Title: Analysis of MAP/PH/1 retrial queueing system with two-stage vacations with imperfect service, N-policy service, delayed feedback, unreliable server and discouragement customer

Authors: G. Ayyappan; N. Arulmozhi

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

Abstract: In the present study, we investigate a continuous-time single server constant retrial queueing with a limitless system of capacity, two-stage vacations that include single working vacation and multiple vacations with imperfect service, N-policy service, delayed feedback, unreliable server, and discouragement customer. Once the operating environment is empty during a normal busy period, it initially takes a working vacation, during which the server can still provide service but at a slower rate. If the system is empty after this working vacation, the server will take a vacation and stop serving entirely. Otherwise, the server resumes its normal service rate. If there are fewer than N customers in orbit after the vacation period ends, the server resumes normal operation. If not, the server starts another vacation. When approaching the system using the matrix-analytic method, steady-state vector, busy period, and cost analysis are generated for this model. Analytical performance indices are assessed numerically.

Keywords: multiple vacation; working vacation; unreliable server; imperfect service; delayed feedback.

DOI: 10.1504/IJMOR.2025.144546

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.1, pp.81 - 110

Received: 21 Jun 2023
Accepted: 28 Jun 2023
Published online: 19 Feb 2025 *

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