40*** -0.49*** -0.52*** -0.36** -0.32** -0.32**

Observations

6,586 6,586 6,586 6,586 6,586 6,586 6,586 6,586

Log Likelihood

-13,516 -13,510 -13,506 -13,548 -13,598 -13,486 -13,466 -13,450

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

116

Table 26. Evening peak speed differences and crashes.

Dependent Variable

Crashes (1) (2) (3) (4) (5) (6) (7) (8)

Constant Speed Differences Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume (AADT) 3049,999 AADT 50,000 AADT TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain

0.89*** 0.15 0.000 0.29* 0.29* 0.12 0.13 0.24

0.01 0.07*** 0.06***

-0.03*** -0.02** -0.02*** 0.004 0.09*** 0.01 0.06***
0.06***

0.12***

0.06*** 0.12***

0.54*** 0.47*** 0.45*** 0.48*** 0.45*** 0.44*** 0.44*** 0.48*** 0.69*** 0.63*** 0.56*** 0.54*** 0.57*** 0.52*** 0.53*** 0.54***
-1.40*** -1.46*** -1.43*** -1.37*** -1.41*** -1.40*** -1.39*** -1.38*** 0.24*** 0.27*** 0.28*** 0.27*** 0.28*** 0.28*** 0.28*** 0.27***
0.62*** 0.58*** 0.56*** 0.57*** 0.56*** 0.55*** 0.55*** 0.57*** -1.42*** -1.30*** -1.28*** -1.33*** -1.31*** -1.30*** -1.29*** -1.32***
-0.22 -0.11 -0.12 -0.19 -0.14 -0.15 -0.15 -0.18 -0.60*** -0.47*** -0.47*** -0.55*** -0.50*** -0.50*** -0.50*** -0.54*** -0.84*** -0.71*** -0.72*** -0.80*** -0.75*** -0.75*** -0.75*** -0.79*** -0.63*** -0.50*** -0.51*** -0.59*** -0.52*** -0.53*** -0.53*** -0.58***

Observations Log Likelihood

6,586 6,586 6,586 6,586 6,586 6,586 6,586 6,586 -13,941 -13,877 -13,854 -13,875 -13,865 -13,849 -13,851 -13,875

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

117

Table 27. Nighttime speed percentiles and crashes.

Dependent Variable = Crashes

(1) (2)

(3) (4) (5) (6) (7) (8)

Constant

0.46** 0.78***

Speed Percentiles

5th

-0.04***

15th

-0.04***

50th

85th

95th

Traffic Volume (AADT)

3049,999

0.39*** 0.39***

50,000

0.64*** 0.61***

TMC Length

Short TMC

-1.22*** -1.19***

Total TMC Length (miles)

0.32*** 0.33***

Land Use Context

Urban TMC

0.34*** 0.34***

Rural TMC

-0.81*** -0.90***

Ecoregion

Piedmont

0.18 0.11

Ridge and Valley

0.03 -0.04

Southeastern Plain

-0.25 -0.34*

Southern Coastal Plain -0.17 -0.24

1.38*** 1.87*** 1.91*** 1.12*** 0.89*** 0.72**

-0.03*** -0.09**

-0.02**

0.11***

-0.04***

-0.02 -0.02** -0.10***

-0.04***

0.00

0.01

-0.04***

0.00 0.02

0.43*** 0.46*** 0.46*** 0.41*** 0.41*** 0.43*** 0.60*** 0.65*** 0.67*** 0.60*** 0.61*** 0.62***

-1.06*** -1.05*** -1.08*** -1.12*** -1.15*** -1.03*** 0.33*** 0.32*** 0.30*** 0.33*** 0.33*** 0.32***

0.30*** 0.30*** 0.34*** 0.31*** 0.31*** 0.30*** -0.95*** -0.98*** -1.01*** -0.92*** -0.85*** -0.78***

0.06 -0.10 -0.42* -0.30

0.02 -0.16 -0.46** -0.35*

0.01 -0.20 -0.47** -0.36*

0.09 -0.06 -0.37* -0.27

0.14 0.00 -0.30 -0.21

0.18 0.04 -0.27 -0.18

Observations Log Likelihood

4,289 4,289 4,289 4,289 4,289 4,289 4,289 4,289 -6,838 -6,848 -6,847 -6,867 -6,892 -6,842 -6,828 -6,807

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

118

Table 28. Nighttime speed differences and crashes.

