GEORGIA DOT RESEARCH PROJECT 10-22 FINAL REPORT FREEWAY TRAVEL-TIME ESTIMATION AND FORECASTING OFFICE OF RESEARCH 15 KENNEDY DRIVE FOREST PARK, GA 30297-2534 Technical Report Documentation Page 1. Report No.: 2. Government Accession No.: FHWA-GA-12-1022 4. Title and Subtitle: Freeway Travel-time Estimation and Forecasting 3. Recipient's Catalog No.: 5. Report Date: September 2012 6. Performing Organization Code: 7. Author(s): Angshuman Guin, Ph.D., Jorge Laval, Ph.D., Bhargava R. Chilukuri 8. Performing Organization Report No. 10-22 9. Performing Organization Name and Address: Georgia Tech Research Corporation School of Civil and Environ. Engineering 790 Atlantic Drive Atlanta, GA 30332-0355 12. Sponsoring Organization Name and Address: Georgia Department of Transportation, Office of Materials and Research; 15 Kennedy Drive; Forest Park, GA 302972534 10. Work Unit No.: 11. Contract or Grant No.: 13. Type of Report & Period Covered: Final; August 2010 September 2012 14. Sponsoring Agency Code: 15. Supplementary Notes: Prepared in cooperation with the US Department of Transportation, Federal Highway Administration 16. Abstract: This project presents a microsimulation-based framework for generating short-term forecasts of travel time on freeway corridors. The microsimulation model that is developed (GTsim), replicates freeway capacity drop and relaxation phenomena critical for modeling non-steady state conditions. This framework is evaluated offline on a real-world freeway corridor by using data from manual counts and the Georgia Department of Transportation's video detection system. The travel time forecasts are compared with ground truth travel time data; the comparison demonstrated the efficacy of this framework to produce realistic forecasts. The study results showed that this framework can provide sufficiently accurate 5-minute and 10-minute forecasts and that it outperforms state-of-the-practice methods such as instantaneous travel time. 17. Key Words Travel-time forecasting. 18. Distribution Statement 19. Security Class (This 20. Security Class (This Page) 21. No of Pages Report) Unclassified 77 Unclassified Form DOT F 1700.7 (8/72) Reproduction of form and completed page is authorized 22. Price GDOT Research Project No. RP 10-22 Final Report FREEWAY TRAVEL-TIME ESTIMATION AND FORECASTING By Angshuman Guin, Ph.D., Principal Investigator Jorge Laval, Ph.D., co-Principal Investigator Bhargava R. Chilukuri, Graduate Research Assistant School of Civil and Environmental Engineering Georgia Institute of Technology Contract with Georgia Department of Transportation In cooperation with US Department of Transportation Federal Highway Administration September 2012 The contents of this report reflect the views of the authors who are responsible for the facts and 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. Table of Contents 1 Introduction .......................................................................................................................... 1 1.1 Objective........................................................................................................................ 2 2 Literature Review.................................................................................................................. 3 2.1 Travel-time Estimation Algorithms............................................................................... 5 2.1.1 Direct Methods .......................................................................................................... 5 2.1.2 Indirect Methods........................................................................................................ 9 2.2 Travel-time Forecast Algorithms ................................................................................ 12 2.2.1 Statistical Methods .................................................................................................. 12 2.2.2 Simulation Methods................................................................................................. 16 3 Prediction Framework........................................................................................................ 20 4 Data Collection and Preliminary Analysis ........................................................................ 23 4.1 Traffic Volume Data Collection .................................................................................. 26 4.2 Bluetooth Data Collection ........................................................................................... 27 4.3 Velocity Data Collection ............................................................................................. 29 5 Traffic Flow Simulation Application................................................................................. 33 5.1 Process Flow................................................................................................................ 33 5.2 Critical Modules .......................................................................................................... 34 6 Methodology........................................................................................................................ 41 i 6.1 Origin Destination Matrix Estimation Algorithm ....................................................... 43 6.2 Calibration and Validation .......................................................................................... 45 7 Results and Discussion ....................................................................................................... 49 7.1 Analysis of Bluetooth Data ......................................................................................... 49 7.2 Analysis of Simulation Results ................................................................................... 52 8 Conclusion .......................................................................................................................... 60 9 References ........................................................................................................................... 62 ii List of Figures Figure 1. Popular Travel-time Estimation and Prediction methods .............................................. 