An enhanced SPSA algorithm for the calibration of Dynamic Traffic Assignment models

Simultaneous perturbation stochastic approximation (SPSA) is an efficient and well established optimization method that approximates gradients from successive objective function evaluations. It is especially attractive for high-dimensional problems and has been successfully applied to the calibration of Dynamic Traffic Assignment (DTA) models. This paper presents an enhanced SPSA algorithm, called Weighted SPSA (W-SPSA), which incorporates the information of spatial and temporal correlation in a traffic network to limit the impact of noise and improve convergence and robustness. W-SPSA appears to outperform the original SPSA algorithm by reducing the noise generated by uncorrelated measurements in the gradient approximation, especially for DTA models of sparsely correlated large-scale networks and a large number of time intervals. Comparisons between SPSA and W-SPSA have been performed through rigorous synthetic tests and the application of W-SPSA for the calibration of real world DTA networks is demonstrated with a case study of the entire expressway network in Singapore.     

Calibration of traffic flow models using a memetic algorithm

A Memetic Algorithm (MA) for the calibration of microscopic traffic flow simulation models is proposed in this study. The proposed MA includes a combination of genetic and simulated annealing algorithms. The genetic algorithm performs the exploration of the search space and identifies a zone where a possible global solution could be located. After this zone has been found, the simulated annealing algorithm refines the search and locates an optimal set of parameters within that zone. The design and implementation of this methodology seeks to enable the generalized calibration of microscopic traffic flow models. Two different Corridor Simulation (CORSIM) vehicular traffic systems were calibrated for this study. All parameters after the calibration were within reasonable boundaries. The calibration methodology was developed independently of the characteristics of the traffic flow models. Hence, it is easily used for the calibration of any other model. The proposed methodology has the capability to calibrate all model parameters, considering multiple performance measures and time periods simultaneously. A comparison between the proposed MA and the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was provided; results were similar between the two. However, the effort required to fine-tune the MA was considerably smaller when compared to the SPSA. The running time of the MA-based calibration was larger when it was compared to the SPSA running time. The MA still required some knowledge of the model in order to set adequate optimization parameters. The perturbation of the parameters during the mutation process must have been large enough to create a measurable change in the objective function, but not too large to avoid noisy measurements.     

W-SPSA in practice: Approximation of weight matrices and calibration of traffic simulation models

The development and calibration of complex traffic models demands parsimonious techniques, because such models often involve hundreds of thousands of unknown parameters. The Weighted Simultaneous Perturbation Stochastic Approximation (W-SPSA) algorithm has been proven more efficient than its predecessor SPSA (Spall, 1998), particularly in situations where the correlation structure of the variables is not homogeneous. This is crucial in traffic simulation models where effectively some variables (e.g. readings from certain sensors) are strongly correlated, both in time and space, with some other variables (e.g. certain OD flows). In situations with reasonably sized traffic networks, the difference is relevant considering computational constraints. However, W-SPSA relies on determining a proper weight matrix (W) that represents those correlations, and such a process has been so far an open problem, and only heuristic approaches to obtain it have been considered.This paper presents W-SPSA in a formally comprehensive way, where effectively SPSA becomes an instance of W-SPSA, and explores alternative approaches for determining the matrix W. We demonstrate that, relying on a few simplifications that marginally affect the final solution, we can obtain W matrices that considerably outperform SPSA. We analyse the performance of our proposed algorithm in two applications in motorway networks in Singapore and Portugal, using a dynamic traffic assignment model and a microscopic traffic simulator, respectively.     

A network wide simulation strategy of alternative fuel vehicles

This paper presents an integrated simulator “CUIntegration” to evaluate routing strategies based on energy and/or traffic measures of effectiveness for any Alternative Fuel Vehicles (AFVs). The CUIntegration can integrate vehicle models of conventional vehicles as well as AFVs developed with MATLAB-Simulink, and a roadway network model developed with traffic microscopic simulation software VISSIM. The architecture of this simulator is discussed in this paper along with a case study in which the simulator was utilized for evaluating a routing strategy for Plug-in Hybrid Electric Vehicles (PHEVs) and Electric Vehicles (EVs). The authors developed a route optimization algorithm to guide an AFV based on that AFV driver’s choice, which included; finding a route with minimum (1) travel time, (2) energy consumption or (3) a combination of both. The Application Programming Interface (API) was developed using Visual Basic to simulate the vehicle models/algorithms developed in MATLAB and direct vehicles in a roadway network model developed in VISSIM accordingly. The case study included a section of Interstate 83 in Baltimore, Maryland, which was modeled, calibrated and validated. The authors considered a worst-case scenario with an incident on the main route blocking all lanes for 30 min. The PHEVs and EVs were represented by integrating the MATLAB-Simulink vehicle models with the traffic simulator. The CUIntegration successfully combined vehicle models with a roadway traffic network model to support a routing strategy for PHEVs and EVs. Simulation experiments with CUIntegration revealed that routing of PHEVs resulted in cost savings of about 29% when optimized for the energy consumption, and for the same optimization objective, routing of EVs resulted in about 64% savings.     

