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Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution

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  • Vyacheslav Abramov

Abstract

The paper studies a multiserver retrial queueing system withm servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon arrival all servers are busy, then the customer goes to the secondary queue, orbit, and after some random time retries more and more to occupy a server. A service time of each customer is exponentially distributed random variable with parameter μ 1 . A time between retrials is exponentially distributed with parameter μ 2 for each customer. Using a martingale approach the paper provides an analysis of this system. The paper establishes the stability condition and studies a behavior of the limiting queue-length distributions as μ 2 increases to infinity. As μ 2 →∞, the paper also proves the convergence of appropriate queue-length distributions to those of the associated “usual” multiserver queueing system without retrials. An algorithm for numerical solution of the equations, associated with the limiting queue-length distribution of retrial systems, is provided. Copyright Springer Science + Business Media, Inc. 2006

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  • Vyacheslav Abramov, 2006. "Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution," Annals of Operations Research, Springer, vol. 141(1), pages 19-50, January.
    • Handle: RePEc:spr:annopr:v:141:y:2006:i:1:p:19-50:10.1007/s10479-006-5292-x
    DOI: 10.1007/s10479-006-5292-x
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    References listed on IDEAS

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    6. Bong Choi & Yong Chang & Bara Kim, 1999. "MAP 1 , MAP 2 /M/c retrial queue with guard channels and its application to cellular networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 231-248, December.
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    Cited by:

    1. Lyes Ikhlef & Ouiza Lekadir & Djamil Aïssani, 2016. "MRSPN analysis of Semi-Markovian finite source retrial queues," Annals of Operations Research, Springer, vol. 247(1), pages 141-167, December.
    2. Rami Atar & Anat Lev-Ari, 2018. "Optimizing buffer size for the retrial queue: two state space collapse results in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 225-255, December.

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