4 Figure 2. Real-time Travel-time estimation and prediction framework...................................... 20 Figure 3: Study Corridor (background: http://maps.google.com) .............................................. 25 Figure 4: Bluetooth Data Collection Locations (background: http://maps.google.com) ........... 27 Figure 5: Actual Travel-time Data collected by Bluetooth devices ........................................... 29 Figure 6: Time space speed plot of the study corridor on March 7, 2012.................................. 30 Figure 7: Time Series of Speed of the NaviGAtor station #2850032 ........................................ 31 Figure 8: Process Flow for the Simulation Application .............................................................. 35 Figure 9: Transportation Network background for the Application............................................ 36 Figure 10: Sample Network......................................................................................................... 37 Figure 11: Sample Animation snapshot ...................................................................................... 38 Figure 12: ITT, RTT, ATT and Bluetooth data on the corridor .................................................. 51 Figure 13: Simulation results vs. Bluetooth Data on the corridor ............................................... 54 Figure 14: Travel-time Predictions for Different Time Horizons on the Corridor...................... 54 Figure 15: Comparison of Travel-time Predictions for Different Horizons on the Corridor ...... 55 Figure 16: Y-Y Plot of 1st Prediction TT and ITT against Bluetooth Data ................................. 57 Figure 17: Comparison of variability in 1st Prediction, 2nd prediction, 3rd prediction and ITT... 58 iii List of Tables Table 1. Calibrated Parameters.................................................................................................... 46 Table 2. RMSE and MAPE ......................................................................................................... 59 iv Executive Summary Real-time traffic information provided by GDOT has proven invaluable for commuters in the Georgia freeway network. The increasing number of Variable Message Signs, addition of services such as My-NaviGAtor, NaviGAtor-to-go etc. and the advancement of the 511 traffic information system will require the Traffic Management Center to provide more detailed and accurate traffic information to an increasing number of users. In this context, the ability to forecast traffic conditions (both in space and time) would augment the services provided by NaviGAtor by allowing users to plan ahead for their trip. Forecasts built into the estimation model will make the travel-time estimates more accurate by reducing the use of stale data. Additionally, spatial forecast can help GDOT provide reliable information in areas with temporary outages in coverage; e.g. outages due to detector or cameras malfunction. The vast majority of real-time travel-time estimation algorithms proposed in the literature are based on data mining techniques. Unfortunately, this approach is unable to produce reliable forecasts because it does not take into account traffic dynamics (e.g., via a simulation model). In Germany, a simulation-based forecast system is in place at most metropolitan areas, with very favorable user impacts. Although successful, the German example is based on a type of simulation model (a Cellular Automata model) that has critical drawbacks: difficulty of calibration, inability to incorporate different user classes (e.g., cars and trucks), and inadequate capability of replicating detailed traffic dynamics on freeways. The model proposed in this study overcomes these drawbacks by incorporating the latest advances in traffic flow theory and simulation. The proposed prediction framework for real-time travel-time estimation and prediction is shown in Figure 2. The two main components of this framework are the micro-simulation and traffic v sensor infrastructure on the freeways. The micro-simulation runs faster than real-time using the data reported by the traffic sensors to give travel-time estimates and predictions. Real-time Travel-time estimation and prediction framework The traffic sensors provide time series of traffic volumes and speeds at both the boundaries of the network and also on mid-segments. The traffic volumes at the network boundaries are used for estimating dynamic origin-destination matrices. The traffic volumes and speeds on the midsections are used to determine initial queues used for the simulation. The vehicle trajectories produced by the simulation are used by a dynamic OD estimation module to generate OD matrices for the next simulation run. The dynamic OD matrices are validated with the historic OD matrices before being used as input in the next simulation run. The vehicle trajectories generated by the simulation are used to generate travel-time forecasts. The study was performed by simulating a 6.5 miles long EB/SB I-285 corridor between GA-400 and I-85 for 2 hours during the evening peak period (from 15:00 to 17:00). The volume data was manually extracted from videos recorded using GDOT's traffic monitoring cameras. Bluetooth vi data was collected from select overpasses in the corridor in the same day as the traffic volume data collection to serve as travel-time ground truth. The OD matrix was changed every 5 minutes and a new simulation was initiated every time with new initial queue and new OD flows. Six travel-time forecasts were made for every simulation run. The predictions made every 5 minutes were compared with the Bluetooth travel-time data collected in the field. The following plot of travel-time predictions for different time horizons on the corridor show that the predictions made during each simulation run follow the pattern observed with the Bluetooth data. During congestion buildup, the forecasts show an increase in travel-time for prediction horizons. Eventually, after the corridor gets congested, the forecasted travel-times flatten out. Travel-time