J W C van Lint

Online Learning Solutions for Freeway Travel Time Prediction

Providing travel time information to travelers on available route alternatives in traffic networks is widely believed to yield positive effects on individual drive behavior and (route/departure time) choice behavior, as well as on collective traffic operations in terms of, for example, overall time savings and-if nothing else-on the reliability of travel times. As such, there is an increasing need for fast and reliable online travel time prediction models. Previous research showed that data-driven approaches such as the state-space neural network (SSNN) are reliable and accurate travel time predictors for freeway routes, which can be used to provide predictive travel time information on, for example, variable message sign panels. In an operational context, the adaptivity of such models is a crucial property. Since travel times are available (and, hence, can be measured) for realized trips only, adapting the parameters (weights) of a data-driven travel time prediction model such as the SSNN is particularly challenging. This paper proposes a new extended Kalman filter (EKF) based online-learning approach, i.e., the online-censored EKF method, which can be applied online and offers improvements over a delayed approach in which learning takes place only as realized travel times are available.

Freeway travel time prediction with state-space neural networks: Modeling state-space dynamics with recurrent neural networks

An approach to freeway travel time prediction based on recurrent neural networks is presented. Travel time prediction requires a modeling approach that is capable of dealing with complex nonlinear spatio-temporal relationships among flows, speeds, and densities. Based on the literature, feedforward neural networks are a class of mathematical models well suited for solving this problem. A drawback of the feed-forward approach is that the size and composition of the input time series are inherently design choices and thus fixed for all input. This may lead to unnecessarily large models. Moreover, for different traffic conditions, different sizes and compositions of input time series may be required, a requirement not satisfied by any feedforward data-driven method. The recurrent neural network topology presented is capable of dealing with the spatiotemporal relationships implicitly. The topology of this neural net is derived from a state-space formulation of the travel time prediction problem, which is in line with traffic flow theory. The performance of several versions of this state-space neural network was tested on synthetic data from a densely used highway stretch in the Netherlands. The neural network models were capable of accurately predicting travel times experienced, producing about zero mean normally distributed residuals, rarely outside 10% of the real expected travel times. Moreover, analyses of the internal states and weight configurations revealed that the neural networks could develop an internal model linked to the underlying traffic processes.

Improving a Travel-Time Estimation Algorithm by Using Dual Loop Detectors

An algorithm is presented for off-line estimation of route-level travel times for uninterrupted traffic flow facilities, such as motorway corridors, based on time series of traffic-speed observations taken from the sections that constitute a route. The proposed method is an extension of the widely used trajectory method. The novelty of the presented method is that trajectories are based on the assumption of piecewise linear (and continuous at section boundaries) vehicle speeds rather than piecewise constant (and discontinuous at section boundaries) speeds. From these assumptions, mathematical expressions are derived that describe the trajectories within each section. These expressions can be used to replace their existing counterparts in the traditional trajectory methods. A comparison of the accuracy of the new method and of the existing method was carried out by using simulated data. This comparison showed that the root-mean-square error (RMSE) value for the new method is about half the RMSE value for the existing method. When this RMSE is decomposed in a bias and a residual error, it turns out that the existing method significantly overestimates the travel time. However, the largest part of the reduction of the RMSE value is still caused by a reduction of the residual error. In other words, if both methods are corrected for their bias, the new method performs significantly better.An algorithm is presented for off-line estimation of route-level travel times for uninterrupted traffic flow facilities, such as motorway corridors, based on time series of traffic-speed observations taken from the sections that constitute a route. The proposed method is an extension of the widely used trajectory method. The novelty of the presented method is that trajectories are based on the assumption of piecewise linear (and continuous at section boundaries) vehicle speeds rather than piecewise constant (and discontinuous at section boundaries) speeds. From these assumptions, mathematical expressions are derived that describe the trajectories within each section. These expressions can be used to replace their existing counterparts in the traditional trajectory methods. A comparison of the accuracy of the new method and of the existing method was carried out by using simulated data. This comparison showed that the root-mean-square error (RMSE) value for the new method is about half the RMSE value for the existing method. When this RMSE is decomposed in a bias and a residual error, it turns out that the existing method significantly overestimates the travel time. However, the largest part of the reduction of the RMSE value is still caused by a reduction of the residual error. In other words, if both methods are corrected for their bias, the new method performs significantly better.

