Efficient multiple model particle filtering for joint traffic state estimation and incident detection

This article proposes an efficient multiple model particle filter (EMMPF) to solve the problems of traffic state estimation and incident detection, which requires significantly less computation time compared to existing multiple model nonlinear filters. To incorporate the on ramps and off ramps on the highway, junction solvers for a traffic flow model with incident dynamics are developed. The effectiveness of the proposed EMMPF is assessed using a benchmark hybrid state estimation problem, and using synthetic traffic data generated by a micro-simulation software. Then, the traffic estimation framework is implemented using field data collected on Interstate 880 in California. The results show the EMMPF is capable of estimating the traffic state and detecting incidents and requires an order of magnitude less computation time compared to existing algorithms, especially when the hybrid system has a large number of rare models.     

Analytical and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model

In this article, we propose a computational method for solving the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) semi-analytically for arbitrary piecewise-constant initial and boundary conditions, and for arbitrary concave fundamental diagrams. With these assumptions, we show that the solution to the LWR PDE at any location and time can be computed exactly and semi-analytically for a very low computational cost using the cumulative number of vehicles formulation of the problem. We implement the proposed computational method on a representative traffic flow scenario to illustrate the exactness of the analytical solution. We also show that the proposed scheme can handle more complex scenarios including traffic lights or moving bottlenecks. The computational cost of the method is very favorable, and is compared with existing algorithms. A toolbox implementation available for public download is briefly described, and posted at http://traffic.berkeley.edu/project/downloads/lwrsolver.     

A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure.     

Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment

The paper proposes a first-order macroscopic stochastic dynamic traffic model, namely the stochastic cell transmission model (SCTM), to model traffic flow density on freeway segments with stochastic demand and supply. The SCTM consists of five operational modes corresponding to different congestion levels of the freeway segment. Each mode is formulated as a discrete time bilinear stochastic system. A set of probabilistic conditions is proposed to characterize the probability of occurrence of each mode. The overall effect of the five modes is estimated by the joint traffic density which is derived from the theory of finite mixture distribution. The SCTM captures not only the mean and standard deviation (SD) of density of the traffic flow, but also the propagation of SD over time and space. The SCTM is tested with a hypothetical freeway corridor simulation and an empirical study. The simulation results are compared against the means and SDs of traffic densities obtained from the Monte Carlo Simulation (MCS) of the modified cell transmission model (MCTM). An approximately two-miles freeway segment of Interstate 210 West (I-210W) in Los Ageles, Southern California, is chosen for the empirical study. Traffic data is obtained from the Performance Measurement System (PeMS). The stochastic parameters of the SCTM are calibrated against the flow-density empirical data of I-210W. Both the SCTM and the MCS of the MCTM are tested. A discussion of the computational efficiency and the accuracy issues of the two methods is provided based on the empirical results. Both the numerical simulation results and the empirical results confirm that the SCTM is capable of accurately estimating the means and SDs of the freeway densities as compared to the MCS.     

A dynamic traffic assignment model for a continuum transportation system

A predictive continuum dynamic user-optimal (PDUO-C) model is formulated in this study to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers within a region with a dense urban road network. The modeled region is arbitrary in shape with a single central business district (CBD) and travelers continuously distributed over the region. Within this region, the road network is represented as a continuum and travelers patronize a two-dimensional continuum transportation system to travel to the CBD. The PDUO-C model is solved by a promising solution algorithm that includes elements of the finite volume method (FVM), the finite element method (FEM), and the explicit total variation diminishing Runge-Kutta (TVD-RK) time-stepping method. A numerical example is given to demonstrate the utility of the proposed model and the effectiveness of the solution algorithm in solving this PDUO-C problem.     

