Complutense University Library

Computational analysis of the maximal queue length in the MAP/M/c retrial queue

Artalejo, Jesús R. and Chakravarthy, S. R. (2006) Computational analysis of the maximal queue length in the MAP/M/c retrial queue. Applied Mathematics and Computation, 183 (2). pp. 1399-1409. ISSN 0096-3003

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:

View download statistics for this eprint

==>>> Export to other formats


We consider a multi-server retrial queueing model in which arrivals occur according to a Markovian arrival process. Using continuous-time Markov chain with absorbing states, we determine the distribution of the maximum number of customers in a retrial orbit. Illustrative numerical examples that reveal some interesting results are presented.

Item Type:Article
Uncontrolled Keywords:Markovian arrival process; Retrial; Busy period; Queueing; Algorithmic probability
Subjects:Sciences > Mathematics > Operations research
ID Code:15500

A.S. Alfa, K.P. Sapna Isotupa, An M/PH/k retrial queue with finite number of sources, Computers and Operations Research 31 (2004) 1455–1464.

J.R. Artalejo, G.I. Falin, Standard and retrial queueing systems: A comparative analysis, Revista Matematica Complutense 15 (2002) 101–129.

J.R. Artalejo, J.R., A. Economou, M.J. Lopez-Herrero, Algorithmic analysis of the maximum queue length in a busy period for the M/M/c retrial queue, Informs Journal on Computing, in press.

L. Breuer, A.N. Dudin, V.I. Klimenok, A retrial BMAP/PH/N system, Queueing Systems 40 (2002) 433–457.

S.R. Chakravarthy, The batch Markovian arrival process: A review and future work, in: A. Krishnamoorthy et al. (Eds.), Advances in Probability Theory and Stochastic Processes, Notable Publications Inc., NJ, 2000, pp. 21–39.

S.R. Chakravarthy, A.N. Dudin,Amulti-server retrial queue withBMAParrivals and group services, Queueing Systems 42 (2002) 5–31.

S.R. Chakravarthy, A.N. Dudin, Analysis of a retrial queuing model with MAP arrivals and two types of customers, Mathematical and Computer Modelling 37 (2003) 343–363.

S.R. Chakravarthy, A multi-server queueing model with Markovian arrivals and multiple thresholds, Asia-Pacific Journal of Operational Research, in press.

S.R. Chakravarthy, A. Krishnamoorthy, V.C. Joshua, Analysis of a multi-server queue with search of customers from the orbit, Performance Evaluation 63 (2006) 776–798.

B.D. Choi, Y. Chang, MAP1, MAP2/M/c with retrial queue with the retrial group of finite capacity and geometric loss, Mathematical and Computer Modelling 30 (1999) 99–113.

B.D. Choi, Y. Chang, B. Kim, MAP1, MAP2/M/c retrial queue with guard channels and its application to cellular networks, Top 7 (1999) 231–248.

J.E. Diamond, A.S. Alfa, Matrix analytic methods for a multi-server retrial queue with buffer, Top 7 (1999) 249–266.

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

A. Gomez-Corral, On extreme values of orbit lengths in M/G/1 queues with constant retrial rate, OR Spectrum 23 (2001) 395–409.

A. Gomez-Corral, A bibliographical guide to the analysis of retrial queues through matrix analytic techniques, Annals of Operations Research 141 (2006) 163–191.

M.J. Lopez-Herrero, M.F. Neuts, The distribution of the maximum orbit size of anM/G/1 retrial queue during a busy period, in: J.R. Artalejo, A. Krishnamoorthy (Eds.), Notable Publications Inc., NJ, 2002, pp. 219–231.

D.M. Lucantoni, New results on the single server queue with a batch Markovian arrival process, Stochastic Models 7 (1991) 1–46.

M. Marcus, H. Minc, A Survey of Matrix Theory and Matrix Inequalities, Allyn & Bacon, Boston, MA, 1964.

M.F. Neuts, The distribution of the maximum length of a Poisson queue during a busy period, Operations Research 12 (1964) 281–285.

M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, MD, 1981.

M.F. Neuts, Structured Stochastic Matrices of M/G/1 type and their Applications, Marcel Dekker, NY, 1989.

M.F. Neuts, Models based on the Markovian arrival process, IEICE Transactions on Communications E75B (1992) 1255–1265.

R.F. Serfozo, Extreme values of birth and death processes and queues, Stochastic Processes and their Applications 27 (1988) 291–306.

Y.W. Shin, Multi-server retrial queue with negative customers and disasters, in: B.D. Choi (Ed.), Proceedings of the Fifth

International Workshop on Retrial Queues, TMRC, Korea University, Seoul, 2004, pp. 53–60.

Deposited On:06 Jun 2012 08:18
Last Modified:13 May 2014 17:22

Repository Staff Only: item control page