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Algorithmic approximations for the busy period distribution of the M/M/c retrial queue

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Artalejo, Jesús R. and Economou, A. and López Herrero, María Jesús (2007) Algorithmic approximations for the busy period distribution of the M/M/c retrial queue. European journal of operational research, 176 (3). pp. 1687-1702. ISSN 0377-2217

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Official URL: http://www.sciencedirect.com/science/article/pii/S0377221705008684


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Abstract

In this paper we deal with the main multiserver retrialqueue of M/M/c type with exponential repeated attempts. This model is known to be analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused by the retrial feature. For this reason several models have been proposed for approximating its stationary distribution, that lead to satisfactory numerical implementations. This paper extends these studies by developing efficient algorithmic procedures for calculating the busyperioddistribution of the main approximation models of Wilkinson [Wilkinson, R.I., 1956. Theories for toll traffic engineering in the USA, The Bell System Technical Journal 35, 421–514], Falin [Falin, G.I., 1983. Calculations of probability characteristics of a multiline system with repeated calls, Moscow University Computational Mathematics and Cybernetics 1, 43–49] and Neuts and Rao [Neuts, M.F., Rao, B.M., 1990. Numerical investigation of a multiserver retrial model, Queueing Systems 7, 169–190]. Moreover, we develop stable recursive schemes for the computation of the busyperiod moments. The corresponding distributions for the total number of customers served during a busyperiod are also studied. Several numerical results illustrate the efficiency of the methods and reveal interesting facts concerning the behavior of the M/M/cretrialqueue.


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The authors thank the support received from the research project MTM2005-01248. A. Economou was supported by the University of Athens grant ELKE/70/4/6415 and by the Greek Ministry of Education and European Union program PYTHAGORAS/2004.

Uncontrolled Keywords:Queueing; M/M/c retrial queue; Generalized truncation models; Busy period; First-step analysis;Numerical inversion; Algorithmic probability
Subjects:Sciences > Mathematics > Operations research
ID Code:15455
Deposited On:01 Jun 2012 10:47
Last Modified:18 Feb 2019 10:48

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