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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