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M/M/1 Retrial Queue with Collisions and Transmission Errors

Author

Listed:
  • Lamia Lakaour

    (Bejaia University)

  • Djamil Aïssani

    (Bejaia University)

  • Karima Adel-Aissanou

    (Bejaia University)

  • Kamel Barkaoui

    (Conservatoire National des Arts et Métiers)

Abstract

In this paper, an M/M/1 retrial queue with collisions and transmission errors is considered. The collision may occur when a primary arriving customer finds the server busy while the transmission errors usually occur due to an erroneous packet or due to a non-ideal channel condition. We apply the generating function method to derive the joint distribution of the server state and the orbit length in steady state and we obtain important system characteristics. Finally, we present numerical examples to show the applicability of the model.

Suggested Citation

  • Lamia Lakaour & Djamil Aïssani & Karima Adel-Aissanou & Kamel Barkaoui, 2019. "M/M/1 Retrial Queue with Collisions and Transmission Errors," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1395-1406, December.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9680-x
    DOI: 10.1007/s11009-018-9680-x
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    References listed on IDEAS

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    1. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    2. N/A, 1999. "Research in Progress," ILR Review, Cornell University, ILR School, vol. 53(1), pages 170-170, October.
    3. V. Jailaxmi & R. Arumuganathan & M. Senthil Kumar, 2017. "Performance analysis of an M/G/1 retrial queue with general retrial time, modified M-vacations and collision," Operational Research, Springer, vol. 17(2), pages 649-667, July.
    4. N/A, 1999. "Research in Progress," ILR Review, Cornell University, ILR School, vol. 52(2), pages 330-333, January.
    5. N/A, 1999. "Research in Progress," ILR Review, Cornell University, ILR School, vol. 52(4), pages 663-663, July.
    6. 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.
    7. N/A, 1999. "Research in Progress," ILR Review, Cornell University, ILR School, vol. 52(3), pages 496-499, April.
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