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Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors

Author

Listed:
  • Wei Xu

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China)

  • Liwei Liu

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China)

  • Linhong Li

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China)

  • Zhen Wang

    (School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China)

  • Sabine Wittevrongel

    (SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University, B-9000 Gent, Belgium)

Abstract

This paper considers a retrial G-queue with collisions, transmission errors, and a finite number of sources, where service and repair time are both general distributions. The number of sources (terminals) is finite and a source cannot generate new requests until the channel (server) finishes its work, i.e., the rate at which new primary requests are generated varies inversely with the number of data frame (customer) in the system. A collision occurs when service requests arrive at a busy channel, and transmission errors prevent data frames from leaving the system after completing service. Two types of arrivals are considered. Negative customers will break down the system in the busy state and remove the customer under service. The application of our model is indicated, with a particular emphasis on communication networks such as the local-area networks (LAN) with CSMA/CD protocol. Recursive formulas have been derived to calculate the stationary joint distributions and the Laplace transform of reliability function by applying the discrete transformations method along with the supplementary variables technique (SVT). Furthermore, the comparative performance and reliability analysis have been conducted numerically. Numerical examples are provided to investigate the sensitivity of different parameters on performance measures and reliability indicators.

Suggested Citation

  • Wei Xu & Liwei Liu & Linhong Li & Zhen Wang & Sabine Wittevrongel, 2023. "Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3532-:d:1218002
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    References listed on IDEAS

    as
    1. Antonio Gómez-Corral & Tuan Phung-Duc, 2016. "Retrial queues and related models," Annals of Operations Research, Springer, vol. 247(1), pages 1-2, December.
    2. Dieter Fiems, 2023. "Retrial queues with constant retrial times," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 347-365, April.
    3. Lamia Lakaour & Djamil Aissani & Karima Adel-Aissanou & Kamel Barkaoui & Sofiane Ziani, 2022. "An unreliable single server retrial queue with collisions and transmission errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(4), pages 1085-1109, February.
    4. Dieter Fiems, 2022. "Retrial queues with generally distributed retrial times," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 189-191, April.
    5. Falin, G. I. & Artalejo, J. R., 1998. "A finite source retrial queue," European Journal of Operational Research, Elsevier, vol. 108(2), pages 409-424, July.
    6. Velika I. Dragieva & Tuan Phung-Duc, 2020. "A finite-source M/G/1 retrial queue with outgoing calls," Annals of Operations Research, Springer, vol. 293(1), pages 101-121, October.
    7. Ekaterina Lisovskaya & Ekaterina Fedorova & Radmir Salimzyanov & Svetlana Moiseeva, 2022. "Resource Retrial Queue with Two Orbits and Negative Customers," Mathematics, MDPI, vol. 10(3), pages 1-19, January.
    8. Zidani Nesrine & Djellab Natalia, 2018. "On the multiserver retrial queues with negative arrivals," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 13(2), pages 219-242.
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