Title: Numerical investigation of phase type inventory queueing system with (s, S) policy, degrading service, single vacation, closedown, breakdown, repair and impatient customers

Authors: G. Ayyappan; S. Meena

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

Abstract: This analyses an inventory queueing system with degrading service, single vacation, breakdown, repair, closedown, and impatient customers. We assume that an arrival follows the Markovian arrival process, and that the server will provide them with phase-type services. The (s, S) policy to replenish the items and the replenishing duration follow an exponential distribution. The arriving customer should get the service whenever the inventory item level is positive. Otherwise, they must wait in front of the service station. The rate of service will decrease until the degradation is resolved. The number of customers in the system, the inventory level, and server status may all be determined in a steady state. Numerous key performance indicators are defined, busy period analysis is obtained, and cost analysis is obtained. To make our mathematical concept clearer, a few numerical examples are provided.

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

DOI: 10.1504/IJMOR.2026.154507

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.2, pp.231 - 260

Received: 29 Jun 2024
Accepted: 07 Aug 2024
Published online: 02 Jul 2026 *

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