Routing of autonomous vehicles for system optimal flows and average travel time equilibrium over time

Abstract

We envisage a transportation management center (TMC) for future autonomous vehicles that distributes the traffic over a cycle comprising many days in such a manner that the average travel time (AVT) of vehicles of the same origin–destination (OD) over the cycle is identical at equilibrium while the entire network achieves system optimal (SO) flows every day. Vehicles are assigned to a set of paths, with different proportions of time within the cycle on different paths, but with the same AVT over the cycle at equilibrium. Since AVT is the same for each user, it is inherently fair to every-one. Thus, not only do users gain by subscribing to this system but the overall system also, as SO flows are followed each day. We then model the case of mixed equilibrium (ME), wherein drivers are given the option to subscribe to the TMC path combinations and hence assist in achieving SO, while non-subscribers only minimize their own private costs and follow their user equilibrium (UE) paths, which typically have shorter times than the corresponding AVT. To counter this, a tolling scheme is imposed on non-subscribers, i.e., UE users, based on their value-of-time (VOT) distribution and the travel time difference between subscribers' AVT and non-subscribers' UE time at ME. In the end, the total cost of travel of non-subscribers, toll plus UE time, is equal to the corresponding AVT of subscribers. The efficiency of this system is shown through numerical studies. Finally, the impact of market penetration and different VOT distributions on AVT and toll are investigated through sensitivity analysis.