H.J. van Zuylen

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.

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.

Microscopic Traffic Data Collection by Remote Sensing

To gain insight into the behavior of drivers during congestion, and to develop and test theories and models that describe congested driving behavior, very detailed data are needed. A new data-collection system prototype is described for determining individual vehicle trajectories from sequences of digital aerial images. Software was developed to detect and track vehicles from image sequences. In addition to longitudinal and lateral position as a function of time, the system can determine vehicle length and width. Before vehicle detection and tracking can be achieved, the software handles correction for lens distortion, radiometric correction, and orthorectification of the image. The software was tested on data collected from a helicopter by a digital camera that gathered high-resolution monochrome images, covering 280 m of a Dutch motorway. From the test, it was concluded that the techniques for analyzing the digital images can be applied automatically without much problem. However, given the limited stability of the helicopter, only 210 m of the motorway could be used for vehicle detection and tracking. The resolution of the data collection was 22 cm. Weather conditions appear to have a significant influence on the reliability of the data: 98% of the vehicles could be detected and tracked automatically when conditions were good; this number dropped to 90% when the weather conditions worsened. Equipment for stabilizing the camera—gyroscopic mounting—and the use of color images can be applied to further improve the system.

A fuzzy decision support system for traffic control centers

We present a fuzzy decision support system that can be used in traffic control centers to provide a limited list of appropriate combinations of traffic control measures for a given traffic situation. The system is part of a larger traffic decision support system (TDSS) that can assist the operators of traffic control centers when they have to reduce non-recurrent congestion using a network-wide approach. The kernel of the system is a fuzzy case base that is constructed using simulated scenarios. By using the case base and fuzzy interpolation the decision support system generates a ranked list of combinations of traffic control measures. The best combinations can then be examined in more detail by other modules of the TDSS that evaluate or predict their performance using macroscopic or microscopic traffic simulation. At a later stage the fuzzy decision system will be complemented with an adaptive learning feature and with a set of fuzzy rules that incorporate heuristic knowledge of experienced traffic operators.

Localized Extended Kalman Filter for Scalable Real-Time Traffic State Estimation

Current or historic traffic states are essential input to advanced traveler information, dynamic traffic management, and model predictive control systems. As traffic states are usually not perfectly measured and are everywhere, they need to be estimated from local and noisy sensor data. One of the most widely applied estimation methods is the Lighthill-Whitham and Richards (LWR) model with an extended Kalman filter (EKF). A large disadvantage of the EKF is that it is too slow to perform in real time on large networks. To overcome this problem, the novel localized EKF (L-EKF) is proposed in this paper. The logic of the traffic network is used to correct only the state in the vicinity of a detector. The L-EKF does not use all information available to correct the state of the network; the resulting accuracy is equal, however, if the radius of the local filters is sufficiently large. In two experiments, it is shown that the L-EKF is much faster than the traditional Global EKF (G-EKF), that it scales much better with the network size, and that it leads to estimates with nearly the same accuracy as the G-EKF and when the spacing between detectors is varied somewhere between 0.7 and 5.1 km. Compared with the G-EKF, the L-EKF is a highly scalable solution to the state estimation problem.

Impact of Traffic Flow on Travel Time Variability of Freeway Corridors

Travel time variability is determined by variations in demand and capacity. Knowledge about these demand and supply factors can help improve the reliability of travel time and hence the quality of traveling. The precise nature of the relationship between, for example, variations in inflows and travel time variation is still largely unknown. This paper uses empirical traffic data from both Regiolab-Delft in the Netherlands and the Beijing Olympic area to analyze the variability of travel times depending on inflow conditions. Preliminary analysis shows that travel time variability is a function of inflow characterized by two so-called critical inflows (critical transition inflow λ1 and critical capacity inflow λ2, which are both lower than capacity). These critical inflow levels subdivide traffic into a fluent traffic region, a transition traffic region, and a capacity traffic region. Variation of inflow has little or no effect on travel time variation below λ1. But both demand and capacity variations have a positive correlation with travel time variability in between λ1 and λ2. When volumes are above λ2, the inflow slightly affects the travel time variability. Under all inflow levels, the variation in capacity appears to have more impact on travel time variability than does the variation of traffic flow.

