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Title

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

Author(s)

Abramov, Vyacheslav M.

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 μ1. A time between retrials is exponentially distributed with parameter μ2 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 μ2 increases to infinity. As μ2→∞, 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.

Publication type

Journal article

Source

Annals of Operations Research, Vol. 141, no. 1 (Jan 2006), pp. 19-50

Publication year

2006

FOR Code(s)

01 Mathematical Sciences;  08 Information and Computing Sciences;  15 Commerce, Management, Tourism and Services

Keyword(s)

Martingales and semimartingales;  Multiserver retrial queues;  Queue-length distribution;  Stochastic calculus

Publisher

Springer

ISSN

0254-5330

Publisher URL

http://dx.doi.org/10.1007/s10479-006-5292-x

Copyright

Copyright © Springer Science + Business Media, Inc. 2006. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. The definitive version is available at www.springer.com.

Full text

Peer reviewed