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

Abstract

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 , 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.

The Energy-Efficient Dynamic Route Planning for Electric Vehicles

“…The model can be formulated as a linear multiobjective 0-1 integer programming model. To minimize the energy consumption and actual travel time, two objective functions are shown in (18) and (19), that is, minimizing energy consumption and actual travel time. Both two objective functions have a linear form with respect to decision variables .…”

“…Aziz et al [17] presented the system optimal approach for dynamic traffic assignment with an embedded traffic flow model and the signal control optimization considering intersection delay and lost time from phase switches in the objective function. Han et al [18,19] presented a traffic signal optimization problem to illustrate the unique advantages of applying the continuum signal model instead of the on-andoff model. Feng et al [20] presented a real-time adaptive signal phase allocation algorithm using connected vehicle data to optimize the phase sequence and duration, which can minimize the total vehicle delay and the queue length.…”

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

“…In that case, a uniform random variable between 0 and 1 must be generated and then compared with the control link capacity to determine if a vehicle is allowed to leave for the next link at each time step. This issue can also be addressed with continuum signal models where there is no need to explicitly model 0–1 controls ( 48 ).…”

Capacitated transit service network design with boundedly rational agents

“…Han et al (2015a) first presented a rigorous continuity result for the path delay operator, which is the fundamental importance to the existence of DUE conditions, based on the Lighthill-Whitham-Richards (LWR) network model capable of capturing physical queues and spillback, by assuming that the network supply is bounded away from zero or is within desired boundedness. In addition, Han et al (2015b) proposed a bi-level model for traffic network signal control problems where a continuum signal model is employed to ensure the existence of DUE in the lower level problem. As a remark, the dynamic user equilibrium studied in the last two decades is usually analytically expressed of Nash-like equilibrium condition (Han et al, 2015a).…”