Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers

• Published in: Annals of operations research Vol. 247; no. 1; pp. 291 - 317
• Main Authors: Taleb, Samira, Aissani, Amar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2016; Springer; Springer Nature B.V
• Subjects: Breakdowns; Business and Management; Combinatorics; Customer relationship management; Customer services; Customers; Failure; Failure analysis; Mathematical analysis; Mathematical models; Methods; Operations research; Operations Research/Decision Theory; Preventive maintenance; Query processing; Queues; Queuing; Random variables; S.I.: Retrial Queues and Related Models; Science; Servers; Studies; Theory of Computation; Passive and active breakdowns; Persistent and impatient customers; Retrial queue; Preventive maintenance; Stationary distribution
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-016-2217-1

In this paper we study a new version of an unreliable retrial queue with persistent and impatient customers. The considered model takes into account corrective and preventive maintenances. If a preventive action occurs in a busy period, then it is postponed to an ulterior date. We give the necessary and sufficient condition for the system to be stable and obtain the joint distribution of the server state and the number of orbiting customers in the system in terms of generating functions. Some performance measures are derived. From the reliability view point, we analyze the time to the first failure of the server. The effect of the system parameters on the performance measures is shown through an illustrative numerical example.