Dynamic Load Balancing of Selfish Drivers between Spatially Distributed Electrical Vehicle Charging Stations

This paper considers an electrical vehicle recharging infrastructure made up of physically separate stations serving spatially distributed requests for charge. Arriving EVs receive feedback on transport times to each station, and waiting times at congested stations, based on which they make a selfish selection. We present a fluid model of the resulting dynamics, in particular modeling queueing delays as a function of fluid queues, and two different models of client departures: given sojourn times, or given service times. In each case, the joint load balancing dynamics is related to a convex program, suitable variant of a centralized optimal transport problem. In particular, we use Lagrange duality to show the correspondence between equilibrium points and optima, and to analyze the convergence properties of the dynamics. The results have similarities and differences with classical work on selfish routing for transportation networks. We present illustrative simulations, which also explore the validity of the model beyond the fluid assumption.