Dynamic Routing and Queuing for Mixed Autonomy with Traffic Responsive Intersection Signaling

The presence of autonomous vehicles requires changes in the traditional traffic models for human–driven vehicles. In this paper, we consider the scenario when autonomous vehicles and human–driven vehicles are both selfishly routing on the urban transportation networks. We propose a continuous dynamic routing model of mixed autonomy (human– driven/autonomous vehicles) under inelastic demands, which also takes into account queuing dynamics. The proposed model accounts for the ability of autonomous vehicles to maintain shorter headways than human–driven vehicles in both the routing and queuing dynamics. We first examine the resulting equilibria under a fixed-time traffic intersection signalling policy from a static perspective and then employ a traffic responsive signalling policy to stabilize the traffic flow and movement queue dynamics under feasible demands of mixed autonomy vehicles. We establish the stability of the resulting model equilibria via the use of dissipativity tools for population games. We also present a numerical example to illustrate the stability results.