Equilibrium customer behavior in the M/M/1 retrial queue with working vacations and a constant retrial rate

  • Nam H. Do
  • Tien Van Do
  • Agassi Melikov
Original Paper


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.


Retrial 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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Analysis, Design and Development of ICT systems (AddICT) Laboratory, Department of Networked Systems and ServicesBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Division of Knowledge and System Engineering for ICT, Faculty of Information TechnologyTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Institute of Cybernetics National Academy of Sciences of AzerbaijanBakuAzerbaijan

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