Highway voting system: Embracing a possible paradigm shift in traffic data acquisition

The integration of internet and mobile phones has opened the door to a new wave of utilizing private vehicles as probes not only for performance evaluation but for traffic control as well, gradually replacing the role of traffic surveillance systems as the dominant source of traffic data. To prepare for such a paradigm shift, one needs to overcome some key institutional barriers, in particular, the privacy issue. A Highway Voting System (HVS) is proposed to address this issue in which drivers provide link- and/or path-based vehicle data to the traffic management system in the form of “votes” in order to receive favorable service from traffic control. The proposed HVS offers a platform that links data from individual vehicles directly with traffic control. In the system, traffic control responds to voting vehicles in a way similar to the current system responding to prioritized vehicles and providing the requested services accordingly. We show in the paper that the proposed “voting” system can effectively resolve the privacy issue which often hampers traffic engineers from getting detailed data from drivers. Strategies to entice drivers into “voting” so as to increase the market penetration level under all traffic conditions are discussed. Though the focus of the paper is on addressing the institutional issues associated with data acquisition from individual vehicles, other research topics associated with the proposed system are identified. Two examples are given to demonstrate the impact of the proposed system on algorithm development and traffic control.     

c-SPSA: Cluster-wise simultaneous perturbation stochastic approximation algorithm and its application to dynamic origin–destination matrix estimation

The simultaneous perturbation stochastic approximation (SPSA) algorithm has been used in the literature for the solution of the dynamic origin–destination (OD) estimation problem. Its main advantage is that it allows quite general formulations of the problem that can include a wide range of sensor measurements. While SPSA is relatively simple to implement, its performance depends on a set of parameters that need to be properly determined. As a result, especially in cases where the gradient of the objective function changes quickly, SPSA may not be as stable and even diverge. A modification of the SPSA algorithm, referred to as c-SPSA, is proposed which applies the simultaneous perturbation approximation of the gradient within a small number of carefully constructed “homogeneous” clusters one at a time, as opposed to all elements at once. The paper establishes the theoretical properties of the new algorithm with an upper bound for the bias of the gradient estimate and shows that it is lower than the corresponding SPSA bias. It also proposes a systematic approach, based on the k-means algorithm, to identify appropriate clusters. The performance of c-SPSA, with alternative implementation strategies, is evaluated in the context of estimating OD flows in an actual urban network. The results demonstrate the efficiency of the proposed c-SPSA algorithm in finding better OD estimates and achieve faster convergence and more robust performance compared to SPSA with fewer overall number of function evaluations.     

A verification approach for knowledge-based systems

Knowledge-based systems (KBS) represent a novel computer-based approach for dealing with practical traffic engineering problems. As traffic engineers adapt and apply KBS technological tenets, there is a need to reflect on exactly how development efforts should proceed and, particularly, on how a KBS should be verified as “correct.” Such experience is likely to accrue from hindsight; what went right—or wrong—during an actual KBS project. Unfortunately, hindsight does not provide direct experience with the application of a specific development paradigm. In this paper, we detail our experiences in applying a specific verification framework (based on traditional software engineering tenets) during a traffic engineering KBS development effort. Our experiences with this paradigm provide useful insights to other researchers involved in traffic engineering KBS development projects.     