An integrated real-time traffic signal system for transit signal priority,incident detection and congestion management

This paper presents a traffic control system that can work standalone to handle various boundary conditions of the recurrent, non-recurrent congestion, transit signal priority and downstream blockage conditions to improve the overall traffic network vehicular productivity and efficiency. The control system uses field detectors’ data to determine the boundary conditions of all incoming and exit links. The developed system is interfaced with CORSIM micro-simulation for rigorous evaluations with different types of signal phase settings. The comparative performance of this control logic is quite satisfactory for some of the most frequently used phase settings in the network with a high number of junctions under highly congested conditions.     

Using high-resolution event-based data for traffic modeling and control: An overview

Research on using high-resolution event-based data for traffic modeling and control is still at early stage. In this paper, we provide a comprehensive overview on what has been achieved and also think ahead on what can be achieved in the future. It is our opinion that using high-resolution event data, instead of conventional aggregate data, could bring significant improvements to current research and practices in traffic engineering. Event data records the times when a vehicle arrives at and departs from a vehicle detector. From that, individual vehicle’s on-detector-time and time gap between two consecutive vehicles can be derived. Such detailed information is of great importance for traffic modeling and control. As reviewed in this paper, current research has demonstrated that event data are extremely helpful in the fields of detector error diagnosis, vehicle classification, freeway travel time estimation, arterial performance measure, signal control optimization, traffic safety, traffic flow theory, and environmental studies. In addition, the cost of event data collection is low compared to other data collection techniques since event data can be directly collected from existing controller cabinet without any changes on the infrastructure, and can be continuously collected in 24/7 mode. This brings many research opportunities as suggested in the paper.     

Applications of wavelet transform for analysis of freeway traffic: Bottlenecks, transient traffic, and traffic oscillations

This paper demonstrates the capabilities of wavelet transform (WT) for analyzing important features related to bottleneck activations and traffic oscillations in congested traffic in a systematic manner. In particular, the analysis of loop detector data from a freeway shows that the use of wavelet-based energy can effectively identify the location of an active bottleneck, the arrival time of the resulting queue at each upstream sensor location, and the start and end of a transition during the onset of a queue. Vehicle trajectories were also analyzed using WT and our analysis shows that the wavelet-based energies of individual vehicles can effectively detect the origins of deceleration waves and shed light on possible triggers (e.g., lane-changing). The spatiotemporal propagations of oscillations identified by tracing wavelet-based energy peaks from vehicle to vehicle enable analysis of oscillation amplitude, duration and intensity.     

Integration of signal timing estimation model and dynamic traffic assignment in feedback loops: system design and case study

This paper presents an integrated framework for effective coupling of a signal timing estimation model and dynamic traffic assignment (DTA) in feedback loops. There are many challenges in effectively integrating signal timing tools with DTA software systems, such as data availability, exchange format, and system coupling. In this research, a tight coupling between a DTA model with various queue‐based simulation models and a quick estimation method Excel‐based signal control tool is achieved and tested. The presented framework design offers an automated solution for providing realistic signal timing parameters and intersection movement capacity allocation, especially for future year scenarios. The framework was used to design an open‐source data hub for multi‐resolution modeling in analysis, modeling and simulation applications, in which a typical regional planning model can be quickly converted to microscopic traffic simulation and signal optimization models. The coupling design and feedback loops are first demonstrated on a simple network, and we examine the theoretically important questions on the number of iterations required for reaching stable solutions in feedback loops. As shown in our experiment, the current coupled application becomes stable after about 30 iterations, when the capacity and signal timing parameters can quickly converge, while DTA's route switching model predominately determines and typically requires more iterations to reach a stable condition. A real‐world work zone case study illustrates how this application can be used to assess impacts of road construction or traffic incident events that disrupt normal traffic operations and cause route switching on multiple analysis levels. Copyright © 2014 John Wiley & Sons, Ltd.     

