Title: Analysis of a variant working vacation queue with customer impatience and server breakdowns

Authors: P. Vijaya Laxmi; P. Rajesh; T.W. Kassahun

Addresses: Department of Applied Mathematics, Andhra University, Visakhapatnam – 530 003, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam – 530 003, India ' Department of Applied Mathematics, Andhra University, Visakhapatnam – 530 003, India

Abstract: This paper analyses an infinite buffer single server variant working vacation queueing model in which the arriving customer may balk and the server is subject to breakdown. The service times during regular busy period and working vacation period, vacation times, breakdown times and repair times are assumed to be exponentially distributed and are mutually independent. In working vacation period, the customer may renege due to impatience. We derive the probability generating function of the steady-state probabilities and obtain the closed form expressions of the system size. In addition, we obtain some performance measures and a total expected profit function per unit time is designed to determine the optimal values at the maximum profit. We employ the particle swarm optimisation method to solve the profit optimisation problem.

Keywords: queue; balking; reneging; variant working vacations; server breakdowns; particle swarm optimisation; PSO.

DOI: 10.1504/IJOR.2021.114839

International Journal of Operational Research, 2021 Vol.40 No.4, pp.437 - 459

Received: 16 Feb 2018
Accepted: 30 May 2018

Published online: 28 Apr 2021 *

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