Dependent Variable

Crashes (1) (2) (3) (4) (5) (6) (7) (8)

Constant

-0.36 -1.01*** -1.01*** -0.55** -0.89*** -0.96*** -0.94*** -0.69***

Speed Differences

Low Speed Difference (Median-15th)

0.02**

-0.02** -0.02* -0.02* 0.01*

High Speed Difference (85th-Median)

0.09***

0.11*** 0.06*** 0.09***

Speed Dispersion (95th-5th)

0.07***

0.03**

Excessive Speed Differences (95th-85th)

0.09***

0.03** 0.09***

Traffic Volume (AADT)

3049,999

0.37*** 0.33*** 0.35*** 0.39*** 0.34*** 0.35*** 0.35*** 0.38***

50,000

0.71*** 0.59*** 0.60*** 0.66*** 0.57*** 0.57*** 0.57*** 0.66***

TMC Length

Short TMC

-1.16*** -1.12*** -1.06*** -1.05*** -1.05*** -1.04*** -1.04*** -1.09***

Total TMC Length (miles)

0.23*** 0.26*** 0.27*** 0.25*** 0.27*** 0.27*** 0.27*** 0.25***

Land Use Context

Urban TMC

0.54*** 0.51*** 0.50*** 0.50*** 0.50*** 0.49*** 0.49*** 0.50***

Rural TMC

-1.14*** -1.09*** -1.10*** -1.15*** -1.11*** -1.11*** -1.11*** -1.12***

Ecoregion

Piedmont

-0.01 0.03 0.02 -0.02 0.01 0.01 0.01 -0.01

Ridge and Valley

-0.31 -0.23 -0.24 -0.30 -0.25 -0.24 -0.24 -0.27

Southeastern Plains

-0.52** -0.47** -0.50** -0.56*** -0.50** -0.50** -0.50** -0.53**

Southern Coastal Plain -0.37* -0.30 -0.33 -0.38* -0.32 -0.32 -0.32 -0.35*

Observations Log Likelihood

4,289 4,289 4,289 4,289 4,289 4,289 4,289 4,289 -7,001 -6,955 -6,953 -6,980 -6,951 -6,947 -6,948 -6,978

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

119

Table 29. Overnight speed percentiles and crashes.

Dependent Variable = Crashes

(1) (2) (3) (4) (5) (6) (7) (8)

Constant

-1.15*** -0.88*** -0.32 0.12 0.137 -0.31 -0.46 -0.42

Percentile Speed

5th

-0.03***

-0.01* -0.05***

15th

-0.03***

0.00

0.07***

50th

-0.04***

-0.03 -0.02** -0.08**

85th

-0.04***

0.00

0.00

95th

-0.04***

0.03 0.00

Traffic Volume (AADT)

3049,999

0.22*** 0.23*** 0.26*** 0.28*** 0.28*** 0.26*** 0.25*** 0.26***

50,000

0.28* 0.27* 0.29* 0.33** 0.34** 0.29* 0.28* 0.30*

TMC Length

Short TMC

-1.70*** -1.66*** -1.62*** -1.64*** -1.66*** -1.62*** -1.64*** -1.65***

Total TMC Length (miles) 0.32*** 0.33*** 0.34*** 0.34*** 0.33*** 0.34*** 0.34*** 0.34***

Land Use Context

Urban TMC

0.87*** 0.85*** 0.82*** 0.83*** 0.87*** 0.82*** 0.82*** 0.81***

Rural TMC

-0.55*** -0.60*** -0.63*** -0.63*** -0.64*** -0.63*** -0.59*** -0.55***

Ecoregion

Piedmont

0.63** 0.61** 0.63** 0.64** 0.63** 0.63** 0.64** 0.67**

Ridge and Valley

0.35 0.35 0.37 0.36 0.32 0.37 0.39 0.41

Southeastern Plain

0.24 0.21 0.22 0.21 0.17 0.22 0.24 0.27

Southern Coastal Plain

0.58** 0.56* 0.57** 0.56* 0.53* 0.57** 0.59** 0.61**

Observations Log Likelihood

4,336 4,336 4,336 4,336 4,336 4,336 4,336 4,336 -4,867 -4,866 -4,858 -4,863 -4,875 -4,858 -4,856 -4,849

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

120

Table 30. Overnight speed differences and crashes.

