STABILITY OF RETRIAL QUEUЕING SYSTEM M/D/1 WITH LOSSES

Authors

  • O. V. Koba V. M. Glushkov Institute of Cybernetics

DOI:

https://doi.org/10.18372/1990-5548.47.10435

Keywords:

Call, retrial queueing system, stability, queueing system, waiting time

Abstract

A stability condition is derived for a retrial queueing system with a Poisson input withparameter  and constant service time. If the virtual waiting time is less than a constant a, thenthe call can be serviced; otherwise, it is repeated in exponentially distributed time or is lost with aprobability q. The notion of system stability is defined. Two theorems are proved, defined theconditions for stability of system

Author Biography

O. V. Koba, V. M. Glushkov Institute of Cybernetics

DSc (Phys. and Math.). Associate Professor. Leading researcher. Department of mathematical methods in reliability theory of complex systems

References

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

J. A. Artolejo and A. Gomez-Corral, Retrial Queueing Sistems: A Computational Approach, Springer-Verlag, Berlin—Heidelberg, 2008.

T. Yang and J. G. C. Templeton, “A survey on retrial queues,” Queueing Systems, no. 3, 201–233, 1987.

G. Falin, “A survey of retrial queues,” Queueing Systems, no. 7, 127–167, 1990.

J. Artalejo, “A classified bibliography of research in retrial queueing.” Progress in 1990-1999. Top. no. 7, 1999. pp. 187–211.

J. Artalejo, “A classified bibliography of research in retrial queueing.” Progress in 2000-2009. Mathematical and Computer Modeling, vol 51, 2010, pp. 1071–1081.

S. V. Pustova, “Investigation of call centers as retrial queueing systems”, Cybern. Syst. Analysis, vol. 46, no. 3, pp. 494–499, 2010.

S. F. Yashkov, Queue Analysis in a Computer, Radio i Svyaz', Moscow, 1989. [in Russian]

D. Yu. Kuznetsov and A. A.Nazarov, Adaptive random access network, Deltaplan, Tomsk, 2002. [in Russian] 10. L. