Coupled Queueing and Charging Game Model with Energy Capacity Optimization

With the rise of Electric Vehicles (EV), the demand in the stations - both for a parking spots equipped with plugging devices and for electricity to charge the batteries - is increasing. This motivates us to study how we can improve the quality of service at the stations. We model the arrival of EV in several stations and consider a criterium of choice of the station for the users. In our model, EV arrive at the stations according to a Poisson process with a random quantity of energy needed to have a fully charged battery and a random parking time, both following an exponential distribution. We quantify the quality of the service as the probability of leaving the station with a fully charged battery. The stations are characterized by their number of spots and the way they share the power between the EV users. In this model, we study the best way to share power in order to improve this quality of service.