A Link-based Mixed Integer LP Approach for Adaptive Traffic Signal Control

This paper is concerned with adaptive signal control problems on a road network, using a link-based kinematic wave model (Han et al., 2012). Such a model employs the Lighthill-Whitham-Richards model with a triangular fundamental diagram. A variational type argument (Lax, 1957; Newell, 1993) is applied so that the system dynamics can be determined without knowledge of the traffic state in the interior of each link. A Riemann problem for the signalized junction is explicitly solved; and an optimization problem is formulated in continuous-time with the aid of binary variables. A time-discretization turns the optimization problem into a mixed integer linear program (MILP). Unlike the cell-based approaches (Daganzo, 1995; Lin and Wang, 2004; Lo, 1999b), the proposed framework does not require modeling or computation within a link, thus reducing the number of (binary) variables and computational effort. The proposed model is free of vehicle-holding problems, and captures important features of signalized networks such as physical queue, spill back, vehicle turning, time-varying flow patterns and dynamic signal timing plans. The MILP can be efficiently solved with standard optimization software.Comment: 15 pages, 7 figures, current version is accepted for presentation at the 92nd Annual Meeting of Transportation Research Boar

On the continuum approximation of the on-and-off signal control on dynamic traffic networks

In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the on-and-off nature of signal operation. While accurate, the use of binary variables can cause problems when studying large networks with many intersections. Instead, the signal control can be approximated through a continuum approach where the on-and-off control variable is replaced by a continuous priority parameter. Advantages of such approximation include elimination of the need for binary variables, lower time resolution requirements, and more flexibility and robustness in a decision environment. It also resolves the issue of discontinuous travel time functions arising from the context of dynamic traffic assignment. Despite these advantages in application, it is not clear from a theoretical point of view how accurate is such continuum approach; i.e., to what extent is this a valid approximation for the on-and-off case. The goal of this paper is to answer these basic research questions and provide further guidance for the application of such continuum signal model. In particular, by employing the Lighthill-Whitham-Richards model (Lighthill and Whitham, 1955; Richards, 1956) on a traffic network, we investigate the convergence of the on-and-off signal model to the continuum model in regimes of diminishing signal cycles. We also provide numerical analyses on the continuum approximation error when the signal cycles are not infinitesimal. As we explain, such convergence results and error estimates depend on the type of fundamental diagram assumed and whether or not vehicle spillback occurs to the signalized intersection in question. Finally, a traffic signal optimization problem is presented and solved which illustrates the unique advantages of applying the continuum signal model instead of the on-and-off model

Network flow solution method for optimal evacuation traffic routing and signal control with nonuniform threat

An efficient two-stage network flow approach is proposed for the determination of optimal scenarios for integrated traffic routing and signal timing in the evacuation of real-sized urban networks with several threat zones, where the threat levels may be nonuniform across zones. The objective is to minimize total exposure to the threat (severity multiplied by duration) for all evacuees during the evacuation. In the problem formulation, traffic flow dynamics are based on the well-known point queue model in a time-expanded network representation. The proposed solution approach is adapted from a general relaxation-based decomposition method in a network flow formulation. The decomposition method is developed on the basis of insights into the optimal flow of traffic at intersections in the solution of the evacuation routing problem. As for efficiency, the computation time associated with the decomposition method for solving the integrated optimal routing and signal control problem is equivalent to the time required for solving the same optimal routing problem (without optimizing the intersection control plan) because the computation time required for determining the optimal signal control is negligible. The proposed solution method proves to be optimal. The method is implemented and applied to a real-sized evacuation scenario in the transportation network of Tucson, Arizona. The method is stress-tested with some inflated demand scenarios, and computation aspects are reported

Real-Time Dynamic Traffic Control Based on Traffic-State Estimation

The accurate depiction of the existing traffic state on a road network is essential in reducing congestion and delays at signalized intersections. The existing literature in the optimization of signal timings either utilizes prediction of traffic state from traffic flow models or limited real-time measurements available from sensors. Prediction of traffic state based on historic data cannot represent the dynamics of change in traffic demand or network capacity. Similarly, data obtained from limited point sensors in a network provides estimates which contain errors. A reliable estimate of existing traffic state is, therefore, necessary to obtain signal timings which are based on the existing condition of traffic on the network. This research proposes a framework which utilizes estimates of traffic flows and travel times based on real-time estimated traffic state for obtaining optimal signal timings. The prediction of traffic state from the Cell Transmission Model (CTM) and measurements from traffic sensors are combined in the recursive algorithm of Extended Kalman Filter (EKF) to obtain a reliable estimate of existing traffic state. The estimate of traffic state obtained from the CTM-EKF model is utilized in the optimization of signal timings using Genetic Algorithm (GA) in the proposed CTM-EKF-GA framework. The proposed framework is applied to a synthetic signalized intersection and the results are compared with a model-based optimal solution and simulated reality. The optimal delay estimated by CTM-EKF-GA framework is only 0.6% higher than the perfect solution, whereas the delay estimated by CTM-GA model is 12.9% higher than the perfect solution

