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Queueing system with a constant retrial rate, non-reliable server and threshold-based recovery

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  • Efrosinin, Dmitry
  • Winkler, Anastasia

Abstract

In this paper, we examine a Markovian queueing system which is composed of a retrial queue with constant retrial rate and a non-reliable server. Upon arrival a customer occupies the server if it is idle, otherwise it goes to the retrial queue. The customer at the head of the retrial queue is allowed to retry for service. When the server is busy, the server is subject to breakdowns or failures that occur according to a Poisson process. In the failed state the server can be repaired at a repair facility with exponential repair time with respect to the threshold policy: the repair starts when the number of customers in the system reaches some prespecified threshold level q [greater-or-equal, slanted] 1. We perform a steady-state analysis of the corresponding continuous-time Markov chain, derive mean performance characteristics and waiting time distribution as well as calculate optimal threshold level to minimize the long-run average losses for the given cost structure.

Suggested Citation

  • Efrosinin, Dmitry & Winkler, Anastasia, 2011. "Queueing system with a constant retrial rate, non-reliable server and threshold-based recovery," European Journal of Operational Research, Elsevier, vol. 210(3), pages 594-605, May.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:3:p:594-605
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    References listed on IDEAS

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    1. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
    2. Artalejo, J. R. & Gomez-Corral, A. & Neuts, M. F., 2001. "Analysis of multiserver queues with constant retrial rate," European Journal of Operational Research, Elsevier, vol. 135(3), pages 569-581, December.
    3. 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.
    4. 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. Dmitry Efrosinin & Anastasia Winkler & Pinzger Martin, 2015. "Confidence Intervals for Performance Measures of M/M/1 Queue with Constant Retrial Policy," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-12, December.
    2. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    3. Konstantin Avrachenkov & Evsey Morozov, 2014. "Stability analysis of GI/GI/c/K retrial queue with constant retrial rate," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 273-291, June.
    4. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    5. Jain, Madhu & Bhagat, Amita & Shekhar, Chandra, 2015. "Double orbit finite retrial queues with priority customers and service interruptions," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 324-344.
    6. Chen, Wu-Lin & Wang, Kuo-Hsiung, 2018. "Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 476-486.
    7. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik, 2023. "Robustness of the cμ -Rule for an Unreliable Single-Server Two-Class Queueing System with Constant Retrial Rates," Mathematics, MDPI, vol. 11(18), pages 1-14, September.

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