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Strategic Joining in an M/M/1 Constant Retrial Queue with Reserved Idle Time Under N-Policy

  • Jinting WangEmail author
  • Lulu Li
Chapter
Part of the Communications in Computer and Information Science book series (CCIS, volume 1102)

Abstract

This paper considers an M/M/1 constant retrial queueing model with reserved idle time under N-policy. A customer can occupy the server instantaneously when the server is turned on and idle upon arrival. After the service of the last customer, the server stays idle for some random time. During this period, if a customer arrives, he obtains service immediately. Otherwise, the sever will shut down for saving energy and be reactivated if the number of waiting customers in retrial orbit reaches a given threshold \(N(N>1)\). The probabilities of the server in different states are derived through generating function method. Moreover, based on the reward-cost function and the expected payoff, all customers will decide whether to join or balk the system upon arrival. Given these strategic behaviors we establish the net profit of the service provider per unit of time. Finally, some numerical examples are presented to illustrate the necessity of the reserved idle time’s existence from the perspective of the service provider. It is found the longer the reserved idle time, the greater the server’s profit.

Keywords

Retrial queue Reserved idle time N-policy Equilibrium strategies 

References

  1. 1.
    Burnetas, A., Economou, A.: Equilibrium customer strategies in a single server Markovian queue with setup times. Queueing Syst. 56(3), 213–228 (2007).  https://doi.org/10.1007/s11134-007-9036-7MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Doshi, B.T.: Queueing systems with vacations—a survey. Queueing Syst. 1(1), 29–66 (1986).  https://doi.org/10.1007/BF01149327MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Economou, A., Kanta, S.: Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper. Res. Lett. 36(6), 696–699 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Economou, A., Kanta, S.: Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue. Naval Res. Logistics 58, 107–122 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Edelson, N.M., Hilderbrand, D.K.: Congestion tolls for Poisson queuing processes. Econometrica J. Econometric Soc. 43, 81–92 (1975)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Guo, P., Hassin, R.: Strategic behavior and social optimization in Markovian vacation queues. Oper. Res. 59(4), 986–997 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Guo, P., Hassin, R.: Strategic behavior and social optimization in Markovian vacation queues: the case of heterogeneous customers. Eur. J. Oper. Res. 222(2), 278–286 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Guo, P., Li, Q.: Strategic behavior and social optimization in partially-observable Markovian vacation queues. Oper. Res. Lett. 41(3), 277–284 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hassin, R.: Rational Queueing. CRC Press, Boca Raton (2016)CrossRefGoogle Scholar
  10. 10.
    Hassin, R., Haviv, M.: To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Springer, Boston (2003). doi: 10.1007/978-1-4615-0359-0CrossRefGoogle Scholar
  11. 11.
    Naor, P.: The regulation of queue size by levying tolls. Econometrica J. Econometric Soc. 37, 15–24 (1969)CrossRefGoogle Scholar
  12. 12.
    Takagi, H.: Queueing analysis: a foundation of performance analysis. Vacation Priority Syst. 1 (1991)Google Scholar
  13. 13.
    Tian, N., Zhang, Z.G.: Vacation Queueing Models: Theory and Applications. Springer, Boston (2006). doi: 10.1007/978-0-387-33723-4CrossRefGoogle Scholar
  14. 14.
    Wang, J., Zhang, X., Huang, P.: Strategic behavior and social optimization in a constant retrial queue with the N-policy. Eur. J. Oper. Res. 256(3), 841–849 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Management Science and EngineeringCentral University of Finance and EconomicsBeijingPeople’s Republic of China
  2. 2.Department of MathematicsBeijing Jiaotong UniversityBeijingPeople’s Republic of China

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