Specification and calibration of a microscopic model for pedestrian dynamic simulation at signalized intersections: A hybrid approach

Macroscopic pedestrian models for bidirectional flow analysis encounter limitations in describing microscopic dynamics at crosswalks. Pedestrian behavior at crosswalks is typically characterized by the evasive effect with conflicting pedestrians and vehicles and the following effect with leading pedestrians. This study proposes a hybrid approach (i.e., route search and social force-based approach) for modeling of pedestrian movement at signalized crosswalks. The key influential factors, i.e., leading pedestrians, conflict with opposite pedestrians, collision avoidance with vehicles, and compromise with traffic lights, are considered. Aerial video data collected at one intersection in Beijing, China were recorded and extracted. A new calibration approach based on a genetic algorithm is proposed that enables optimization of the relative error of pedestrian trajectory in two dimensions, i.e., moving distance and angle. Model validation is conducted by comparison with the observed trajectories in five typical cases of pedestrian crossing with or without conflict between pedestrians and vehicles. The characteristics of pedestrian flow, speed, acceleration, pedestrian-vehicle conflict, and the lane formation phenomenon were compared with those from two competitive models, thus demonstrating the advantage of the proposed model.     

Variability in sound power levels: Implications for static and dynamic traffic models

Classically, one mean vehicle representative of each category is used by both static and dynamic traffic noise prediction models. The spectrum associated with this mean vehicle is determined from a linear statistical regression analysis based on measurement campaigns on a track or in situ. However, the variability of individual vehicle emissions can influence predictions and hinder comparison between static and dynamic models. In order to estimate the induced bias, statistical analysis of the distributions of sound power levels emitted by the individual passage of vehicles during 82 measurement campaigns was carried out. The results show that 92% of the residual regression distributions are Gaussian and that standard deviations can reach 3.6 dBA. The value of the proposed correction term for this case study could reach 1.4 dBA for light vehicles and 1.2 dBA for heavy vehicles. This analysis also shows that the variability in sound power levels and thus the corresponding corrections are higher at the lowest speeds that correspond to urban driving conditions.     

Mathematical characterization of spatiotemporal congested traffic patterns: mixed speed data analysis in the greater Toronto and Hamilton area,Canada

This paper formulates a comprehensive methodology for analyzing, quantifying and identifying congestion characteristics based on speed distribution. Utilizing vehicle speed data, a mathematical approach is applied, in order to characterize roadway segments, in terms of travel reliability, congestion severity and duration. We argue that the Gaussian mixture model (GMM) and its parameter combination is the appropriate tool if we are to obtain quantitative congestion measures and rank roadway performance. A significant contribution of our approach is that it is based on assumptions regarding mixed components as well as speed distribution and can be applied to large databases. We test our framework on the greater Toronto and Hamilton area in Ontario, Canada, and conclude that congestion quantification through the application of the GMM can be successfully accomplished. Results indicate that speed patterns differ significantly between counties as well as days of the week.     

Model based urban traffic control,part I: Local model and local model predictive controllers

This paper is the first in a series of reports presenting a framework for the hierarchical design of feedback controllers for traffic lights in urban networks. The goal of the research is to develop an easy to understand methodology for designing model based feedback controllers that use the current state estimate in order to select the next switching times of traffic lights. In this paper we introduce an extension of the cell transmission model that describes with sufficient accuracy the major causes of delay for urban traffic. We show that this model is computationally fast enough such that it can be used in a model predictive controller that decides for each intersection, taking into account the vehicle density as estimated along all links connected to the intersection, what switching time minimizes the local delay for all vehicles over a prediction horizon of a few minutes. The implementation of this local MPC only requires local online measurements and local model information (unlike the coordinated MPC, to be introduced in the next paper in this series, that takes into account interactions between neighbouring intersections). We study the performance of the proposed local MPC via simulation on a simple 4 by 4 Manhattan grid, comparing its delay with an efficiently tuned pretimed control for the traffic lights, and with traffic lights controlled according to the max pressure rule. These simulations show that the proposed local MPC controller achieves a significant reduction in delay for various traffic conditions.     