Predictions for Different Time Horizons on the Corridor vii The following figure shows a comparative plot of the probe travel-times or actual travel-times (ATT) with the simulated and instantaneous speed travel-times (ITT). The instantaneous traveltime is based on the speeds across the corridor at a single instant and is a close approximation of the methodology typically used by Transportation Management Centers for travel-times posted on variable message signs. Comparison of Travel-time Predictions for Different Horizons on the Corridor The following Y-Y plot of ATT vs ITT and 1st prediction (simulated) travel-times shows that the 1st prediction results are closer to the actual travel-times than the ITT estimates. The 1st prediction travel-time data points shown in red are the instances when the sample sizes from Bluetooth data are less than 10. Apart from the outlier points, it can be seen that the performance of the simulation is superior to the ITT method under dynamic conditions, whereas the performance becomes comparable under heavy, stable congestion. viii Y-Y Plot of 1st Prediction TT and ITT against Bluetooth Data This study demonstrated the use of a simulation based framework to make short-term travel-time predictions in real-time. The results show that sufficiently accurate 5-minute and 10-minute predictions can be made using this framework. The lessons learned from the study stresses that it is critical to adequately calibrate the simulation model and for this purpose it is essential to accurately calibrate the vehicle detection sensors. Currently, the simulation is manually initiated each time a new OD matrix becomes available. For a seamless implementation, the initiation process needs to be automated. In future studies the researcher would like to automate the simulation to run continuously by getting sufficient predictions from a run, pausing the simulation until the next OD update is available, and updating the OD flows and initial queues. When incidents occur, the corresponding lane blockage can be incorporated in the simulation before predictions are made. ix Acknowledgments The authors of this report wish to thank the Georgia Department of Transportation for its support and assistance throughout this effort, in particular the efforts of Binh Bui, David Jared, Mark Demidovich and W. Grant Waldrop. In addition the authors wish to thank the USDOT for the support from a companion project provided through the University Transportation Center program. x 1 Introduction Real-time traffic information provided by GDOT has proven invaluable for commuters in the Georgia freeway network. The increasing number of Variable Message Signs, addition of services such as My-NaviGAtor, NaviGAtor-to-go etc. and the advancement of the 511 traffic information system will require the Traffic Management Center to provide more detailed and accurate traffic information to an increasing number of users. In this context, the ability to forecast traffic conditions (both in space and time) would augment the services provided by NaviGAtor by allowing users to plan ahead for their trip. Forecasts built into the estimation model will make the travel-time estimates more accurate by reducing the use of stale data. Additionally, spatial forecast can help GDOT provide reliable information in areas with temporary outages in coverage; e.g. outages due to detector or cameras malfunction. The vast majority of real-time travel-time estimation algorithms proposed in the literature are based on data mining techniques [1-5]. Unfortunately, this approach is unable to produce reliable forecasts because it does not take into account traffic dynamics (e.g., via a simulation model). In Germany, a simulation-based forecast system [6] is already in place at most metropolitan areas, with very favorable user impacts. Although successful, the German example is based on a type of simulation model (a Cellular Automata model) that has critical drawbacks: difficult to calibrate, unable to incorporate different user classes (e.g., cars and trucks), and not proven to replicate detailed traffic dynamics on freeways. The model proposed in this project [7-9] overcomes these drawbacks by incorporating the latest advances in traffic flow theory and simulation. The enhanced travel-time estimation methodology developed in this research would substantially increase the accuracy of the estimates provided by GDOT to the commuters via the Changeable 1 Message Signs, the Georgia-NaviGAtor website, the *DOT service and the 511 service. This will not only improve the credibility of the estimates, but will allow people to better schedule their commutes or take less congested alternative routes in order to avoid congestion. 1.1 Objective The objectives of this project are: Incorporate recent advances in traffic flow theory and simulation to build a framework able to predict the onset and propagation of congestion across the Metropolitan Atlanta freeway network Demonstrate proof of this concept by generating realistic real time travel-time forecasts on a freeway corridor based on short-term forecasts of future congestion levels in the network obtained from simulation 2 2 Literature Review Travel-time is one of the performance measures used by transportation agencies to evaluate the operation of freeway systems. The Federal Highway Administration (FHWA) issued a memorandum in 2004 that encouraged all the transportation agencies to display travel-time information on the dynamic message signs [10]. Travel-time on freeway sections can be generally classified into: Instantaneous Travel-time Reactive Travel-time Predictive Travel-time Instantaneous Travel-time refers to the average travel-time observed on a small roadway segment along a corridor. The average total travel-time along the corridor is obtained by adding the instantaneous travel-time on each of its segments. The inherent assumption made is that the traffic conditions on each of the segments remain unaltered between when the vehicle enters and exits the freeway corridor. This assumption holds true during free-flow conditions but fails at the border of free-flow and congestion. This assumption results in underestimating travel-time at the onset of congestion and overestimating at the dissipation of congestion. Reactive Travel-time refers to the travel-time of the vehicle that just exited the corridor. While this type of travel-time measurement is precise and is based on actual travel-time observed in the field, this measurement does not mean that a driver who just entering the corridor upstream will have the same travel-time. It has been shown that this is not a good measure for online travel-time prediction [11]. 