A loss queueing game for electric vehicle charging performance evaluation

The demand of electricity at the Charging Stations (CSs) by Electric Vehicle (EV) users is tremendously increasing. However, EV users still face limited resources at the CSs, both in terms of the number of parking spaces equipped with a charging point, and in terms of available power. This paper deals with the choice of a CS among two CSs by the EV users in a competitive environment. The stochastic nature of arrivals and departures at the CSs is modeled by a queueing system. A queueing game is studied where the EV users are the players and choose the CS that gives the highest expected energy received. An approximation of the expected energy received at the CSs is theoretically provided and the quality of this approximation is numerically illustrated and analyzed through simulations. The existence and uniqueness of the equilibrium of the game is proved, and bounds on the Price of Anarchy (PoA) are also provided. Moreover, the model is simulated using a discrete event framework and a sensitivity analysis of the main metrics of the system with respect to the average parking duration and the power sizing coefficient is provided. The results show that the utility of EV users at equilibrium is close to the optimal utility. This study can help a Charging Point Operator (CPO) to design incentives for EV users in order for instance to limit the parking duration so as to improve the social welfare of the EV users.