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

Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control

We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data-driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic

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

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

A heuristic explicit model predictive control framework for Eco-trajectory planning: Theoretical analysis and case study

The trajectory planning problem (TPP) has become increasingly crucial in the research of next-generation transportation systems, but it presents challenges due to the non-linearity of its constraints. One specific case within TPP, namely the Eco-trajectory Planning Problem (EPP), poses even greater computational difficulties due to its nonlinear, high-order, and non-convex objective function. This paper proposes a heuristic explicit predictive model control (heMPC) framework to address the eco-trajectory planning problem in scenarios without lane-changing behavior. The heMPC framework consists of an offline module and an online module. In the offline module, we build an optimal eco-trajectory batch by optimizing a series of simplified EPPs considering different system initial states and terminal states, which is equivalent to the lookup table in the general eMPC framework. The core idea of the offline module is to finish all potential optimization and computing in advance to avoid any form of online optimization in the online module. In the online module, we provide static and dynamic trajectory planning algorithms. Both algorithms greatly improve the computational efficiency of planning and only suffer from a limited extent of optimality losses through a batch-based selection process because any optimization and calculation are pre-computed in the offline module. The latter algorithm is also able to face possible emergencies and prediction errors. Both theoretical analysis and numerical are shown and discussed to test the computational quality and efficiency of the heMPC framework under a mixed-traffic flow environment that incorporates human-driving vehicles (HDV) and connected and automated vehicles (CAV) with different market penetration rates (MPR)