3 Predictive Travel-time refers to the forecasted travel-times that are expected to be experienced by drivers who enter the corridor at that time instant or in future. This is the most useful information from a driver's perspective, but the most difficult one to forecast accurately. Forecasting traveltime during congested conditions is particularly challenging since small instability in conditions can result in significantly varying spatial and temporal travel velocities. In this chapter, the methods and algorithms used in the literature to measure instantaneous and reactive travel-times are grouped as Travel-time Estimation methods. Similarly, methods used for calculating predictive travel-time will be called Travel-time Prediction methods. Figure 1 describes different methods used for Travel-time Estimation and Prediction. The rest of this chapter briefly describes each of these methods. Figure 1. Popular Travel-time Estimation and Prediction methods 4 2.1 Travel-time Estimation Algorithms The travel-time estimation methods provide information to understand the current traffic conditions on the roadways. This information can be estimated by directly measuring the traveltime (here after called Direct methods) or by measuring traffic variables such as velocity, occupancy, and flow and estimating travel-time information (here after called Indirect methods). 2.1.1 Direct Methods The following paragraphs briefly describe four popular methods; probe vehicle technique, license plate recognition technique, signature matching, and transponder based systems used to directly measure the travel-time in the field. 2.1.1.1 Probe Vehicle Technique Probe vehicle technique is a common method that consists of vehicle(s) specifically dispatched to drive with the traffic stream to collect travel-time data. The Travel-time Data Collection Handbook [11] defines the following three driving styles that the agencies can adopt for the probe vehicles: Average car - vehicle travels according to the driver's judgment of the average velocity of the traffic stream Floating car - driver "floats" with the traffic by attempting to safely pass as many vehicles as pass the probe vehicle Maximum car - vehicle is driven at posted velocity limit unless impeded by actual traffic conditions or safety considerations. 5 Even though floating car driving style is the most commonly referenced, most agencies use a hybrid of the floating car and average car styles for their travel-time studies. Travel-time data can be collected using electronic instruments such as Distance Measurement Instrument (DMI) or Global Positioning System (GPS) to automatically record vehicle location and velocity at preset checkpoints or time intervals. 2.1.1.2 License Plate Matching License plate matching (LPM) technique consists of measuring travel-time by matching license plate information at various checkpoints. The license plate characters and arrival times are collected at various checkpoints and the license plates are matched to compute the travel-times between the check points. The check points are typically spaced half a mile to two miles on arterials and one mile to five miles on the freeways. Even though there are equations to calculate the sample size under different conditions, generally a minimum sample size of 50 license plate matches is used to determine the average travel-time for a roadway segment [12]. One of the important requirements of this technique is synchronizing the clocks at various checkpoints. Since the vehicle velocities may vary significantly by lane during peak hours (and hence the travel-times), a representative sample of license plates should be collected from all through lanes. One of the advantages of the automated License Plate Recognition (LPR) technology is that, by knowing the local Division of Motor Vehicles policy on the vehicle license plate syntax, one can program the system to exclude information from trucks and trolley vehicles that do not travel at regular traffic velocity. However, the accuracy of data from the LPR is sensitive to poor visibility conditions. [13, 14]. Moreover, collecting and storing license plate information can result in 6 privacy issues. Therefore, transportation agencies have to ensure safe disposal of the license plate information after extracting the travel-time data. 2.1.1.3 Signature Matching Method In the signature matching method the travel-time is calculated by matching (correlating) unique vehicle signatures between sequential observation points. This is similar to the LPM techniques, but utilizes the widely spread existing detector infrastructure instead of installing new LPM technology. The signature matching method can be used with Inductance Loop Detectors (ILD), weigh-in-motion sensors, video cameras, and laser scanning detectors. With the use of ILD, the travel-time can be calculated in multiple ways, on the basis of the reidentification of particular vehicles in consecutive loop detectors by means of characteristic length [15, 16] or particular inductive signature on the detector [17, 18, 19]. For video camera based detectors, visual vehicle signatures from wayside cameras [20, 21] and vehicle dimension matching for the laser based detectors [22] were developed. Coifman and Cassidy [23] developed an improved signature matching algorithm by incorporating platoon matching. This algorithm estimates average travel-time by matching unique features of vehicle platoons such as the position and/or distribution of vehicle gaps or unique vehicles. However, this methods is heavily is reliant on proper functioning of sensors and will quickly deteriorate the quality of the travel-time information if the percent of sensor failure is moderately large. 