Exact formulation and comparison between the user optimum and system optimum solution for routing privately owned automated vehicles

The possibility of having driverless cars on the streets seems to be more real than ever. In this paper, we focus on developing exact methods that can determine the effects of privately owned automated vehicles (AVs) and how switching to those vehicles is going to change mobility in urban environments. The considered problem determines the routes of family owned AVs that minimize the transportation costs of that family while considering the possibility of using public transport as an alternative for some trips. We introduce a novel exact linear formulation for this problem which includes a linearized traffic congestion model and which is able to solve the user and system optimum variant of the problem to optimality. The introduced formulation can easily be adapted to consider the current situation with conventional vehicles and a situation where not only the travel time costs of the driver but also costs of the other passengers are taken into account. The main advantage of our novel formulation is that the optimal results can be obtained to explore potential changes of flows with vehicle automation in small networks. We investigated the behavior of the system, given the described scenarios, by applying our formulation to a case study.