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

• Published in: Operational research Vol. 21; no. 1; pp. 621 - 643
• Main Authors: Gao, Shan, Dong, Hua, Wang, Xianchao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2021; Springer Nature B.V
• Subjects: Business and Management; Computational Intelligence; Customers; Maintenance; Management Science; Operations Research; Operations Research/Decision Theory; Original Paper; Pricing; Queues; Queuing theory; Unreliable retrial queue; Primary 60K25; Secondary 90B22; Equilibrium analysis; Pricing analysis; Single vacation; Limited idle period
• ISSN: 1109-2858; 1866-1505
• DOI: 10.1007/s12351-018-0437-7

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.