Complutense University Library

A discrete-time Geo([X])/G/1 retrial queue with control of admission


Artalejo, Jesús R. and Atencia, I. and Moreno, P. (2005) A discrete-time Geo([X])/G/1 retrial queue with control of admission. Applied Mathematical Modelling , 29 (11). pp. 1100-1120. ISSN 0307-904X

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


Official URL:


This paper analyses adiscrete-timeGeo/G/1retrialqueue with batch arrivals in which individual arriving customers have acontrol of admission. We study the underlying Markov chain at the epochs immediately after the slot boundaries making emphasis on the computation of its steady-state distribution. To this end we employ numerical inversion and maximum entropy techniques. We also establish a stochastic decomposition property and prove that the continuous-timeM/G/1retrialqueue with batch arrivals and control of admission can be approximated by our discrete-time system. The outcomes agree with known results for special cases.

Item Type:Article
Additional Information:

The authors thank the referee for his comments on an earlier version of this paper. This research is supported by the DGINV through the project BFM2002-02189.

Uncontrolled Keywords:Control of admission; Discrete-time model; Markov chain; Maximum entropy; Numerical inversion; Stochastic ecomposition
Subjects:Sciences > Mathematics > Operations research
ID Code:15586

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

J.R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Modell. 30 (1999) 1–6.

G.I. Falin, A survey of retrial queues, Queue. Syst. 7 (1990) 127–168.

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

T. Yang, J.G.C. Templeton, A survey on retrial queues,Queue. Syst. 2 (1987) 201–233.

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

T. Yang, H. Li, On the steady-state queue size distribution of the discrete-time Geo/G/1 queue with repeated customers, Queue. Syst. 21 (1995) 199–215.

I. Atencia, P. Moreno, A discrete-time Geo/G/1 retrial queue with general retrial times, Queue. Syst. 48 (2004) 5–21.

I. Atencia, P. Moreno, Discrete-time Geo[X]/GH/1 retrial queue with Bernoulli feedback, Comput. Math. Appl. 47 (2004) 1273–1294.

B.D. Choi, J.W. Kim, Discrete-time Geo1,Geo2/G/1 retrial queueing system with two types of calls, Comput. Math.Appl. 33 (1997) 79–88.

H. Li, T. Yang, Geo/G/1 discrete time retrial queue with Bernoulli schedule, Eur. J. Operat. Res. 111 (1998) 629–649.

H. Li, T. Yang, Steady-state queue size distribution of discrete-time PH/Geo/1 retrial queues, Math. Comput. Model. 30 (1999) 51–63.

M. Takahashi, H. Osawa, T. Fujisawa, Geo[X]/G/1 retrial queue with non-preemptive priority, Asia-Pacific J. Operat. Res. 16 (1999) 215–234.

T. Meisling, Discrete time queueing theory, Operat. Res. 6 (1958) 96–105.

H. Bruneel, B.G. Kim, Discrete-time Models for Communication Systems Including ATM, Kluwer Academic Publishers, Boston, 1993.

J.J. Hunter, Mathematical Techniques of Applied Probability. Discrete-time Models: Techniques and Applications, vol. 2, Academic Press, New York, 1983.

H. Takagi, Queueing analysis: A Foundation of Performance Evaluation. Discrete-time Systems, vol. 3, North-Holland, Amsterdam, 1993.

M.E. Woodward, Communication and Computer Networks:Modelling with Discrete-time Queues, IEEE Computer Society Press, Los Alamitos, California, 1994.

B.D. Choi, Y.W. Shin, W.C. Ahn,Retrial queues with collision arising from unslotted CSMA/CD protocol,Queue. Syst. 11 (1992) 335–356.

M.Y. Kitaev, V.V. Rykov, Controlled Queueing Systems, CRC Press, Boca Raton, 1995.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran. The Art of Scientific Computing, Cambridge University Press, Cambridge, 1992.

J.R.Artalejo,G.I.Falin,M.J.Lopez-Herrero,A second order analysis of the waiting time in the M/G/1 retrial queue, Asia-Pacific J. Operat. Res. 19 (2002) 131–148.

G.I. Falin, M. Martin, J.R. Artalejo, Information theoretic approximations for the M/G/1 retrial queue, Acta Inform. 31 (1994) 559–571.

D.D. Kouvatsos, Entropy maximization and queueing networks models, Ann. Operat. Res. 48 (1994) 63–126.

A.Gravey,G.Hebuterne,Simultaneity in discrete-time single server queues with Bernoulli inputs,Perform.Eval.14 (1992) 123–131.

S.W. Fuhrmann, R.B. Cooper, Stochastic decomposition in the M/G/1 queue with generalized vacations, Operat. Res. 33 (1985) 1117–1129.

J.R. Artalejo, G.I. Falin, Stochastic decomposition for retrial queues, Top 2 (1994) 329–342.

T. Yang, M.J.M. Posner, J.G.C. Templeton, H. Li, An approximation method for the M/G/1 retrial queue with general retrial times, Eur. J. Operat. Res. 76 (1994) 552–562.

J.R. Artalejo, I. Atencia, On the single server retrial queue with batch arrivals, Sankhya: The Indian J. Stat. 66 (2004) 140–158.

H.C. Tijms, A First Course in Stochastic Models, Wiley, Chichester, 2003.

Deposited On:12 Jun 2012 08:15
Last Modified:06 Feb 2014 10:27

Repository Staff Only: item control page