Capacity modeling and routing for traffic networks with mixed autonomy

Transportation infrastructure is entering a stage of mixed use whereby vehicles are capable of varying levels of autonomy, and investigating the potential benefits of this mixed infrastructure is a critical step to fully realizing the mobility benefits of autonomy. In this paper, we consider a mixed traffic profile where a fraction of vehicles are smart and able to form platoons, and the remaining are regular and manually driven. We develop two models for road capacity under mixed autonomy that are based on the fundamental behavior of autonomous technologies such as adaptive cruise control. Moreover, we formulate an optimal routing problem of mixed traffic for the first capacity model with two parallel roads. We first study the case that a planner aims to minimize the social cost of the system, and has control over both regular and smart traffic flows. We prove that this optimization problem is convex for the chosen road delay function, and fully characterize its optimal solution. We further study the case that only smart vehicles can be controlled and the regular vehicles choose their route selfishly according to the best response to the routing choice of smart vehicles. Finally, we provide extensive numerical studies that corroborate our analytical results.