Distributed Scheduling of Charging for On-Demand Electric Vehicle Fleets

Consider a fleet of N autonomous electric vehicles (EVs), where EV n has a battery state ß_n. Customers arrive at rate ? and each customer requests a trip that costs some battery charge b. The goal is to coordinate the pick-ups and charging of the fleet in order to minimize the discounted number of unpicked customers over an infinite time horizon. Solving the dynamic program for this scheduling problem is infeasible since the state space has an exponential size in N. We propose a distributed approach instead where each EV models the fleet as a "field" that picks the customer i.i.d. at random with some pick-up probability a (b). Based on this model, each EV computes its optimal charging and pick-up strategy, and reports which customer they are available to pick-up (as a function of b) or if they decided to charge. The server computes a maximal matching between customers and EVs, taking into account their reported availability. The process continues iteratively as each EV recomputes its optimal response to the new empirical a (b). We prove that the optimal local strategy is a threshold policy with respect to ß_n, where the threshold depends on a (b) and b. We also prove that the empirical pick-up probability a (b) converges to the true stationary probability, which explains why our algorithm converges to an equilibrium. We then study our algorithm in simulations, that show that at equilibrium, its performance is significantly better than that of an uncoordinated charging strategy. Therefore, our solution has low-complexity but is still sophisticated enough to coordinate the charging of the fleet.