Equilibrium customer behavior in the M/M/1 retrial queue with working vacations and a constant retrial rate
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In this paper, we investigate the M/M/1 retrial queue with working vacations and a constant retrial rate. In the queue, customers decide about the entry based on the information upon their arrival instants. Scenarios regarding the availability of information (i.e., the server is occupied or not, and the server is on the vacation or not) for customers are compared. We derive the closed form solution for the stationary probabilities of the queue. Social optimizing and Nash equilibrium strategies for joining the system are investigated. Based on numerical results, the social benefit rate is best when customers know all information about the server.
KeywordsRetrial queue Vacations Strategic behavior
The authors thank reviewers for critical comments that helped the authors to improve the presentation of this paper. The research of N. H. Do is supported by the OTKA K123914 project. The research of T. V. Do has been carried out within the project Thematic Research Cooperation Establishing Innovative Informatic and Info-communication Solutions, which is partially financed by the European Social Fund under Grant Number EFOP-3.6.2-16-2017-00013.
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