A robust stochastic framework for reliability and cost-optimized planning of electric vehicle charging networks under service uncertainty and customer impatience

The rapid global transition to electric mobility has increased the necessity for efficient EV charging infrastructure. However, efficient charging operations are still challenging because of operational inefficiencies, such as long waiting periods, inconsistent service provisioning, and customer impatience. The current research introduces a queueing framework for reliability-based and cost-optimized modeling of EV charging networks, incorporating service uncertainty and customer impatience. The suggested framework incorporates a finite-capacity queueing architecture combining customer balking, reneging behavior, partial server breakdowns, and threshold-based repair mechanisms. The system dynamics are explicitly expressed by Chapman–Kolmogorov differential–difference equations. Subsequently, the steady-state probability distribution is derived employing a matrix-analytic solution approach. From such formulations, closed-form expressions are obtained for significant performance indicators, such as queue length, waiting time, overall system throughput, and server utilization. Unlike existing queueing-based EV charging methods that separately examine congestion or reliability, the proposed approach efficiently integrates customer impatience, partial server breakdown, and threshold-based repair mechanisms within a unique finite-capacity queueing architecture. Furthermore, an integrated cost-optimization framework is developed, incorporating multiple operational, service, maintenance, and behavioral cost components under a unified analytical structure. As a result, the suggested approach enables the investigation of economically efficient and reliability-based charging system architectures. Besides, a detailed parametric and sensitivity analysis is conducted to evaluate the effects of arrival intensity, service rates, breakdown frequencies, repair thresholds, and impatience rates on system reliability, congestion, and total cost. The results provide strategic managerial insights into balancing reliability investments, maintenance scheduling, and user satisfaction in dynamic EV charging environments. Overall, the proposed method enables robust cost optimization of sustainable EV charging networks under diverse operational uncertainty conditions.