Abstract
This paper treats an M/M/1 retrial queue with an unreliable server, where the server is subject to random breakdowns and repairs when he is serving a customer. Whenever the server becomes idle, he will spare a limited period to wait possible new arrivals or repeated customers if any. If no customer arrives during this period, the server will take a single vacation. Under a given reward-cost structure, arriving customers have to decide to balk or to enter the orbit if they find the server unavailable at their arrival epochs. Firstly, we study some important performance measures. Secondly, we derive the equilibrium joining strategies for the customers, respectively, in noncooperative and cooperative cases. Thirdly, we study the pricing problem that the social planner faces to eliminate the gap between the individual optimal and socially optimal strategies. Finally, we present some numerical examples to illustrate the effect of some system parameters on optimal joining probabilities and Maximum of social welfare.
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16 February 2021
A Correction to this paper has been published: https://doi.org/10.1007/s12351-019-00497-x
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Acknowledgements
The authors thank the referees for their helpful comments on an earlier version of this paper. This work is supported by National Natural Science Foundation of China under Grant Nos. 11701319, 61672006, the Natural Science Foundation of Anhui Higher Education Institutions of China under Grant Nos. KJ2017A340, KJ2014ZD21, KJ2016A875 and KJ2018A0346, Fuyang Municipal Government-Fuyang Normal College Horizontal Cooperation projects in 2017 (NO. XDHXTD201709).
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Gao, S., Dong, H. & Wang, X. Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation. Oper Res Int J 21, 621–643 (2021). https://doi.org/10.1007/s12351-018-0437-7
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DOI: https://doi.org/10.1007/s12351-018-0437-7