7 2.1.1.4 Transponder Based Systems To overcome the limitations of earlier methods, transponder based systems are sometimes used by transportation agencies. These utilize electronic transponders or receivers installed in personal, public transit, or commercial vehicles in the traffic stream to collect travel-times. Signpost-based method, Automatic Vehicle Identification (AVI), and GPS based system are some of the traveltime collection applications of the transponder based systems. Signpost-based method is a popular technique used by transit agencies where probe vehicles communicate with transmitters mounted on existing fixed signpost structures. Signpost transmitters are typically spaced 5 miles along bus routes with buses polling every 60 seconds for an odometer reading. While signpost-based method requires simple infrastructure, it has limited coverage area. AVI method has vehicles equipped with electronic tags that communicate with roadside transceivers to identify unique vehicles and collect travel-times between transceivers. Tags are electronically encoded with unique identification (ID) numbers synonymous with the electronic registration number used to determine vehicle ownership in electronic toll collection. The transceivers emit radio frequency (RF) signals within a capture range across one or more freeway lanes. Examples of existing AVI systems include the TranStar system in Houston [24], the TransGuide system in San Antonio [25], and the Transmit system in the New York/New Jersey metropolitan area [26]. AVI technology is proved to provide high accuracy of travel-time data with minimal personnel requirement [27, 28, 29, 30, and 31]. However, the limitations of this method are high infrastructure dependency and clock drift problems. In the GPS method, probe vehicles are equipped with GPS receivers and two-way communication to receive signals from earth-orbiting satellites. The positional information determined from the 8 GPS signals is transmitted to a control center to display real-time position of the probe vehicles from which travel-time information is extracted. There are many applications of automatic vehicle location that employ GPS for vehicle tracking in real-time. These include emergency service vehicles, rental cars, commercial fleets, taxis, and transit vehicles. While this method has low initial and operating cost, privacy issues and occasional loss of communication are some of the concerns with this method. Results obtained by Herrera [32] suggest that a 23% penetration of GPS-enabled cell phones in the drivers' population is enough to provide accurate measurements of the velocity of the traffic stream. 2.1.2 Indirect Methods Indirect methods involve calculating travel-time indirectly using the parameters such as velocity, flow, density, or occupancy from "point" vehicle detection equipment such as Inductive Loop Detectors (ILD), cameras or similar traffic monitoring technologies. Some of the important techniques include extrapolation method, cumulative curve methods and theoretical techniques. 2.1.2.1 Extrapolation Method In the extrapolation technique, the travel-time data is estimated with the use of spot velocities measured by ILD. The average velocity between ILD locations is extrapolated to determine the average travel-time along the segment. Velocity can be directly measured in case of dual loop detectors. However, in case of single loop detectors, velocity is often calculated on the basis of flow, occupancy, and average effective vehicle length. The last parameter is usually calibrated during light traffic conditions by imposing a value for free flow velocity. Hall and Persaud [33] suggested that effective length might be prone to a systematic bias with respect to occupancy. 9 The extrapolation method is simple and can be used for applications that do not require high levels of accuracy. One of the inherent assumptions of this technique is that velocity within a segment can be closely represented by the extrapolation method. Some of the common extrapolation methods include half-distance approach, average velocity approach, and minimum velocity approach, piece-wise constant, piece-wise linear approach, and piece-wise quadratic approach [34, 35]. Several researchers have evaluated various extrapolation techniques with several alternative techniques such as inverse velocity based trajectory method, Kalman filtering, etc. [36, 37, 38, 39, 40, 41, 42, and 43). The main disadvantage of the extrapolation methods is that the accuracy of the estimates decreases with increasing flow conditions. 2.1.2.2 Cumulative Count Method Another approach for travel-time estimation is based on the cumulative arrivals at successive detector stations assuming First In First Out (FIFO) mechanism [44, 45, 46, 47, and 48]. The cumulative number of vehicles to cross the two loop detectors located at either end of a link are measured to determine the link travel-time. If one were to plot the cumulative vehicle count vs. time of these detectors then the travel-time on the link is the distance between the two curves along the time axis. Nam and Drew [47] developed two different equations for travel-time calculations, one for uncongested and one for congestion conditions. Rakha and Zhang [49] later corrected Nam and Drew's equations and showed that delay computations for shockwave analysis and queuing theory were consistent. Using rescaled cumulative curves, Yeon and Elefteriadou [50] examined the accuracy of these above methods comparing with the field-measured travel-time. Yeon and 10 Elefteriadou noted that all three approaches give similar results for freeway sections without entering/exiting ramps. The authors showed that with the presence of ramps between detectors, all the methods perform inadequately on certain segments. However, this method has several practical problems. First, one needs to know the number of vehicles initially located between the two detectors before the algorithm begins (a quantity which is not readily available). Second, loop detectors are notorious for over- and under-counting vehicles. Hence the cumulative flow lines may systematically drift over time giving inaccurate estimates over time (the lines may even cross). 