Optimal Cloud-Based Routing With In-Route Charging of Mobility-on-Demand Electric Vehicles

Mobility-on-Demand (MoD) systems using electric vehicles (EVs) are expected to play a significantly increasing role with urban transportation systems in the near future, to both cope with the massive increases in urban population and reduce carbon emissions. One inconvenience in MoD-EV systems is the need for some customers to perform in-routing charging for almost-out-of-charge EVs. In this paper, we propose a routing scheme that aims to reduce this inconvenience by minimizing the relative excess time spent by MoD-EV systems customers for in-route charging compared to the on-road trip time. By modeling the routing problem between multiple MoD-EV stations with in-route charging as a multi-server queuing system, we formulate our objective as a stochastic convex optimization problem that minimizes the average overall trip time for all customers relatively to their actual trip time without in-route charging. Both single and multiple charging units per charging station are considered in this paper and modeled as M/M/l and M/M/c queues, respectively. For both types of queues, the optimal routing proportions are derived analytically using the Lagrangian analysis and the Karush-Kuhn-Tucker conditions. Simulation results show the merits of our proposed solution in both cases as compared to the shortest time and the random routing decisions. Finally, the proposed method is tested on a real-world scenario, and the computation times are calculated for different settings.