Title: Analysis of batch arrival bulk service priority queue with multiple vacation, close down, setup, differentiate breakdown, and repair

Authors: G. Ayyappan; S. Nithya

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

Abstract: This paper is a steady state analysis of a single server non-preemptive priority queueing system under multiple vacation, close down, setup, differentiate breakdown, and repair. Priority and ordinary customers arrive according to Poisson processes, and their service time based on the general distribution. The server constantly offers a single service for priority and bulk service for ordinary customers. Ordinary customers will only be served if the batch size is more than 'a' or less than or equal to 'b'. We compute the Laplace transforms of the time-dependent probabilities of system states using the probability generating function and supplementary variable technique. Numerical results are obtained which are also examined to facilitate the sensitivity analysis of system descriptions.

Keywords: bulk service; priority queues; batch arrivals; differentiate breakdown; multiple vacation; closedown; setup.

DOI: 10.1504/IJMOR.2025.144552

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.1, pp.1 - 21

Received: 05 Dec 2023
Accepted: 24 Dec 2023
Published online: 19 Feb 2025 *

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