CoSIGN: A parallel algorithm for coordinated traffic signal control

Abstract — The problem of finding optimal coordinated signal timing plans for a large number of traffic signals is a challenging problem because of the exponential growth in the number of joint timing plans that need to be explored as the network size grows. In this paper, we employ the game-theoretic paradigm of fictitious play to iteratively search for a coordinated signal timing plan that improves a system-wide performance criterion for a traffic network. The algorithm is robustly scalable to realistic-size networks modelled with high fidelity simulations. We report results of a case study for the the city of Troy, Michigan, where there are 75 signalized intersections. Under normal traffic conditions, savings in average travel time of more than 20 percent are experienced against a static timing plan, and even against an aggressively tuned automatic signal re-timing algorithm, savings of more than 10 percent are achieved. The efficiency of the algorithm stems from its parallel nature. With a thousand parallel CPUs available, our algorithm finds the plan above in under 10 minutes, while a version of a hill-climbing algorithm makes virtually no progress in the same amount of wall-clock computational time. Index Terms — Coordinated traffic signal control, optimization, area traffic control I

Integrated Special Event Traffic Management Strategies in Urban Transportation Network

How to effectively optimize and control spreading traffic in urban network during the special event has emerged as one of the critical issues faced by many transportation professionals in the past several decades due to the surging demand and the often limited network capacity. The contribution of this dissertation is to develop a set of integrated mathematical programming models for unconventional traffic management of special events in urban transportation network. Traffic management strategies such as lane reorganization and reversal, turning restriction, lane-based signal timing, ramp closure, and uninterrupted flow intersection will be coordinated and concurrently optimized for best overall system performance. Considering the complexity of the proposed formulations and the concerns of computing efficiency, this study has also developed efficient solution heuristics that can yield sufficiently reliable solutions for real-world application. Case studies and extensive numerical analyses results validate the effectiveness and applicability of the proposed models

Surrogate model for real time signal control: theories and applications

Traffic signal controls play a vital role in urban road traffic networks. Compared with fixed-time signal control, which is solely based on historical data, real time signal control is flexible and responsive to varying traffic conditions, and hence promises better performance and robustness in managing traffic congestion. Real time signal control can be divided into model-based and model-free approaches. The former requires a traffic model (analytical or simulation-based) in the generation, optimisation and evaluation of signal control plans, which means that its efficacy in real-world deployment depends on the validity and accuracy of the underlying traffic model. Model-free real time signal control, on the other hand, is constructed based on expert experience and empirical observations. Most of the existing model-free real time signal controls, however, focus on learning-based and rule-based approaches, and either lack interpretability or are non-optimised. This thesis proposes a surrogate-based real time signal control and optimisation framework, that can determine signal decisions in a centralised manner without the use of any traffic model. Surrogate models offer analytical and efficient approximations of complex models or black-box processes by fitting their input-output structures with appropriate mathematical tools. Current research on surrogate-based optimisation is limited to strategic and off-line optimisation, which only approximates the relationship between decisions and outputs under highly specific conditions based on certain traffic simulation models and is still to be attempted for real time optimisation. This thesis proposes a framework for surrogate-based real time signal control, by constructing a response surface that encompasses, (1) traffic states, (2) control parameters, and (3) network performance indicators at the same time. A series of comprehensive evaluations are conducted to assess the effectiveness, robustness and computational efficiency of the surrogate-based real time signal control. In the numerical test, the Kriging model is selected to approximate the traffic dynamics of the test network. The results show that this Kriging-based real time signal control can increase the total throughput by 5.3% and reduce the average delay by 8.1% compared with the fixed-time baseline signal plan. In addition, the optimisation time can be reduced by more than 99% if the simulation model is replaced by a Kriging model. The proposed signal controller is further investigated via multi-scenario analyses involving different levels of information availability, network saturation and traffic uncertainty, which shows the robustness and reliability of the controller. Moreover, the influence of the baseline signal on the Kriging-based signal control can be eliminated by a series of off-line updates. By virtue of the model-free nature and the adaptive learning capability of the surrogate model, the Kriging-based real time signal control can adapt to systematic network changes (such as seasonal variations in traffic demand). The adaptive Kriging-based real time signal control can update the response surface according to the feedback from the actual traffic environment. The test results show that the adaptive Kriging-based real time signal control maintains the signal control performance better in response to systematic network changes than either fixed-time signal control or non-adaptive Kriging-based signal control.Open Acces