A CTMC-Based Performance Analysis of a Finite-Capacity EV Charging Station with Erlang Service and Phase-Type Impatience

Electric vehicle charging stations are often constrained by the number of available chargers and waiting spaces. As demand increases, users may experience waiting, blocking, or abandonment, which can reduce the quality of service. This project develops a continuous-time Markov chain model for evaluating the performance of a finite-capacity EV charging station with Erlang-2 charging service and phase-type customer impatience.
The system is modelled as an M/E₂/s/K queue, where s is the number of chargers and K is the total system capacity. Customer impatience is represented using Erlang-2 and Cox-2 distributions. The steady-state distribution is computed numerically and used to evaluate key queueing performance measures, including blocking probability, abandonment probability, mean queue length, and mean waiting time.
The model is applied to Expressway Service District C, a highway EV charging station with eight chargers. Real charging-session data are used to estimate the arrival and service rates, and the empirical busy-charger distribution is compared with the model-predicted distribution. The results show that the CTMC models closely reproduce the average charger occupancy, utilisation, and throughput. However, differences remain in the full busy-charger distribution, particularly in the probabilities of empty-station and high-occupancy periods.
The sensitivity results show that higher arrival demand and larger charging energy requirements increase congestion and customer loss, while increasing charging power or adding chargers improves system performance. The results also indicate that the impatience distribution affects the split of customer loss between abandonment and blocking. Overall, the study demonstrates that CTMC-based finite-capacity queueing models provide a useful framework for analysing and designing EV charging stations with limited capacity and impatient customers.