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

Sheng Zhu, Jinting Wang () and Bin Liu
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Sheng Zhu: Beijing Jiaotong University
Jinting Wang: Beijing Jiaotong University
Bin Liu: Anhui Jianzhu University

Operational Research, 2020, vol. 20, issue 4, No 10, 2163-2187

Abstract: Abstract This paper considers an almost observable unreliable $$M_{n}{/}G{/}1$$ M n / G / 1 queueing system in which the arriving customers can 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 $$M_{n}{/}G{/}1$$ M n / G / 1 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.

Keywords: Queueing system; Nash equilibrium; Equilibrium strategies; Breakdowns; Repairs; Primary 60K25; Secondary 90B22 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s12351-018-0407-0

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