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A repairable retrial queue under Bernoulli schedule and general retrial policy

Author

Listed:
  • Shan Gao

    (Beijing Jiaotong University
    Fuyang Normal College)

  • Jinting Wang

    (Beijing Jiaotong University)

  • Tien Van Do

    (Budapest University of Technology and Economics)

Abstract

This paper considers a repairable M/G/1 retrial queue with Bernoulli schedule and a general retrial policy, which is motivated by a contention problem in the downlink direction of wireless base stations in cognitive radio networks. Arriving Customers (called primary arrivals) who cannot receive service upon arrival either join the infinite waiting space in front of the server (called as the normal queue) with probability $$q$$ q , or enter the orbit with probability $$1-q$$ 1 - q according to the FCFS discipline. If the server breaks down in the process of the service of a customer, the customer in service either joins the orbit queue or leaves the system forever. First, we study the ergodicity of two related embedded Markov chains and derive stationary distributions. Second, we find the steady-state joint generating function of the number of customers in both queues. Some important performance measures of the system are obtained. Third, the reliability analysis of the system is also given. Finally, numerical examples are given to illustrate the impact of system parameters on the system performance measures.

Suggested Citation

  • Shan Gao & Jinting Wang & Tien Van Do, 2016. "A repairable retrial queue under Bernoulli schedule and general retrial policy," Annals of Operations Research, Springer, vol. 247(1), pages 169-192, December.
    • Handle: RePEc:spr:annopr:v:247:y:2016:i:1:d:10.1007_s10479-015-1885-6
    DOI: 10.1007/s10479-015-1885-6
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    References listed on IDEAS

    as
    1. Gao, Shan & Wang, Jinting, 2014. "Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers," European Journal of Operational Research, Elsevier, vol. 236(2), pages 561-572.
    2. B. Kumar & A. Vijayakumar & D. Arivudainambi, 2002. "An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume," Annals of Operations Research, Springer, vol. 113(1), pages 61-79, July.
    3. Wang, Jinting & Liu, Bin & Li, Jianghua, 2008. "Transient analysis of an M/G/1 retrial queue subject to disasters and server failures," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1118-1132, September.
    4. Li, Hui & Yang, Tao, 1998. "Geo/G/1 discrete time retrial queue with Bernoulli schedule," European Journal of Operational Research, Elsevier, vol. 111(3), pages 629-649, December.
    5. I. Atencia & G. Bouza & P. Moreno, 2008. "An M [X] /G/1 retrial queue with server breakdowns and constant rate of repeated attempts," Annals of Operations Research, Springer, vol. 157(1), pages 225-243, January.
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    Cited by:

    1. Sanga, Sudeep Singh & Jain, Madhu, 2019. "Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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