A Robust and Efficient Method for Fusing Heterogeneous Data from Traffic Sensors on Freeways

Abstract: Fusing freeway traffic data such as spot speeds and travel times from a variety of traffic sensors (loops, cameras, automated vehicle identification systems) into a coherent, consistent, and reliable picture of the prevailing traffic conditions (e.g., speeds, flows) is a critical task in any off- or online traffic management or data archival system. This task is challenging as such data differ in terms of spatial and temporal resolution, accuracy, reliability, and most importantly in terms of spatiotemporal semantics. In this article, we propose a data fusion algorithm (the extended generalized Treiber-Helbing filter [the EGTF]) which, although heuristic in nature, uses basic notions from traffic flow theory and is generic in the sense that it does not impose any restrictions on the way the data are structured in a temporal or spatial way. This implies that the data can stem from any data source, given they provide a means to distinguish between free flowing and congested traffic. On the basis of (ground truth and sensor) data from a micro-simulation tool, we demonstrate that the EGTF method results in accurate reconstructed traffic conditions and is robust to increasing degrees of data corruption. Further research should focus on validating the approach on real data. The method can be straightforwardly implemented in any traffic data archiving system or application which requires consistent and coherent traffic data from traffic sensors as inputs.

Routing Strategies Based on Macroscopic Fundamental Diagram

Traffic management can prevent too many vehicles in a traffic network from reducing traffic performance. In particular, traffic can be routed so that the bottlenecks are not oversaturated. The macroscopic fundamental diagram provides a relationship between the number of vehicles and network performance. Traffic control can be applied on this level to overcome the computational complexity of networkwide control with traditional control levels of links or vehicles. The main questions are (a) how effective traffic control is with aggregate variables compared with full information and (b) whether the shape of the macroscopic fundamental diagram changes under traffic control. A grid network with periodic boundary conditions is used as an example and is split into several subnetworks. The following routing strategies are compared: the shortest paths in distance and time (dynamic due to congestion) and approximations of the path shortest in time but calculated with only variables aggregated for a subnetwork and of the path shortest in time but calculated with only subnetwork accumulation. For the third and fourth routing strategies, only information aggregated over the subnetwork is used. The results show improved traffic flow with detailed information. Effective control is also possible by using aggregated information, but only with the right choice of a subnetwork macroscopic fundamental diagram. Furthermore, when detailed information is used to optimize—and therefore in a subnetwork—the macroscopic fundamental diagram changes.

Real-Time Lagrangian Traffic State Estimator for Freeways

Freeway traffic state estimation and prediction are central components in real-time traffic management and information applications. Model-based traffic state estimators consist of a dynamic model for the state variables (e.g., a first- or second-order macroscopic traffic flow model), a set of observation equations relating sensor observations to the system state (e.g., the fundamental diagrams), and a data-assimilation technique to combine the model predictions with the sensor observations [e.g., the extended Kalman filter (EKF)]. Commonly, both process and observation models are formulated in Eulerian (space-time) coordinates. Recent studies have shown that this model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates. In this paper, we propose a new model-based state estimator based on the EKF technique, in which the discretized Lagrangian Lighthill-Whitham and Richards (LWR) model is used as the process equation, and in which observation models for both Eulerian and Lagrangian sensor data (from loop detectors and vehicle trajectories, respectively) are incorporated. This Lagrangian state estimator is validated and compared with a Eulerian state estimator based on the same LWR model using an empirical microscopic traffic data set from the U.K. The results indicate that the Lagrangian estimator is significantly more accurate and offers computational and theoretical benefits over the Eulerian approach.

Monitoring and Predicting Freeway Travel Time Reliability: Using Width and Skew of Day-to-Day Travel Time Distribution

Generally, the day-to-day variability of route travel times on, for example, freeway corridors is considered closely related to the reliability of a road network. The more that travel times on route r are dispersed in a particular time-of-day (TOD) and day-of-week (DOW) period, the more unreliable travel times on route r are conceived to be. In the literature, many different aspects of the day-to-day travel time distribution have been proposed as indicators of reliability. Mean and variance do not provide much insight because those metrics tend to obscure important aspects of the distribution under specific circumstances. It is argued that both skew and width of this distribution are relevant indicators for unreliability; therefore, two reliability metrics are proposed. These metrics are based on three characteristic percentiles: the 10th, 50th, and 90th percentile for a given route and TOD-DOW period. High values of either metric indicate high travel time unreliability. However, the weight of each metric on travel time reliability may be application- or context-specific. The practical value of these particular metrics is that they can be used to construct so-called reliability maps, which not only visualize the unreliability of travel times for a given DOW-TOD period but also help identify DOW-TOD periods in which congestion will likely set in (or dissolve). That means identification of the uncertainty of start, end, and, hence, length of morning and afternoon peak hours. Combined with a long-term travel time prediction model, the metrics can be used to predict travel time (un)reliability. Finally, the metrics may be used in discrete choice models as explanatory variables for driver uncertainty.

