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Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer

Author

Listed:
  • Nesrine Zidani

    (University Chadli Bendjedid El-Tarf)

  • Natalia Djellab

    (University of Annaba)

Abstract

The paper deals with Markovian multiserver retrial queuing system with exponential abandonments, two types of arrivals: Fresh calls and Handover calls and waiting places in the service area. This model can be used for analysing a cellular mobile network, where the service area is divided into cells. In this paper, the number of customers in the system and in the orbit form a level-dependent quasi-birth-and-death process, whose stationary distribution is expressed in terms of a sequence of rate matrices. First, we derive the Taylor series expansion for nonzero elements of the rate matrices. Then, by the expansion results, we obtain an asymptotic upper bound for the stationary distribution of both the number of busy channels and the number of customers in the orbit. Furthermore, we present some numerical results to examine the performance of the system.

Suggested Citation

  • Nesrine Zidani & Natalia Djellab, 2024. "Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(3), pages 365-407, June.
    • Handle: RePEc:spr:mathme:v:99:y:2024:i:3:d:10.1007_s00186-024-00865-0
    DOI: 10.1007/s00186-024-00865-0
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    References listed on IDEAS

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    1. Phung-Duc, Tuan, 2015. "Asymptotic analysis for Markovian queues with two types of nonpersistent retrial customers," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 768-784.
    2. loane Muni Toke, 2014. "On completion times in a two-class priority queue with impatience," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(3), pages 377-392.
    3. Tuan Phung-Duc, 2014. "Multiserver Retrial Queues With Two Types Of Nonpersistent Customers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-27.
    4. Amit Choudhury & Pallabi Medhi, 2011. "Balking and reneging in multiserver Markovian queuing system," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(4), pages 377-394.
    5. Kazuki Kajiwara & Tuan Phung-Duc, 2016. "Multiserver Queue with Guard Channel for Priority and Retrial Customers," International Journal of Stochastic Analysis, Hindawi, vol. 2016, pages 1-23, March.
    6. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
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