Modified Stackelberg Games Approach for Dynamic Signal Control and Route Choice Equilibrium on Mixed Networks

Abstract

The dynamic signal control and route choice equilibrium are usually integrated into a noncooperative game between the network authority and the road users. There are mainly two problems in most existing optimization methods. Firstly, the authority is often placed in the upper level in bi-level programming models, this pure system-optimization-oriented framework may increase the difficulty in obtaining an equilibrium flow distribution. Secondly, the rate of drivers’ compliance on the control strategy has not been fully investigated, which makes the problem intractable in real time, especially in a connected vehicle (CV) environment. This paper proposes a modified Stackelberg games model to change the format of the authority-user and user-authority dynamically. The direct communication between the authority and users is established, and the drivers’ compliance rate is applied as the level-change threshold index. Considering the difference between the drivers’ realized travel time and the predicted travel time on the variable message sign (VMS), a logit model is formed to calibrate the compliance rate in every time step. Based on a modified wavelet neural network algorithm, the model predictive control (MPC) fulfills the level-change procedure using the software Matlab 2018b. Six benchmarks are applied in a numerical example. The results show that the proposed model with the centralized framework obtains the minimum total travel cost compared with the benchmarks. Combined with the real-time mutual feedback between drivers’ response and control strategy, the level-change procedure potentially maintains the compliance rate within a certain level.