Performance analysis of renewal input queues with multiple vacations and synchronized abandonment

ABSTRACT

This paper studies a single server renewal input queueing model with multiple vacations in the presence of impatient customers. The server follows an exhaustive vacation policy whenever the system is empty. During vacation, waiting customers become impatient and decide independently whether to abandon the system simultaneously or avail service at the vacation completion instant. Using the supplementary variable and difference equation techniques, we obtain the steady-state system-length distributions at pre-arrival and arbitrary epochs. We present the stochastic decomposition structure for the number of customers in the system and derive several performance measures including the sojourn time. Moreover, we examine the impact of various parameters on the system performance measures. A potential application of the model in the inventory management of an e-commerce company with fresh agricultural products is illustrated. Numerical results discuss the effects of the system parameters and provide insight into the performance of such systems.

KEYWORDS:

• Synchronized abandonment
• renewal process
• supplementary variable
• multiple vacations
• GI/M/1 queue
• stochastic decomposition

Acknowledgments

We would like to thank the editor and the anonymous referees for their valuable comments and suggestions which led to the improvement of the presentation in the current form of the paper.

Disclosure Statement

No potential conflict of interest was reported by the authors.