Two distinct ways of using kalman filters to predict urban arterial travel time

Two distinct ways of using Kalman filters to address the problem of short-term urban arterial travel time prediction have been presented in this paper. One is to train a neural network by incorporating the extended Kalman filter. This approach utilizes the extended Kalman filter to find the optimal weight parameters of neural networks. The other is to use the extended Kalman Filter to solve a state space model which is used to describe the dynamic changes of urban transportation systems, and obtain accurate state estimation of traffic variables. The former one can be treated as data-driven approach without more comprehensive knowledge of traffic theories, while the latter is model-based approach requiring general formulation of traffic systems. An empirical data set collected from an urban street in Holland is used to compare the performance of these two ways

Prediction of urban travel times with intersection delays

Although there is an increasing demand for travel time prediction methods, the efforts put on urban streets are until now less than on freeways. In this paper, a macroscopic model of urban link travel time prediction is developed based on measurements collected by single loop detectors. This method divides travel times into two components: link cruising times and intersection delays. For each component the mean prediction and prediction interval were investigated in order to provide a reliable prediction. Prediction intervals around the mean prediction show the plausible range of travel times a vehicle is likely to encounter. Based on simulation data, it is demonstrated that urban link travel time prediction can be executed by this promising method.

Bayesian Training and Committees of State-Space Neural Networks for Online Travel Time Prediction

This paper presents the Bayesian evidence framework that enables a unified way of constructing and training committees of an arbitrary number of models. The main contribution the paper makes is an expansion of this framework for recurrent neural networks, which involves analytically deriving the gradient and the Hessian of the network. State-space neural networks (SSNNs), a special type of recurrent neural networks, are compared with feed-forward neural networks (FFNNs), and the effect of the Bayesian framework on both types is investigated using data from a densely used freeway in the Netherlands. From a cross-validation procedure, it can be concluded that, for a short time horizon, both Bayesian training and recurrency do not lead to improvements, but that, for a longer horizon, both techniques are beneficial. It is shown that the use of a committee leads to improved performance; furthermore, the correlation of the evidence factor, which follows from Bayesian model-fitting, and the generalization performance is compared against the training error and the generalization performance. It is found that the evidence has lower correlation, which is an indication that (a) the data set may be too small, (b) bias exists, (c) the mapping between the input and output data is difficult, and (d) the approximation of the evidence is imperfect. Future research will need to resolve these issues. However, the Bayesian framework will already be beneficial to more complex problems and lead to estimations of error bars on the predictions, which may be useful for many applications.This paper presents the Bayesian evidence framework that enables a unified way of constructing and training committees of an arbitrary number of models. The main contribution the paper makes is an expansion of this framework for recurrent neural networks, which involves analytically deriving the gradient and the Hessian of the network. State-space neural networks (SSNNs), a special type of recurrent neural networks, are compared with feed-forward neural networks (FFNNs), and the effect of the Bayesian framework on both types is investigated using data from a densely used freeway in the Netherlands. From a cross-validation procedure, it can be concluded that, for a short time horizon, both Bayesian training and recurrency do not lead to improvements, but that, for a longer horizon, both techniques are beneficial. It is shown that the use of a committee leads to improved performance; furthermore, the correlation of the evidence factor, which follows from Bayesian model-fitting, and the generalization performance is compared against the training error and the generalization performance. It is found that the evidence has lower correlation, which is an indication that (a) the data set may be too small, (b) bias exists, (c) the mapping between the input and output data is difficult, and (d) the approximation of the evidence is imperfect. Future research will need to resolve these issues. However, the Bayesian framework will already be beneficial to more complex problems and lead to estimations of error bars on the predictions, which may be useful for many applications.

Speed and acceleration distributions at a traffic signal analyzed from microscopic real and simulated data

Modeling realistic driving behavior at signalized intersections is crucial for many applications, for instance to determine the traffic signal performance, to assess the effect of different control strategies, or to estimate traffic emissions. In these applications, often microscopic models are used to simulate the trajectory of each vehicle. Despite the possibility to model vehicles with great detail and at fractions of a second, speed, acceleration and deceleration characteristics are determined by parameters that are rarely calibrated using real data, and default parameters are often chosen. This is because collecting real vehicle trajectories near traffic signals is a challenging task. This paper presents a method to collect such dataset using image processing techniques. This methodology allows one to obtain vehicle trajectories near a signal control, and to measure individual vehicles speeds and accelerations at a microscopic level. We focus on the analysis the empirical distributions of speeds and accelerations observed with this unique dataset near and up to a few meters upstream of the stop-sign. We compared these distributions with the results of repeated simulations of two microscopic software programs, using default parameters. Some inconsistencies were found with this comparison, which suggests that the two analyzed microscopic simulation programs run with default parameters do not provide realistic results for this type of road sections.