Level-Change Stackelberg Games Model for the Combined Traffic Assignment–Signal Control Equilibrium on Networks

Combined traffic assignment–signal control equilibrium is usually integrated into a non-cooperative games model between the network authority and road users. Unlike a pure Wardropian equilibrium, in reality there may be both competition and cooperation between authority and users. Authority has always been regarded as the upper level in classical bi-level formulations, but this placement may increase the difficulty of obtaining a global optimal solution between authority and users. This paper proposes a level-change Stackelberg (LC Stackelberg) model that embraces both authority–user and user–authority formulations. The model is calibrated by a model predictive control (MPC) controller. A route-choice probability model is used to estimate flow burden on two parallel routes. Meanwhile, the difference of route-choice probability between the two parallel paths is regarded as the level-change threshold. A generalized autoregressive conditional heteroscedasticity (GJR-GARCH) model is used as a triggering function in the MPC controller to fulfill the level-change procedure. A modified wavelet neural network algorithm is used to seek the global optimal solution. Cournot, Stackelberg, and Monopoly, combined with a fixed-time control policy based on the Webster method, were chosen as benchmarks in a numerical example to test model validity. The results show that the LC Stackelberg model obtains the minimum total travel time compared with other models. Furthermore, the level-change between authority and users could also decrease route choice probability on one specific path, indicating the model’s potential application in urban networks.

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