Transient Analysis of Single Server Queue with State Dependent Breakdowns

Modern service systems are increasingly reliant on efficient and reliable operations to maintain high levels of performance and resource utilization. System failures and service interruptions in these situations can have a major impact on operational effectiveness, congestion levels, and overall system reliability. This study develops a transient analytical framework for a single-server queueing system with idle and operational failures, where breakdowns may occur during both busy and idle periods. Upon failure, all customers present in the system are removed, and no new arrivals are accepted until the repair process is completed, resulting in a system-clearing failure mechanism. The proposed framework captures the transient impact of system-clearing failures and repair processes, providing a time-dependent characterization of a model that has been investigated predominantly from a steady-state perspective. By allowing failure rates to vary with the system state, the proposed model captures a broader range of realistic operating conditions and reliability behaviors. Analytical tractability is achieved using Laplace transform and generating function techniques to derive key performance measures, including system reliability, availability, mean queue length, and failure frequency. Discrete-event simulations validate the analytical results and confirm their accuracy. Numerical findings illustrate the impact of state-dependent failure behavior on system performance and provide insights for reliability assessment, maintenance planning, and operational decision-making in complex environments.