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A NOTE ON THE BUSY PERIOD OF THE M/G/1 QUEUE WITH FINITE RETRIAL GROUP

Published online by Cambridge University Press:  15 December 2006

Jesus R. Artalejo
Affiliation:
Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain, E-mail: jesus_artalejo@mat.ucm.es; antonio_gomez@mat.ucm.es
A. Gómez-Corral
Affiliation:
Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain, E-mail: jesus_artalejo@mat.ucm.es; antonio_gomez@mat.ucm.es

Abstract

We consider an M/G/1 retrial queue with finite capacity of the retrial group. We derive the Laplace transform of the busy period using the catastrophe method. This is the key point for the numerical inversion of the density function and the computation of moments. Our results can be used to approach the corresponding descriptors of the M/G/1 queue with infinite retrial group, for which direct analysis seems intractable.

Type
Research Article
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Artalejo, J.R., Economou, A., & Lopez-Herrero, M.J. (2006). Algorithmic approximations for the busy period of the M/M/c retrial queue. European Journal of Operational Research, to appear.
Artalejo, J.R. & Falin, G.I. (1996). On the orbit characteristics of the M/G/1 retrial queue. Naval Research Logistics 43: 11471161.Google Scholar
Artalejo, J.R. & Lopez-Herrero, M.J. (2000). On the busy period of the M/G/1 retrial queue. Naval Research Logistics 47: 115127.Google Scholar
Falin, G.I. & Templeton, J.G.C. (1997). Retrial queues. London: Chapman & Hall.
Kleinrock, L. (1975). Queueing systems. Vol. I: Theory. New York: Wiley.
Lopez-Herrero, M.J. (2006). A maximum entropy approach for the busy period of the M/G/1 retrial queue. Annals of Operations Research 141: 271281.Google Scholar
Tijms, H.C. (2003). A first course in stochastic models. Chichester: Wiley.CrossRef
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