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Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation

Shan Gao (), Hua Dong and Xianchao Wang
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Shan Gao: Fuyang Normal College
Hua Dong: Qufu Normal University
Xianchao Wang: Fuyang Normal College

Operational Research, 2021, vol. 21, issue 1, No 22, 643 pages

Abstract: 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.

Keywords: Unreliable retrial queue; Limited idle period; Single vacation; Equilibrium analysis; Pricing analysis; Primary 60K25; Secondary 90B22 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s12351-018-0437-7

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