Optimality versus run time for isolated signalized intersections

Simulation-based optimization of traffic signal timing has become pervasive and popular, in the field of traffic engineering. When the underlying simulation model is well-trusted and/or well-calibrated, it is only natural that typical engineers would want their signal timing optimized using the judgment of that same model. As such, it becomes important that the heuristic search methods typically used by these optimizations are capable of locating global optimum solutions, for a wide range of signal systems. However off-line and real-time solutions alike offer just a subset of the available search methods. The result is that many optimizations are likely converging prematurely on mediocre solutions. In response, this paper compares several search methods from the literature, in terms of both optimality (i.e., solution quality) and computer run times. Simulated annealing and genetic algorithm methods were equally effective in achieving near-global optimum solutions. Two selection methods (roulette wheel and tournament), commonly used within genetic algorithms, exhibited similar effectiveness. Tabu searching did not provide significant benefits. Trajectories of optimality versus run time (OVERT) were similar for each method, except some methods aborted early along the same trajectory. Hill-climbing searches always aborted early, even with a large number of step-sizes. Other methods only aborted early when applied with ineffective parameter settings (e.g. mutation rate, annealing schedule). These findings imply (1) today’s products encourage a sub-optimal “one size fits all” approach, (2) heuristic search methods and parameters should be carefully selected based on the system being optimized, (3) weaker searches abort early along the OVERT curve, and (4) improper choice of methods and/or parameters can reduce optimization benefits by 22–33%.     

Real-time network-wide traffic signal optimization considering long-term green ratios based on expected route flows

We propose a novel real-time network-wide traffic signal control scheme which is (1) applicable under modern data technologies, (2) flexible in response to variations of traffic flows due to its non-cyclic feature, (3) operable on a network-wide and real-time basis, and (4) capable of considering expected route flows in the form of long-term green time ratios for intersection movement. The proposed system has a two-level hierarchical architecture: (1) strategy level and (2) control level. Considering the optimal states for a long-term period found in the strategy level, the optimal signal timings for a short-term period are calculated in the control level which consists of two steps: (1) queue weight update and (2) signal optimization. Based on the ratio of the cumulative green time to the desired green time is the first step to update the queue weights, which are then used in the optimization to find signal timings for minimum total delay. A parametric queue weight function is developed, discussed and evaluated. Two numerical experiments were given. The first demonstrated that the proposed system performs effectively, and the second shows its capability in a real-world network.     

Trajectory data reconstruction and simulation-based validation against macroscopic traffic patterns

This paper shows that the behavior of driver models, either individually or entangled in stochastic traffic simulation, is affected by the accuracy of empirical vehicle trajectories. To this aim, a “traffic-informed” methodology is proposed to restore physical and platoon integrity of trajectories in a finite time–space domain, and it is applied to one NGSIM I80 dataset. However, as the actual trajectories are unknown, it is not possible to verify directly whether the reconstructed trajectories are really “nearer” to the actual unknowns than the original measurements. Therefore, a simulation-based validation framework is proposed, that is also able to verify indirectly the efficacy of the reconstruction methodology. The framework exploits the main feature of NGSIM-like data that is the concurrent view of individual driving behaviors and emerging macroscopic traffic patterns. It allows showing that, at the scale of individual models, the accuracy of trajectories affects the distribution and the correlation structure of lane-changing model parameters (i.e. drivers heterogeneity), while it has very little impact on car-following calibration. At the scale of traffic simulation, when models interact in trace-driven simulation of the I80 scenario (multi-lane heterogeneous traffic), their ability to reproduce the observed macroscopic congested patterns is sensibly higher when model parameters from reconstructed trajectories are applied. These results are mainly due to lane changing, and are also the sought indirect validation of the proposed data reconstruction methodology.     

Automatic calibration of fundamental diagram for first‐order macroscopic freeway traffic models

Despite its importance in macroscopic traffic flow modeling, comprehensive method for the calibration of fundamental diagram is very limited. Conventional empirical methods adopt a steady state analysis of the aggregate traffic data collected from measurement devices installed on a particular site without considering the traffic dynamics, which renders the simulation may not be adaptive to the variability of data. Nonetheless, determining the fundamental diagram for each detection site is often infeasible. To remedy these, this study presents an automatic calibration method to estimate the parameters of a fundamental diagram through a dynamic approach. Simulated flow from the cell transmission model is compared against the measured flow wherein an optimization merit is conducted to minimize the discrepancy between model‐generated data and real data. The empirical results prove that the proposed automatic calibration algorithm can significantly improve the accuracy of traffic state estimation by adapting to the variability of traffic data when compared with several existing methods under both recurrent and abnormal traffic conditions. Results also highlight the robustness of the proposed algorithm. The automatic calibration algorithm provides a powerful tool for model calibration when freeways are equipped with sparse detectors, new traffic surveillance systems lack of comprehensive traffic data, or the case that lots of detectors lose their effectiveness for aging systems. Furthermore, the proposed method is useful for off‐line model calibration under abnormal traffic conditions, for example, incident scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

