Analysis of Customers’ Impatience in a Repairable Retrial Queue under Postponed Preventive Actions

SYNOPTIC ABSTRACT

In this article, we analyze an unreliable retrial queue with persistent and impatient customers having different general service distributions. The server is subject to active and passive breakdowns. A persistent customer whose service is interrupted enters the orbit, while an impatient one leaves the system. Two types of arbitrarily distributed maintenances are considered: preventive for improving system performances and preventing breakdowns, and corrective for restoring the service when a failure occurs. If a preventive maintenance occurs in a busy period, then it is postponed to an ulterior random date. We give the necessary and sufficient condition for the system to be stable. We obtain the joint probability distribution of the server state and the number of customers in orbit in terms of Laplace and z-transforms. Some performance measures are derived and numerical results are given. Moreover, a cost minimization problem is considered.

KEY WORDS AND PHRASES:

• Impatience
• Laplace and z-transforms
• maintenance
• performance measures
• piece-wise Markov process
• preemptive-repeat different
• retrial queues
• unreliable server

Acknowledgments

The authors thank the anonymous referees for giving great interest to this article.