2.1.2.3 Theoretical Methods Dailey [51] used cross-correlation of the flow at the upstream and downstream detectors to estimate travel-time between two single-loop detectors placed 0.5 miles apart. While this method is robust, this method requires constant calibration during changes in traffic regimes to provide accurate results. Petty et al. [52] suggested a model for estimating travel-time directly from flow and occupancy data, based on the assumption that the vehicles that arrive at an upstream point during a given interval of time have a common probability distribution of travel-times to a downstream point. All the methods described above estimate Instantaneous Travel-time and Reactive Travel-time. The following subsection describes travel-time forecasting methods used to calculate the Predictive Travel-time. 11 2.2 Travel-time Forecast Algorithms As show in Figure 1, there are two major categories of methods for forecasting travel-time; statistical methods and simulation based methods. The statistical methods use statistical tools on the historic and real time data to derive models to predict travel-time. On the other hand, simulation methods use traffic flow models and congestion propagation phenomenon to forecast travel-time 2.2.1 Statistical Methods The statistical models can be broadly divided into four categories; Regression models, Time series models, Artificial Neural Networks models, and Kalman filter based models. 2.2.1.1 Regression Models These models predict travel-time using linear regression with a stepwise variable selection method [53, 54]. These models typically use historical and/or real-time flow and occupancy data from the detectors as explanatory variables to determine the response variable, travel-time. Kwon et al. [55] used linear regression and advanced statistical methods such as tree methods to develop models for predicting travel-time. Later, Rice and Van Zwet [56] and Zhang and Rice [57] proposed methods to predict freeway travel-time using a linear model in which the coefficients vary as smooth function of the departure time. Instead of using flow and occupancy, Chakraborty and Kikuchi [58] used bus travel-times and developed a simple linear equation using regression to predict automobile travel-time based on the bus travel-time. 12 Some researchers also fit the historic travel-time data to probabilistic distributions and used them to predict travel-time (53, 59, 60, and 61). Others have used historic velocity profile and location data to develop prediction models [6, 63, and 64]. However, these models are found to perform well during short-term prediction horizon under normal traffic condition but are less accurate during congestion onset and congested conditions. Also, there models perform poorly in the presence of incidents and other special traffic conditions. 2.2.1.2 Time Series Models These models utilize the time series information of velocity, flow, occupancy, and/or travel-time data to derive predictive models. Several researchers used flow and occupancy to derive auto regressive prediction model [65, 66]. D'Angelo et al. [67], Al-Deek [68], and Ishak and Al-Deek [4] later used nonlinear time series with multifractal analysis to develop prediction models. The univariate time series models have been found to provide superior performance in accurately predicting travel-times compared to many complex algorithmic and hybrid methods developed in recent times. However, to improve the accuracy of predictions obtained by the univariate models, Stathapoulos and Karlaftis [69] developed a multivariate time series model using traffic flow parameters. Kamarianakis and Prastacos [70] compared the forecasting performance of two univariate and two multivariate models and found that multivariate time series models performed better than univariate models for short term traffic predictions. On the other hand, Williams and Hoel [71] used the Box and Jenkins technique, more specifically, Autoregressive Integrated Moving Average (ARIMA) technique to develop a one-step prediction model for traffic flow at smaller time steps. Later, Guin [72] developed an ARIMA model to predict travel-time and found that the models showed a strong weekly seasonality and produced 13 reliable predictions on a short time scale. While the time series models are found to perform better under normal flow conditions, their performance was found to deteriorate rapidly with the onset of congestion, or under any unusual conditions. 2.2.1.3 Artificial Neural Networks Models Artificial Neural Network (ANN) is a non-linear statistical data model consisting of an interconnected group of nodes that processes information using a connectionist approach to computation. Cherrett et al. [73] reported the use of a feed-forward ANN model for the prediction of link journey time. Later, Ohba et al. [74] proposed a travel-time prediction model using a mixed structure type neural network system. Park and Rilett [75], Park et al. [76], Rilett and Park [77], and Kisgyorgy and Rilett [3], suggested modifications such as clustering techniques, modular neural network, expanded input nodes, and spectral basis neural network to ANN to account for nonlinear nature of travel-time data for prediction. Kisgyorgy and Rilett's models have indicated that the travel-time prediction error can be as small as approximately 4%. Several researchers have used advanced methods in neural networks to develop travel-time prediction models. Matsui and Fujita [78] used fuzzy reasoning and You and Kim [79] used nonparametric regression and GIS technology to predict travel-time. Jiang and Zhang [8] used mix-structure neural network model that can predict travel-time of roadway segments without detectors, based on the data from segments with detectors. Similarly, Van Lint et al. [44] investigated using state space neural networks, Wei et. al. [81] used advanced neural network, and Dharia and Adeli [82] used counter-propagation neural networks, for the forecasting of freeway link travel-time. Though these ANN models produced accurate results, developing these models is complex and needs good calibration. 