Fastlane: New Multiclass First-Order Traffic Flow Model

The heterogeneity of traffic is a significant if not dominant factor in accurately modeling freeway traffic flow operations. For example, high truck percentages may induce congestion at much lower volumes, and hence different network traffic conditions may result than with low truck percentages. This implies that traffic models for real-time decision support systems in traffic management centers should provide the means to account for traffic heterogeneity. A new, multiclass, first-order traffic model is presented that provides these means and is implemented in the decision-support system BOSS-Offline, operational in all five highway traffic management centers in the Netherlands. FASTLANE differs from earlier multiclass first-order macroscopic traffic models in that it calculates the dynamics in terms of state-dependent (instead of constant) passenger-car equivalents, which is in line with both theory and empirical microscopic data. The model is numerically solved by an efficient and stable Godunov-based solver while maintaining a dynamic and realistic representation of class-specific flows and densities throughout the network. In two synthetic test cases and one based on real data, the workings of FASTLANE under different truck percentages and different conditions are demonstrated.The heterogeneity of traffic is a significant if not dominant factor in accurately modeling freeway traffic flow operations. For example, high truck percentages may induce congestion at much lower volumes, and hence different network traffic conditions may result than with low truck percentages. This implies that traffic models for real-time decision support systems in traffic management centers should provide the means to account for traffic heterogeneity. A new, multiclass, first-order traffic model is presented that provides these means and is implemented in the decision-support system BOSS-Offline, operational in all five highway traffic management centers in the Netherlands. FASTLANE differs from earlier multiclass first-order macroscopic traffic models in that it calculates the dynamics in terms of state-dependent (instead of constant) passenger-car equivalents, which is in line with both theory and empirical microscopic data. The model is numerically solved by an efficient and stable Godunov-based solver while maintaining a dynamic and realistic representation of class-specific flows and densities throughout the network. In two synthetic test cases and one based on real data, the workings of FASTLANE under different truck percentages and different conditions are demonstrated.

Bayesian Combination of Travel Time Prediction Models

Short-term prediction of travel time is a central topic in contemporary intelligent transportation system (ITS) research and practice. Given the vast number of options, selecting the most reliable and accurate prediction model for one particular scientific or commercial application is far from a trivial task. One possible way to address this problem is to develop a generic framework that can automatically combine multiple models running in parallel. Existing combination frameworks use the error in the previous time steps. However, this method is not feasible in online applications because travel times are available only after they are realized; it implies that errors on previous predictions are unknown. A Bayesian combination framework is proposed instead. The method assesses whether a model is likely to produce good results from the current inputs given the data with which it was calibrated. A powerful feature of this method is that it automatically balances a good model fit with model complexity. With the use of two simple linear regression models as a showcase, this Bayesian combination is shown to improve prediction accuracy for real-time applications, but the method is sensitive in the event that all models are biased in a similar way. It is therefore recommended to increase the number and the diversity of the prediction models to be combined.Short-term prediction of travel time is a central topic in contemporary intelligent transportation system (ITS) research and practice. Given the vast number of options, selecting the most reliable and accurate prediction model for one particular scientific or commercial application is far from a trivial task. One possible way to address this problem is to develop a generic framework that can automatically combine multiple models running in parallel. Existing combination frameworks use the error in the previous time steps. However, this method is not feasible in online applications because travel times are available only after they are realized; it implies that errors on previous predictions are unknown. A Bayesian combination framework is proposed instead. The method assesses whether a model is likely to produce good results from the current inputs given the data with which it was calibrated. A powerful feature of this method is that it automatically balances a good model fit with model complexity. With t...

Empirical Evaluation of New Robust Travel Time Estimation Algorithms

Travel times are key statistics for traffic performance, policy, and management evaluation purposes. Estimating travel times from local traffic speeds collected with loops or other sensors has been a relevant and lively research area. The most widespread and arguably most flexible algorithms developed for this purpose fall into the class of trajectory methods, which reconstruct synthetic vehicle trajectories on the basis of measured spot speeds and encompass various assumptions on which speeds prevail between traffic sensors. From these synthetic trajectories, average travel times can be deduced. This paper reviews and compares a number of these algorithms against two new trajectory algorithms based on spatiotemporal filtering of speed and 1/speed (slowness). On the basis of real data (from induction loops and an automated vehicle identification system), it is demonstrated that these new algorithms are more accurate (in terms of bias and residual error) than previous algorithms, and more robust with respe...Travel times are key statistics for traffic performance, policy, and management evaluation purposes. Estimating travel times from local traffic speeds collected with loops or other sensors has been a relevant and lively research area. The most widespread and arguably most flexible algorithms developed for this purpose fall into the class of trajectory methods, which reconstruct synthetic vehicle trajectories on the basis of measured spot speeds and encompass various assumptions on which speeds prevail between traffic sensors. From these synthetic trajectories, average travel times can be deduced. This paper reviews and compares a number of these algorithms against two new trajectory algorithms based on spatiotemporal filtering of speed and 1/speed (slowness). On the basis of real data (from induction loops and an automated vehicle identification system), it is demonstrated that these new algorithms are more accurate (in terms of bias and residual error) than previous algorithms, and more robust with respect to increasing amounts of missing data.