Proportional Fairness for EV Charging in Overload

This paper studies a charging facility for electrical vehicles (EVs) at a parking garage, under the assumption that the infrastructure has a limited power capacity. In situations of overload, scheduling decisions must be made on which EVs to charge, possibly taking into account users’ sojourn times. We propose a fluid model that tracks service and sojourn times for a large population, enabling analytical studies of the distribution of service in steady state, for different policies. These results raise the issue of fairness in the distribution of partial service. We introduce a new policy called least laxity ratio to achieve a suitable notion of proportional fairness. We test our results in simulation, including a real data-set with time-varying load. Our results show that our conclusions remain valid in this scenario, in particular the proposed policy performs well under an objective empirical measure of fairness.