14 2.2.1.4 Kalman Filter Models The Kalman filter [83] is recursive estimator used for filtering measurements that are observed over time and contain noise and other inaccuracies to estimate true values of measurements and their associated calculated values. It also produces forecasts by predicting a value, estimating the uncertainty of the predicted value, and computing a weighted average of the predicted value and the measured value. Thus, this method enables the prediction of the state variable to be continually updated as new observation becomes available. Szeto and Gazis [84], Okutani and Stephanedes [85] and Okutani [86] used Kalman filtering to estimate traffic volumes, density and trip distribution. Later Stephanedes and Kwon [87] used Kalman filtering to determine real-time demand diversion. Chien et al. [88] used Kalman filtering algorithm on a combination of historical and real-time data for short term prediction of traveltime. They found that predictions using link-based travel-times are more accurate than prediction using path-based travel-times. Kuchipudi et al. [89] developed a model in which both path-based data and link-based data are used to predict travel-times. The travel-times were chosen based on the prediction error obtained using those two data sources. Later researchers have developed adaptive least squares method, which was a special case of the Kalman filtering approach. Thus, all the statistical methods can be categorized as data driven approaches that treat traffic dynamics as `black boxes' and use statistical relations from past data (e.g. volumes, velocities, densities, travel-times, etc.) to infer future travel-times. The fundamental deficiency of these methods is that they cannot provide satisfactory prediction during non-recurrent congestion due to work zones, incidents, and special events, during which travel-time prediction is more important. 15 2.2.2 Simulation Methods On the other hand traffic simulation models use traffic flow knowledge to predict the traffic conditions on the corridor, and integrate mathematical algorithms to predict travel-time. There are three types of simulation models used for travel-time prediction, Macroscopic, Mesoscopic, and Microscopic simulation models. The following paragraphs describe METANET, DynaMIT, and Cellular Automata based models that belong to the above categories of traffic simulation models. 2.2.2.1 Macroscopic Models Macroscopic models treat traffic flow as fluid streams. The traffic flow characteristics such as density, flow, and mean velocity are the average values of the traffic stream. The most popular macroscopic model is the LWR model, a first order model developed by Lighthill and Whitham [90] and Richards [91]. Later higher order models were developed to overcome the limitations of the first order model. METANET is a macroscopic simulation model based on second order traffic flow model [92]. In addition to the traffic simulation, METANET also has the capability of taking control actions such as ramp metering and route guidance. METANET has two distinct modes of operation, with or without destination-oriented mode. Since this is a macroscopic model, variables such as density, velocity and flow, represent the average behavior of traffic at certain times and locations. The time and space arguments are discretized. See [93] for a detailed description of the model. This simulation model is used to model A10 ring road motorway of the Amsterdam network in both directions [94]. The total length of the network is 143 km and engulfs Amsterdam. The total number of links that was used to model the motorway network is 654 and divided into a total of 16 291 segments. The length of each segment ranges from 400 to 800 m. This network is used to capture the congestion dynamics and develop control strategies and provide ATIS information to commuters. One of the drawbacks of macroscopic models is that these models only produces aggregate measures and do not guarantee replicating driver behavior at microscopic levels. 2.2.2.2 Mesoscopic Models While macroscopic modeling deals with average values of traffic parameters, microscopic models deal with individual car behavior. Mesoscopic models are intermediate and combine the properties of both microscopic and macroscopic simulation models. These models simulate individual vehicles, but describe their activities and interactions based on aggregate (macroscopic) relationships at the network link levels. DYNAMIT is a mesoscopic simulation model developed at MIT for ATIS applications. DynaMIT is a simulation developed by Ben-Akiva et. al. [95] that is used for real-time traveltime estimation and forecasting. It is designed to estimate current state of transportation network and predicts future traffic conditions. This system combines real-time traffic data from surveillance system and historic data for estimation and prediction purposes. The system takes data from historical database and real-time surveillance system as an input. The demand simulator estimates and predicts time-dependent origin-destination matrices and driver decisions in terms of mode and route choices. The supply simulation emulates the interaction between demand and network. The state estimation is done through an iterative process of these two simulators (demand simulation and supply simulation) till it reproduces the real-time surveillance system data. Even though mesoscopic models are relatively more detailed compared to the macroscopic models, they still do not replicate driving behavior at microscopic levels. To overcome this drawback several researchers have used microscopic models. 