Dependent Variable

Crashes (1) (2) (3) (4) (5) (6) (7) (8)

Constant Speed Difference Low Speed Difference (Median-15th) High Speed Difference (85th-Median) Speed Dispersion (95th-5th) Excessive Speed Differences (95th-85th) Traffic Volume (AADT) 3049,999 50,000 TMC Length Short TMC Total TMC Length (miles) Land Use Context Urban TMC Rural TMC Ecoregion Piedmont Ridge and Valley Southeastern Plain Southern Coastal Plain

-1.98*** -2.32*** -2.23*** -1.92*** -2.28*** -2.30*** -2.29*** -2.09***

0.02** 0.07*** 0.05***

-0.01 -0.01 -0.01 0.02* 0.08*** 0.06** 0.08***
0.02

0.04***

0.01 0.04***

0.21** 0.20** 0.21*** 0.23*** 0.20** 0.21** 0.20** 0.21*** 0.32** 0.25* 0.27* 0.32** 0.25* 0.25* 0.25* 0.31**
-1.74*** -1.68*** -1.68*** -1.71*** -1.67*** -1.67*** -1.67*** -1.72*** 0.27*** 0.29*** 0.29*** 0.28*** 0.29*** 0.29*** 0.29*** 0.28***

1.06*** 1.00*** 1.00*** 1.04*** 1.00*** 1.00*** 1.00*** 1.03*** -0.70*** -0.70*** -0.71*** -0.73*** -0.71*** -0.71*** -0.71*** -0.70***

0.47* 0.06 -0.01 0.40

0.48* 0.10 0.02 0.44*

0.47* 0.09 0.01 0.42

0.47* 0.06 -0.02 0.39

0.48* 0.10 0.02 0.44*

0.47* 0.10 0.02 0.44*

0.47* 0.10 0.02 0.44*

0.47* 0.07 0.00 0.40

Observations Log Likelihood

4,336 4,336 4,336 4,336 4,336 4,336 4,336 4,336 -4,932 -4,915 -4,917 -4,929 -4,915 -4,914 -4,914 -4,927

p < 0.10 *p <0.05 ** p < 0.01 *** p < 0.001

121

Figure 25. Scatterplot. TMC length and number of crashes in 2017. 122

Figure 26. Histogram. TMC lengths (miles). 123

Figure 27. Bar chart. Crashes per TMC by AADT range. 124

Figure 28. Scatterplot. Crashes per TMC in relation to TMC length and AADT category. 125

Percentiles

Speed Differences

Table 31. Correlation table of all variables in analysis (correlations greater than |0.7| highlighted in yellow).

