Title: Analysis of MAP/PH/1 retrial inventory queueing system with phase type vacation and unreliable server

Authors: G. Ayyappan; S. Meena

Addresses: Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Puducherry Technological University, Puducherry, India

Abstract: In this study, a retrial queueing inventory system with a fixed retrial rate, single vacation, breakdown, and repair is investigated. We have made the assumption that customers arrive through a Markovian arrival process and that the server will offer phase-type services to them. The (s, S) policy is used to replenish the inventory, and it is anticipated that the replenishing time will follow an exponential distribution. The server goes on vacation if there are no consumers in the orbit, or zero inventory, or both. When a server breaks down, it quickly starts the repair process, and the customer enters the infinite size of the orbit. In the steady state, it is possible to determine the number of customers in the orbit, the inventory level, and the status of the servers. The cost analysis is derived, and several significant performance measurements are established. Furthermore, a few numerical demonstrations are given to clarify our mathematical model.

Keywords: queueing-inventory; Markovian arrival process; phase-type distribution; (s, S)-type policy; retrial; single vacation; breakdown and repair; matrix analytic method.

DOI: 10.1504/IJMOR.2025.148623

International Journal of Mathematics in Operational Research, 2025 Vol.32 No.1, pp.1 - 30

Received: 08 Sep 2023
Accepted: 08 Oct 2023
Published online: 16 Sep 2025 *

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