17 2.2.2.3 Microscopic Models Microscopic simulation models are dynamic and model individual vehicle movements within a transportation network. Each vehicle is moved through the network according to the physical characteristics of the vehicle (length, maximum acceleration rate, etc.), the fundamental rules of motion (e.g. acceleration times time equals velocity, velocity times time equals distance) and rules of driver behavior (car following rules, lane changing rules, etc.). Cellular Automata (CA) models are popular microscopic simulation models used for traffic applications. CA models were first proposed by Von Neumann in 1952 [96]. They were later used for transportation by Cremer and Ludwig in 1986 [97]. CA models have become popular in transportation applications after Nagel and Schreckenberg [98] proposed simple steps to reproduce traffic dynamics on transportation networks. Since then, CA models been widely used to simulate traffic networks [98, 99, 100, 101], freeways [102], intersections [103], roundabouts [104], and toll stations [105]. Due to their design using simple conditions, cellular automata models are very efficient for simulation of large-scale networks. Lane changes are incorporated using a variable, ln {left, right, straight which notes if the vehicle n should change the lane during the actual time-step or not, as explained in detail in [106]. In other words, the lane changing logic works as follows: first, a vehicle checks if it is hindered by the predecessor on its own lane. Then it has to take into account the gap to the successor and to the predecessor on the target lane. If the gaps allow a safe change the vehicle makes a lane change. A systematic approach to lane-changing rules on multi-lane roads is given in [107, 108, 109, 110]. 18 CA based simulation is extensively used in Germany as a part of their autobahn information system [111]. The details of this CA based system can be found at www.autobahn.nrw.de, where the simulated actual traffic state on the freeway network in North Rhine Westphalia is presented. This estimation and forecasting system uses data input from more than 4,000 loop detectors that are installed on the autobahn and deliver minute by minute data. The traffic state information from the CA model is adjusted in accordance with measurements of the real traffic flow provided by the loop detectors. The transportation network comprised of 3,988 links, 830 on- and offramps, and 67 intersections. The overall length of the lanes is approximately 12,200 km, corresponding to more than 8 million cells. This CA model is currently used to graphically present real-time traffic state information and also a prediction time horizon of 30 minutes. CA based models are also developed to estimate traffic state and incident-related travel-time on freeways in US [112,113,114, 115 and 116] used CORSIM to predict travel-time for real world networks, but the latest advances in traffic flow models will be able to replicate the real-world conditions better than the traditional models that cannot reproduce the capacity drop phenomenon and relaxation phenomenon observed on the freeways. 19 3 Prediction Framework The prediction framework for real-time travel-time estimation and prediction is shown in Figure 2. The two main components of this framework are the micro-simulation and traffic sensor infrastructure on the freeways. The micro-simulation will run at faster than real-time using the data reported by the traffic sensors to give travel-time estimates and predictions. Figure 2. Real-time Travel-time estimation and prediction framework The traffic sensors mentioned above could be inductive loops (IDL), video based systems or any other system that collect volume and spot speeds on the freeways. These sensors provide time series of traffic volumes and velocity at both the boundaries of the network and also on midsegments. The traffic volumes at the network boundaries are used for estimating dynamic origin-destination matrices and the traffic volumes and velocity on the mid-sections are used to determine initial queues used for the simulation. The vehicle trajectories produced by the simulation are used by the dynamic OD estimation module described in section 6.1 to generate OD matrices for the next simulation run. The dynamic OD matrices are validated with the historic OD matrices before 20 using as input in the next simulation run. Also, the vehicle trajectories are used to generate traveltime forecasts. In general, the forecast horizon is an important parameter in any prediction framework. There are two kinds of forecast horizons, short-term and long-term. Short term prediction typically represents prediction of five to ten minutes into the future. Long-term prediction refers to longer range prediction, typically in the order of 30 minutes to few hours. However, during non-steady state traffic current traffic data quickly becomes less relevant to make long-term predictions and historical experience could be supplemented to improve the prediction quality. This framework can be written as an algorithm as follows: 1. Let a new simulation be initiated (with new OD flows) at time t = h, 2h, 3h,..ph...nh with prediction horizons are r, 2r, 3r,...mr where n, h, m, r and p are integers. 2. Therefore, at any time t = ph, travel-time predictions are made for t = ph+r, ph+2r, ph+3r,....ph+mr 3. For each simulation run perform the following steps: o Calculate initial queue using queuing analysis on each link. The total number of arrivals and departures are continuously measured across boundaries to calculate the initial queue at the beginning of every simulation. The average speed for each link is estimated based on the speed sensor observations. o Calculate OD matrix using the travel-time predictions made for each origin and destination set in the previous simulation run to calculate the corresponding flows on the ramps. These flows are used in the OD estimation algorithm described in section 6.1 to calculate OD flows. 21 4. Derive vehicle trajectories to make travel-time predictions for different prediction horizons 5. Repeat step 3 for each simulation run If the traffic conditions are stable, the prediction horizon and OD flows changeover period can be sufficiently large to make reliable predictions. 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