Percentiles

Speed Differences

Control Variables

Outcomes

5th

15th

50th

85th

95th

50th-15th 85th-50th 95th-5th 95th-85th AADT

Short TMC

Miles

PSL

Urban

Small Urban

Rural Crashes Injuries

5th

1.00 0.98 0.93 0.88 0.84 -0.58

-0.76 -0.71 -0.49 -0.45 -0.20 0.52 0.72 -0.51 -0.05 0.61 -0.27 -0.19

15th

0.98 1.00 0.97 0.93 0.89 -0.49

-0.77 -0.73 -0.52 -0.47 -0.20 0.55 0.76 -0.52 -0.03 0.61 -0.27 -0.18

50th

0.93 0.97 1.00 0.98 0.95 -0.27

-0.70 -0.69 -0.52 -0.46 -0.17 0.54 0.81 -0.51 -0.02 0.58 -0.28 -0.19

85th

0.88 0.93 0.98 1.00 0.98 -0.16

-0.54 -0.56 -0.45 -0.41 -0.15 0.51 0.85 -0.48 -0.02 0.56 -0.27 -0.18

95th

0.84 0.89 0.95 0.98 1.00 -0.12

-0.46 -0.42 -0.27 -0.37 -0.14 0.49 0.84 -0.45 -0.03 0.53 -0.25 -0.17

Low Speed -0.58 -0.49 -0.27 -0.16 -0.12 1.00

0.57

0.44

0.21

0.22 0.18 -0.23 -0.09 0.22 0.08 -0.31 0.07 0.07

High Speed -0.76 -0.77 -0.70 -0.54 -0.46 0.57

Speed Dispersion

-0.71 -0.73 -0.69 -0.56 -0.42

0.44

1.00

0.91

0.60

0.46 0.20 -0.45 -0.39 0.43 -0.01 -0.47 0.20 0.14

0.91

1.00

0.87

0.44 0.18 -0.43 -0.41 0.42 -0.03 -0.44 0.21 0.15

Excess Speed -0.49 -0.52 -0.52 -0.45 -0.27 0.21

0.60

0.87

1.00

0.32 0.11 -0.32 -0.35 0.32 -0.04 -0.32 0.17 0.12

AADT Short TMC Miles PSL
Urban

-0.45 -0.20 0.52 0.72
-0.51

-0.47 -0.20 0.55 0.76
-0.52

-0.46 -0.17 0.54 0.81
-0.51

-0.41 -0.15 0.51 0.85
-0.48

-0.37 -0.14 0.49 0.84
-0.45

0.22 0.18 -0.23 -0.09
0.22

0.46 0.20 -0.45 -0.39
0.43

0.44 0.18 -0.43 -0.41
0.42

0.32 0.11 -0.32 -0.35
0.32

1.00 0.07 -0.33 -0.25
0.62

0.07 1.00 -0.25 -0.13
0.11

-0.33 -0.25 1.00 0.47
-0.36

-0.25 -0.13 0.47 1.00

0.62 0.11 -0.36 -0.36

-0.22 -0.01 -0.08 -0.05

-0.36 1.00 -0.51

-0.50 -0.11 0.47 0.44
-0.66

0.44 -0.13 0.05 -0.15
0.33

0.36 -0.14 0.10 -0.09
0.29

Small Urban -0.05 -0.03 -0.02 -0.02 -0.03 0.08

Rural Crashes
Injuries

0.61 -0.27

0.61 -0.27

0.58 -0.28

0.56 -0.27

0.53 -0.25

-0.19 -0.18 -0.19 -0.18 -0.17

-0.31 0.07
0.07

-0.01
-0.47 0.20 0.14

-0.03
-0.44 0.21 0.15

-0.04
-0.32 0.17 0.12

-0.22 -0.01 -0.08 -0.05 -0.51 1.00 -0.31 -0.12 -0.11
-0.50 -0.11 0.47 0.44 -0.66 -0.31 1.00 -0.26 -0.22 0.44 -0.13 0.05 -0.15 0.33 -0.12 -0.26 1.00 0.86 0.36 -0.14 0.10 -0.09 0.29 -0.11 -0.22 0.86 1.00

Covariates

Outcome

126

Figure 29. Line graph. Distribution of 5th percentile speeds per TMC by land use. 127

Figure 30. Line graph. Distribution of 15th percentile speeds per TMC by land use. 128

Figure 31. Line graph. Distribution of 50th percentile speeds per TMC by land use. 129

Figure 32. Line graph. Distribution of 85th percentile speeds per TMC by land use. 130

Figure 33. Line graph. Distribution of 95th percentile speeds per TMC by land use. 131

Figure 34. Line graph. Distribution of 5th percentile speeds per TMC by AADT. 132

Figure 35. Line graph. Distribution of 15th percentile speeds per TMC by AADT. 133

Figure 36. Line graph. Distribution of 50th percentile speeds per TMC by AADT. 134

Figure 37. Line graph. Distribution of 85th percentile speeds per TMC by AADT. 135

Figure 38. Line graph. Distribution of 95th percentile speeds per TMC by AADT. 136

Figure 39. Bar chart. Crashes by land use type. 137

Figure 40. Bar chart. TMC mileage by land use type. 138

Figure 41. Bar chart. Crashes by AADT category. 139

Figure 42. Bar chart. TMC mileage by AADT category. 140

ACKNOWLEDGMENTS The authors would like to thank Daniel Arias and David Hogan for their assistance with analysis and writing sections of this report. We would also like to thank our Georgia Department of Transportation technical advisors Sam Harris and David Adams and research manager Brennan Roney.
141

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