A bi-level model of dynamic traffic signal control with continuum approximation. (June 2015) - Han, Ke; Sun, Yuqi; Liu, Hongcheng; Friesz, Terry L.; Yao, Tao
Highlights: A bi-level dynamic Stackelberg game approach for traffic signal control is proposed. The lower-level DUE contains a DNL procedure that employs the continuum signal model. The continuum signal model has a number of advantages over its on-and-off counterpart. DNL that incorporates continuum signal model and vehicle spillback is elaborated. Three metaheuristic methods are used to solve the problem. 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 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.