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A discrete-time Geom/G/1 retrial queue with balking customers and second optional service

Author

Listed:
  • Cai-Min Wei

    (Shantou University)

  • Li Cai

    (Shantou University)

  • Jian-Jun Wang

    (Dalian University of Technology)

Abstract

In this paper, we discuss a discrete-time Geom/G/1 retrial queue with balking customers and second optional service where the retrial time follows a geometrical distribution. If an arriving customer finds the server is busy, he will leave the service area and go to the orbit with probability θ or leave the system with probability 1−θ; otherwise, he will begin his service immediately. In this model, after a customer finishes his first essential service, he may leave the system with probability 1−α or asks for a second optional service with probability α. Through studying the Markov chain underlying the model, we establish the probability generating functions of the orbit size and system size. Finally, some performance measures and numerical examples are presented.

Suggested Citation

  • Cai-Min Wei & Li Cai & Jian-Jun Wang, 2016. "A discrete-time Geom/G/1 retrial queue with balking customers and second optional service," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 344-357, June.
  • Handle: RePEc:spr:opsear:v:53:y:2016:i:2:d:10.1007_s12597-015-0232-7
    DOI: 10.1007/s12597-015-0232-7
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    References listed on IDEAS

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    1. J. Artalejo & J. Falin, 1994. "Stochastic decomposition for retrial queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(2), pages 329-342, December.
    2. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
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    Cited by:

    1. Sanga, Sudeep Singh & Jain, Madhu, 2019. "FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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