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Numerical calculation of the stationary distribution of the main multiserver retrial queue

Artalejo, Jesús R. and Pozo Juan, Mónica del (2002) Numerical calculation of the stationary distribution of the main multiserver retrial queue. Annals of Operations Research , 116 (1-4). pp. 41-56. ISSN 0254-5330

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Abstract

We are concerned with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. It is known that an analytical solution of this queueing model is difficult and does not lead to numerical implementation. Based on appropriate understanding of the physical behavior, an efficient and numerically stable algorithm for computing the stationary distribution of the system state is developed. Numerical calculations are done to compare our approach with the existing approximations.

Item Type:Article
Additional Information:10th Biannual Latin-Ibero-American Conference on Operations Research and Systems (CLAIO. SEP 04-08, 2000. Mexico City, Mexico
Uncontrolled Keywords:Algorithmic probability, Performance analysis, Retrial queues, Stationary distribution
Subjects:Sciences > Mathematics > Operations research
ID Code:15790
References:

J.R. Artalejo, A queueing system with returning customers and waiting line, Operations Research Letters 17 (1995) 191–199.

J.R. Artalejo, Stationary analysis of the characteristics of the M/M/2 queue with constant repeated attempts, Opsearch 33 (1996) 83–95.

J.R. Artalejo, Accessible bibliography on retrial queues, Mathematical and Computer Modelling 30 (1999) 1–6.

J.R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990–1999, Top 7 (1999) 187–211.

J.R. Artalejo, A. Gomez-Corral and M.F. Neuts, Numerical analysis of multiserver retrial queues operating under a full access policy, in: Advances in Algorithmic Methods for Stochastic Models, eds. G. Latouche and P.G. Taylor (Notable Publications, Inc., 2000).

B.D. Choi, Y.C. Kim and Y.W. Lee, The M/M/c retrial queue with geometric loss and feedback, Computers and Mathematics with Applications 36 (1998) 41–52.

J.W. Cohen, Basic problems of telephone traffic theory and the influence of repeated calls, Phillips Telecommunication Review 18 (1957) 49–100.

G.I. Falin, Calculation of probability characteristics of a multiline system with repeat calls, Moscow University Computational Mathematics and Cybernetics 1 (1983) 43–49.

G.I. Falin and J.R. Artalejo, Approximations for multiserver queues with balking/retrial discipline, OR Spektrum 17 (1995) 239–244.

G.I. Falin and J.G.C. Templeton, Retrial Queues (Chapman and Hall, London, 1997).

A. Gomez-Corral and M.F. Ramalhoto, The stationary distribution of a Markovian process arising in the theory of multiserver retrial queueing systems, Mathematical and Computer Modelling 30 (1999)141–158.

T. Hanschke, A matrix continued fraction algorithm for the multi-server repeated order queue, Mathematical and Computer Modelling 30 (1999) 159–170.

Z. Khalil, G.I. Falin and T. Yang, Some analytical results for congestion in subscriber line modules, Queueing Systems 10 (1992) 381–402.

Y.C. Kim, On M/M/3/3 retrial queueing system, Honam mathematical Journal 17 (1995) 141–147.

C. Langaris, Markovian polling systems with mixed service disciplines and retrial customers, Top 7 (1999) 305–322.

M.F. Neuts and B.M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems 7 (1990) 169–190.

C.E.M. Pearce, Extended continued fractions, recurrence relations and two-dimensional Markov processes, Advances in Applied Probability 21 (1989) 357–375.

M.F. Ramalhoto and A. Gomez-Corral, Some decomposition formulae for M/M/r/r+d queues with constant retrial rate, Stochastic Models 14 (1998) 123–145.

S.N. Stepanov,Markov models with retrials: the calculation of stationary performance measures based on the concept of truncation, Mathematical and Computer Modelling 30 (1999) 207–228.

R.I. Wilkinson, Theories for toll traffic engineering in the U.S.A., The Bell System Technical Journal 35 (1956) 421–514.

Deposited On:28 Jun 2012 08:24
Last Modified:06 Feb 2014 10:31

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