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EQUILIBRIUM BALKING STRATEGIES IN THE REPAIRABLE M/M/1 G-RETRIAL QUEUE WITH COMPLETE REMOVALS

Published online by Cambridge University Press:  29 April 2019

Shan Gao ,
Deran Zhang ,
Hua Dong  and
Xianchao Wang
Shan Gao
Affiliation:
School of Mathematics and Statistics, Fuyang Normal College, Fuyang236037, P.R. China E-mail: sgao_09@Yeah.net
Deran Zhang
Affiliation:
Department of Electronics and Information Engineering, Bozhou University, Bozhou 236800, P.R. China E-mail: zhderan@163.com
Hua Dong
Affiliation:
School of Statistics, Qufu Normal University, Shandong 273165, P.R. China E-mail: sddh1978@126.com
Xianchao Wang
Affiliation:
School of Computer and Information Engineering, Fuyang Normal College, Fuyang236037, P.R. China E-mail: wxcdx@126.com
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Abstract

We consider an M/M/1 retrial queue subject to negative customers (called as G-retrial queue). The arrival of a negative customer forces all positive customers to leave the system and causes the server to fail. At a failure instant, the server is sent to be repaired immediately. Based on a natural reward-cost structure, all arriving positive customers decide whether to join the orbit or balk when they find the server is busy. All positive customers are selfish and want to maximize their own net benefit. Therefore, this system can be modeled as a symmetric noncooperative game among positive customers and the fundamental problem is to identify the Nash equilibrium balking strategy, which is a stable strategy in the sense that if all positive customers agree to follow it no one can benefit by deviating from it, that is, it is a strategy that is the best response against itself. In this paper, by using queueing theory and game theory, the Nash equilibrium mixed strategy in unobservable case and the Nash equilibrium pure strategy in observable case are considered. We also present some numerical examples to demonstrate the effect of the information together with some parameters on the equilibrium behaviors.

Keywords

balkingcomplete removalsNash equilibrium strategiesnegative customersretrial queues
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Special Issue 1: Learning, Optimization, and Theory of G-Networks , January 2021 , pp. 138 - 157
Copyright
Copyright © Cambridge University Press 2019

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