Minimizing the total travel time with limited unfairness in traffic networks

Recently developed technologies are changing mobility dramatically. Autonomous and interactive vehicles enable a coordination of the sat-nav devices of traveling vehicles aimed at assigning paths with the goal of eliminating congestion and, more in general, of reducing the total travel time in traffic networks. In this paper we tackle the problem of finding a traffic assignment that minimizes the total travel time on a network, while guaranteeing that the paths of users with the same origin and destination have similar path traversal times. While previous approaches have identified the eligible paths a priori, we propose two mixed integer nonlinear programming models, along with their mixed integer linear approximations, that identify paths that satisfy the desired level of fairness while minimizing the total travel time on thenetwork. The two models differ for the unfairness measure adopted. Computational results show that the total travel time spent in the network is very close to the minimum possible, that is the one obtained by the system optimum solution, while guaranteeing to each user a very low level of experienced unfairness. A heuristic algorithm is also proposed which is shown to generate high quality solutions