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ON MARKOVIAN QUEUES WITH SINGLE WORKING VACATION AND BERNOULLI INTERRUPTIONS

Published online by Cambridge University Press:  11 January 2021

Ruiling Tian ,
Zhe George Zhang Open the ORCID record for Zhe George Zhang [Opens in a new window]  and
Siping Su
Ruiling Tian
Affiliation:
College of Sciences, Yanshan University, Qinhuangdao, 066004 Hebei, China E-mail: tianrl@ysu.edu.cn
Zhe George Zhang
Affiliation:
Beedie School of Business, Simon Fraser University, Burnaby, BC V5A 1S6, Canada College of Business and Economics, Western Washington University, Bellingham, WA 98229, USA E-mail: gzhang@sfu.ca
Siping Su
Affiliation:
College of Business and Economics, Western Washington University, Bellingham, WA 98229, USA
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Abstract

This paper considers the customers’ equilibrium and socially optimal joining–balking behavior in a single-server Markovian queue with a single working vacation and Bernoulli interruptions. The model is motivated by practical service systems where the service rate can be adjusted according to whether or not the system is empty. Specifically, we focus on a single-server queue in which the server's service rate is reduced from a regular to a lower one when the system becomes empty. This lower rate period is called a working vacation for the server which may represent that part of the service facility is under a maintenance process or works on other non-queueing job, or simply for saving the energy (for a machine server case). In this paper, we assume that the working vacation period is terminated after a random period or with probability p after serving a customer in a non-empty system. Such a system is called a queue with single working vacation and Bernoulli interruptions. Customers are strategic and can make choice of joining or balking based on different levels of system information. We consider four scenarios: fully observable, almost observable, almost unobservable, and fully unobservable queue cases. Under a reward-cost structure, we analyze the customer's equilibrium and social-optimal strategies. In addition, the effects of system parameters on optimal strategies are illustrated by numerical examples.

Keywords

Bernoulli vacation interruptionsequilibrium balking strategyqueuing systemsocial welfareworking vacation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 616 - 643
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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