How Will the Presence of Autonomous Vehicles Affect the Equilibrium State of Traffic Networks?

It is known that connected and autonomous vehicles are capable of maintaining shorter headway and distances when they form platoons of vehicles. Thus, such technologies can potentially increase the road capacities of traffic networks. Consequently, it is envisioned that their deployment will also increase the overall network mobility. In this paper, we examine the validity of this expected impact, assuming that drivers select their routes selfishly, in traffic networks with mixed vehicle autonomy, that is, traffic networks with both regular and autonomous vehicles. We consider a nonatomic routing game on a network with inelastic (fixed) demands for a set of network origin destination (O/D) pairs, and study how replacing a fraction of regular vehicles by autonomous vehicles will affect the mobility of the network. Using well-known U.S. Bureau of Public Roads traffic delay models, we show that the resulting Wardrop equilibrium is not necessarily unique for networks with mixed autonomy. Then, we state the conditions under which the total network delay at equilibrium is guaranteed to not increase as the fraction of autonomous vehicles increases. However, we show that when these conditions do not hold, counterintuitive behaviors may occur - the total network delay can grow as the fraction of autonomous cars increases. In particular, we prove that for networks with a single O/D pair, if the road degrees of capacity asymmetry (i.e., the ratio between the road capacity when all vehicles are regular and the road capacity when all vehicles are autonomous) are homogeneous, the total delay is: 1) unique and 2) a nonincreasing continuous function of the fraction of autonomous vehicles in the network. We show that for heterogeneous degrees of capacity asymmetry, the total delay is not unique, and it can further grow as the fraction of autonomous vehicles increases. We demonstrate that similar behaviors may be observed in networks with multiple O/D pairs. We further bound such performance degradations due to the introduction of autonomy in general homogeneous networks.