Title: Analysis of M^[X₁], M^[X₂]/G₁, G₂/1 retrial queue with priority services, differentiate breakdown, delayed repair, Bernoulli feedback, balking and working vacation

Authors: G. Ayyappan; S. Nithya

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

Abstract: In this study, we construct a single server retrial queueing system with two types of breakdowns, delayed repair, Bernoulli feedback, balking and working vacation. Two different categories of customers like priority and ordinary are to be considered. This model proposes non-pre-emptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. For both ordinary and priority customers, the server consistently affords a single service that follows to general distribution. During certain periods, an arriving ordinary customer may balk the system. When the orbit and priority queue are empty after the service is ended, the server takes a single working vacation. In this study, we used probability generating function and supplementary variable technique to solve the Laplace transforms of time-dependent probabilities of system states. In order to accelerate the sensitivity analysis of system descriptions, numerical data are obtained and also examined.

Keywords: retrial queues; batch arrivals; priority queues; working vacation; balking; differentiate breakdown; Bernoulli feedback; delayed repair.

DOI: 10.1504/IJMOR.2024.140347

International Journal of Mathematics in Operational Research, 2024 Vol.28 No.4, pp.491 - 513

Received: 27 Mar 2023
Accepted: 08 Apr 2023
Published online: 05 Aug 2024 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article