Time-dependent congestion pricing system for large networks: Integrating departure time choice,dynamic traffic assignment and regional travel surveys in the Greater Toronto Area

Congestion pricing is one of the widely contemplated methods to manage traffic congestion. The purpose of congestion pricing is to manage traffic demand generation and supply allocation by charging fees (i.e., tolling) for the use of certain roads in order to distribute traffic demand more evenly over time and space. This study presents a framework for large-scale variable congestion pricing policy determination and evaluation. The proposed framework integrates departure time choice and route choice models within a regional dynamic traffic assignment (DTA) simulation environment. The framework addresses the impact of tolling on: (1) road traffic congestion (supply side), and (2) travelers’ choice dimensions including departure time and route choices (demand side). The framework is applied to a simulation-based case study of tolling a major freeway in Toronto while capturing the regional effects across the Greater Toronto Area (GTA). The models are developed and calibrated using regional household travel survey data that reflect the heterogeneity of travelers’ attributes. The DTA model is calibrated using actual traffic counts from the Ontario Ministry of Transportation and the City of Toronto. The case study examined two tolling scenarios: flat and variable tolling. The results indicate that: (1) more benefits are attained from variable pricing, that mirrors temporal congestion patterns, due to departure time rescheduling as opposed to predominantly re-routing only in the case of flat tolling, (2) widespread spatial and temporal re-distributions of traffic demand are observed across the regional network in response to tolling a significant, yet relatively short, expressway serving Downtown Toronto, and (3) flat tolling causes major and counterproductive rerouting patterns during peak hours, which was observed to block access to the tolled facility itself.     

Real-time route diversion control in a model predictive control framework with multiple objectives: Traffic efficiency,emission reduction and fuel economy

In this paper, the route recommendation provided by the traffic management authority, rather than the uncontrollable bifurcation splitting rate, is directly considered as the control variable in the route guidance system; a real-time en-route diversion control strategy with multiple objectives is designed in a Model Predictive Control (MPC) framework with regard to system uncertainties and disturbances. The objectives include not only traffic efficiency, but also emission reduction and fuel economy, which respectively correspond to minimizing the total time spent (TTS), total amount of emissions and fuel consumption for all vehicles moving through a network. In the MPC framework, the routing control problem is transformed to be a constrained combinational optimization, which is solved by the parallel Tabu Search algorithm. Two representative traffic scenarios are tested, and the simulation results show: (1) The room for improvement in each objective by means of route diversion control is not consistent with each other and varies with the utilized traffic scenario. In the peak hour, the routing control can lead to significant improvements in TTS and fuel economy, while a relatively small improvement in emission reduction is achieved; in the off-peak hour, however, it is opposite, which indicates that routing is possibly dispensable from the aspect of improving traffic efficiency, but is required from the aspect of emission reduction. (2) The conflict among the multiple objectives varies with the utilized traffic scenario in route diversion control. Improving traffic efficiency often conflicts with emission reduction in both scenarios. For the objectives of traffic efficiency and fuel economy, they are not conflicting in peak hour, while in the off-peak hour, the two objectives are likely conflicting, and the improvement in one objective can lead to the degradation in the other objective. (3) Regardless of the scenarios of peak hour or off-peak hour, the proposed control strategy can result in a proper trade-off among the three chosen objectives.     

Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

In this paper we formulate the dynamic user equilibrium problem with an embedded cell transmission model on a network with a single OD pair, multiple parallel paths, multiple user classes with elastic demand. The formulation is based on ideas from complementarity theory. The travel time is estimated based on two methods which have different transportation applications: (1) maximum travel time and (2) average travel time. These travel time functions result in linear and non-linear complementarity formulations respectively. Solution existence and the properties of the formulations are rigorously analyzed. Extensive computational experiments are conducted to demonstrate the benefits of the proposed formulations on various test networks.