An integrated traffic-driving simulation framework: Design,implementation, and validation

This paper first describes the process of integrating two distinct transportation simulation platforms, Traffic Simulation models and Driving Simulators, so as to broaden the range of applications for which either type of simulator is applicable. To integrate the two distinct simulation platforms, several technical challenges needed to be overcome including reconciling differences in update frequency, coordinate systems, and the fidelity levels of the vehicle dynamics models and graphical rendering requirements of the two simulators. Following the successful integration, the integrated simulator was validated by having several human subjects drive a 2.5 mile long segment of a signalized arterial in both the virtual environment of the integrated simulator, and in the real-world during the evening “rush hour”. Several aspects of driving behavior were then compared between the human subjects’ driving in the “virtual” and the real world. The comparisons revealed generally similar behavior, in terms of average corridor-level travel time, deceleration/acceleration patterns, lane-changing behavior, as well as energy consumption and emissions production. The paper concludes by suggesting possible extensions of the developed prototype which the researchers are currently pursuing, including integration with a computer networking simulator, to facilitate Connected Vehicle (CV) and Vehicle Ad-hoc Network (VANET) related studies, and a multiple participant component that allows several human drivers to interact simultaneously within the integrated simulator.     

Surveying commuter behavior: Designing motorist information systems

A “Motorist Information Survey” was conducted by University of Washington investigators as part of a project sponsored by the Washington State Department of Transportation (WSDOT) and the Federal Highway Administration under the State's Freeway Arterial Management Effort (FAME). This survey, with responses on 62 variables from 3, 893 Seattle commuters, gathered information about motorist behavior and decision processes, particularly as they relate to the design and delivery of motorist information. Results showed that motorists have greater flexibility as to the ime they leave work than the time they leave home, experience some stress during their commute, and most value saving commute time. Motorists are more likely to change their routes from work than from home, to divert to known routes sooner than to unknown routes, and to be influenced by traffic information, congestion, and time of day. Motorists prefer to receive traffic information before entering the freeway as traffic information has the greatest influence on route choice and departure time and all motorists rely most on commercial radio for receipt of traffic information and find it most useful. A majority of motorists want to see highway advisory radio developed first, followed by a phone hot-line, and a dedicated cable TV station.     

A study of the influence of severe environmental conditions on common traffic congestion features

On the basis of real traffic and environmental data measured on German freeways, we studied common features of traffic congestion under the influence of severe weather conditions. We have found that traffic features [J] and [S] defining traffic phases “wide moving jam” (J) and “synchronized flow” (S) in Kerner's three‐phase theory are indeed common spatiotemporal traffic features. The quantitative parameters for both traffic phases [S] and [J] were investigated in a comparison of “ideal” weather conditions (good visibility and no precipitation) and severe weather situations (icy road, wind, precipitation, etc.). We showed spatiotemporal congested patterns in several space–time diagrams based on the Automatic Tracking of Moving Jams/Forecasting of Traffic Objects (ASDA/FOTO) model reconstruction for roadside detectors. A statistical study of traffic phase [J] parameters was presented, showing the average values and standard deviation of the quantities. Similarities and differences were analyzed, and some consequences for vehicular applications were discussed to cope with severe weather conditions. Copyright © 2013 John Wiley & Sons, Ltd.     

A mixed Bayesian network for two-dimensional decision modeling of departure time and mode choice

The modeling of travel decision making has been a popular topic in transportation planning. Previous studies focused on random-utility discrete choice models and machine learning methods. This paper proposes a new modeling approach that utilizes a mixed Bayesian network (BN) for travel decision inference. The authors use a predetermined BN structure and calculate priori and posterior probability distributions of the decision alternatives based on the observed explanatory variables. As a “utility-free” decision inference method, the BN model releases the linear structure in the utility function but assumes the traffic level of service variables follow multivariate Gaussian distribution conditional on the choice variable. A real-world case study is conducted by using the regional travel survey data for a two-dimensional decision modeling of both departure time choice and travel mode choice. The results indicate that a two-dimensional mixed BN provides better accuracy than decision tree models and nested logit models. In addition, one can derive continuous elasticity with respect to each continuous explanatory variable for sensitivity analysis. This new approach addresses a research gap in probabilistic travel decision making modeling as well as two-dimensional travel decision modeling.     

