Discrete-Time Stabilization of Nash Equilibrium for Mixed Traffic Routing

This paper analyzes the routing Nash equilibrium on a discrete-time traffic network consisting of a mix of regular/human-driven vehicles (RVs) and connected- autonomous vehicles (CAVs). We analyze the network in the context of a population game, where each population corresponds to a distinct origin-destination (OD) pair and vehicle type. We propose a novel evolutionary dynamic model governed by the Impartial Pairwise Comparison protocol, where our model satisfies a discrete-time notion of δ-dissipativity and preserves state feasibility for any time-step. Drivers are assumed to adjust their strategies according to a static payoff mechanism, taken as the negative of the path travel time. We leverage these properties to derive sufficient conditions for stability of both homogeneous traffic and mixed traffic with uniform CAV headway. We then study a more realistic payoff model in which the CAV headway depends on the type of vehicle being followed. For this case, we propose a routing algorithm for the CAV payoff developed using feedback about the system and derive sufficient conditions under which a globally stabilizing controller exists. Furthermore, we formulate the control design as an optimization problem to improve the system convergence rate, and we support our findings with numerical simulations.