Bounds and Limit Theorems for a Layered Queueing Model in Electric Vehicle Charging

TL;DR

This paper models a layered queueing system for EV charging stations with limited parking and charging rates, developing bounds and approximations to analyze the fraction of vehicles fully charged and system performance.

Contribution

It introduces a novel layered queueing model for EV charging stations with finite resources and derives bounds and asymptotic approximations for key performance metrics.

Findings

Derived bounds for the fraction of fully charged EVs.

Developed fluid and diffusion approximations for the queueing process.

Validated approximations with numerical simulations.

Abstract

The rise of electric vehicles (EVs) is unstoppable due to factors such as the decreasing cost of batteries and various policy decisions. These vehicles need to be charged and will therefore cause congestion in local distribution grids in the future. Motivated by this, we consider a charging station with finitely many parking spaces, in which electric vehicles arrive in order to get charged. An EV has a random parking time and a random charging time. Both the charging rate per vehicle and the charging rate possible for the station are assumed to be limited. Thus, the charging rate of uncharged EVs depends on the number of cars charging simultaneously. This model leads to a layered queueing network in which parking spaces with EV chargers have a dual role, of a server (to cars) and customers (to the grid). We are interested in the performance of the aforementioned model, focusing on the fraction of vehicles that get fully charged. To do so, we develop several bounds and asymptotic (fluid and diffusion) approximations for the vector process, which describes the total number of EVs and the number of not fully charged EVs in the charging station, and we compare these bounds and approximations with numerical outcomes.