Oper Res Int J https://doi.org/10.1007/s12351-018-0407-0 ORIGINAL PAPER Equilibrium joining strategies in the M ∕G∕1 queue with server breakdowns and repairs 1,2 1 3 Sheng Zhu · Jinting Wang · Bin Liu Received: 11 October 2017 / Revised: 10 March 2018 / Accepted: 19 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract This paper considers an almost observable unreliable M ∕G∕1 queue- ing 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 distribu - tions. To obtain the steady-state queue length distribution, we present an auxiliary system called modified M ∕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 Mathematics Subject Classification Primary 60K25; Secondary 90B22 Supported by the
Operational Research – Springer Journals
Published: May 29, 2018
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