Unfairness Avoidance in System Optimal Routing of Traffic Flows

In static traffic assignment problems, the user experienced travel time in a system optimum solution can be much higher than in a user equilibrium solution. On the other hand, the total travel time in a user equilibrium solution can be significantly higher than the total travel time in a system optimum solution. A compromise solution between the two assignments seems to be the right choice for traffic regulators aiming at improving the network performance while satisfying users needs. All works in this field consist in restricting ex-ante the set of eligible paths for each driver. However, when demands flow on the road network, these paths could turn out to be very unfair for users and some excluded paths could be much fairer then the eligible ones. In order to overcome this limitation, in this paper a MILP based approach able to minimize the total travel time spent on the road network while controlling the unfairness experienced by users is proposed. Computational results show that the obtained total travel time is very close to the system optimum one while guaranteeing a very low level of experienced unfairness. The underlying idea is to bound the experienced travel time of each user to a fixed threshold, representing the maximum level of unfairness the regulator decides to allow. The MILP formulation requires the enumeration of all feasible paths from each origin to each destination each one corresponding to a binary variable and, hence, it becomes computationally intractable even considering small road networks. To this aim an efficient and accurate heuristic algorithm is also proposed.