Title: Transient behaviour of a Markovian vacation queue with re-service balking control of admission closedown and setup times

Authors: A. Azhagappan; T. Deepa

Addresses: Department of Mathematics, St. Anne's College of Engineering and Technology, Anna University, Panruti, Tamilnadu – 607110, India ' Department of Mathematics, Idhaya College of Arts and Science for Women, Pondicherry University, Pakkamudayanpet, Puducherry – 605008, India

Abstract: This paper studies an M/M/1 queueing model with single as well as multiple vacation, closedown, setup times, re-service, balking and control of admission. All the arriving customers are not allowed to join the queue all the time. They are either permitted to join the queue or rejected. Whenever the system becomes empty and the server resumes closedown work. If any customer joins the queue before the completion of closedown, the closedown work is interrupted and the server commences an exhaustive busy period. Otherwise, it starts the vacation after the completion of closedown period. During the vacation period, the permitted arrivals may join the queue or balk. At the moment of completion of vacation, the server begins the setup work before the commencement of service. After the service, each customer has the option to get immediate re-service. The transient and stationary system size probabilities are derived. The time-dependent mean and variance are also obtained. Numerical simulations are also presented.

Keywords: the M/M/1 queue; single and multiple vacations; closedown setup times and re-service; balking and admission control.

DOI: 10.1504/IJMOR.2021.115445

International Journal of Mathematics in Operational Research, 2021 Vol.19 No.1, pp.19 - 44

Received: 29 Aug 2019
Accepted: 01 Feb 2020

Published online: 02 Jun 2021 *

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