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

Vyacheslav Abramov ()

Annals of Operations Research, 2006, vol. 141, issue 1, 19-50

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

Keywords: Multiserver retrial queues; Queue-length distribution; Stochastic calculus; Martingales and semimartingales (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-006-5292-x

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