Validation of traffic flow models with respect to the spatiotemporal evolution of congested traffic patterns

We propose a quantitative approach for calibrating and validating key features of traffic instabilities based on speed time series obtained from aggregated data of a series of neighboring stationary detectors. The approach can be used to validate models that are calibrated by other criteria with respect to their collective dynamics. We apply the proposed criteria to historic traffic databases of several freeways in Germany containing about 400 occurrences of congestions thereby providing a reference for model calibration and quality assessment with respect to the spatiotemporal dynamics. First tests with microscopic and macroscopic models indicate that the criteria are both robust and discriminative, i.e., clearly distinguishes between models of higher and lower predictive power.     

Development of a differential route share model for railroad freight traffic

This paper summarizes work undertaken towards development and calibration of a model to predict the distribution of rail freight traffic among competing routes. The model is designed for use in analyzing the traffic effects of changes in the level-of-service on selected rail lines. The model predicts route shares based on the overall network configuration of each railroad participating in a given market. The model selects feasible routes, discards those routes which appear to be too circuitous or costly, and then assigns traffic to the remaining routes in accordance with several network characteristics. It is designed to be sensitive to level-of-service changes, and to simulate the response of shippers and railroads to a competitive environment. A multiple route-finding algorithm was used to find possible routes based on the number of railroads operating at the originating and terminating end of a market. Multiple routes were determined and matched with observed traffic flows from the ICC One-Percent Waybill Sample. Physical network characteristics for each route, including distance, junction frequency, and “impedance,” were calculated from the network model and were correlated with the traffic share observed on each route in the market. A two-stage model was developed to find feasible routes from the set of possible routes and to allocate traffic to feasible routes based on levels-of-service. The model was calibrated on 9,793 routes from 1,199 markets with twenty or more carloads from the 1977 One-Percent Carload Waybill Sample. Model calibration supported the hypothesis that network route characteristics did indeed influence shipper choice of route, and that a normative model could be used to assess relative attractiveness of routes under various railroad corporate ownership restructuring scenarios.     

Calibration of nonlinear car-following laws for traffic oscillation prediction

Frequency-domain analysis has been successfully used to (i) predict the amplification of traffic oscillations along a platoon of vehicles with nonlinear car-following laws and (ii) measure traffic oscillation properties (e.g., periodicity, magnitude) from field data. This paper proposes a new method to calibrate nonlinear car-following laws based on real-world vehicle trajectories, such that oscillation prediction (based on the calibrated car-following laws) and measurement from the same data can be compared and validated. This calibration method, for the first time, takes into account not only the driver’s car-following behavior but also the vehicle trajectory’s time-domain (e.g., location, speed) and frequency-domain properties (e.g., peak oscillation amplitude). We use Newell’s car-following model (1961) as an example and calibrate its parameters based on a penalty-based maximum likelihood estimation procedure. A series of experiments using Next Generation Simulation (NGSIM) data are conducted to illustrate the applicability and performance of the proposed approach. Results show that the calibrated car-following models are able to simultaneously reproduce observed driver behavior, time-domain trajectories, and oscillation propagation along the platoon with reasonable accuracy.     

Analysis of yellow-light running at signalized intersections using high-resolution traffic data

Many accidents occurring at signalized intersections are closely related to drivers’ decisions of running through intersections during yellow light, i.e., yellow-light running (YLR). Therefore it is important to understand the relationships between YLR and the factors which contribute to drivers’ decision of YLR. This requires collecting a large amount of YLR cases. However, existing data collection method, which mainly relies on video cameras, has difficulties to collect a large amount of YLR data. In this research, we propose a method to study drivers’ YLR behaviors using high-resolution event-based data from signal control systems. We used 8 months’ high-resolution data collected by two stop-bar detectors at a signalized intersection located in Minnesota and identified over 30,000 YLR cases. To identify the possible reasons for drivers’ decision of YLR, this research further categorized the YLR cases into four types: “in should-go zone”, “in should-stop zone”, “in dilemma zone”, and “in optional zone” according to the driver’s location when signal turns to yellow. Statistical analysis indicates that the mean values of approaching speed and acceleration rate are significantly different for different types of YLR. We also show that there were about 10% of YLR drivers who cannot run through intersection before traffic light turns to red. Furthermore, based on a strong correlation between hourly traffic volume and number of YLR events, this research developed a regression model that can be used to predict the number of YLR events based on hourly flow rate. This research also showed that snowing weather conditions cause more YLR events.