Performance analysis of a single server finite capacity queue with geometric reneging

We study a single server finite capacity Electric Vehicle(EV) based queueing model that incorporates the impatience of a customer through geometric reneging mechanism, even while service is in progress. The model reflects how prolonged waiting can prompt customers to leave the system, with the likelihood of abandonment following a geometric pattern. By harnessing the power of recursive method, we derive steady-state equations and compute critical performance indicators such as the expected number of customers in the queue and system, average waiting time, blocking probability, service throughput, abandonment rate, distribution of busy periods, and the anticipated number of customers who leave the queue prematurely. To support our analytical results, we conduct extensive numerical analysis, illustrating outcomes through structured tables and graphical representations. Additionally, a cost-based sensitivity analysis is performed to understand how variations in arrival and service rates affect system performance. A practical application of this model is demonstrated in the context of electric vehicle (EV) charging stations, where understanding the effects of customer impatience can inform the design of more efficient energy service infrastructures.