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Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs

Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs This paper considers an almost observable unreliable Mn/G/1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$M_{n}{/}G{/}1$$\end{document} queueing system in which the arriving customerscan observe the queue length upon their arrivals but not the state of the server. The arrival rates are state-dependent and the server is subject to breakdowns when it works. The lifetime of the server and the repair time are independent, and they follow two different general distributions. To obtain the steady-state queue length distribution, we present an auxiliary system called modified Mn/G/1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$M_{n}{/}G{/}1$$\end{document} queueing system. Comparing the unreliable system with the modified system, we derive the steady-state queue length distributions at the arrival instant of a tagged customer. Moreover, we study customers’ equilibrium joining strategies based on a nonlinear waiting cost function. These results provide managerial insights into strategic behaviors of customers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Operational Research Springer Journals

Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs

Zhu, Sheng; Wang, Jinting; Liu, Bin
Operational Research , Volume 20 (4) – Dec 29, 2020
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Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Subject
Business and Management; Operations Research/Decision Theory; Operations Research, Management Science; Computational Intelligence
ISSN
1109-2858
eISSN
1866-1505
DOI
10.1007/s12351-018-0407-0
Publisher site
See Article on Publisher Site

Abstract

This paper considers an almost observable unreliable Mn/G/1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$M_{n}{/}G{/}1$$\end{document} queueing system in which the arriving customerscan observe the queue length upon their arrivals but not the state of the server. The arrival rates are state-dependent and the server is subject to breakdowns when it works. The lifetime of the server and the repair time are independent, and they follow two different general distributions. To obtain the steady-state queue length distribution, we present an auxiliary system called modified Mn/G/1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$M_{n}{/}G{/}1$$\end{document} queueing system. Comparing the unreliable system with the modified system, we derive the steady-state queue length distributions at the arrival instant of a tagged customer. Moreover, we study customers’ equilibrium joining strategies based on a nonlinear waiting cost function. These results provide managerial insights into strategic behaviors of customers.

Journal

Operational Research – Springer Journals

Published: Dec 29, 2020

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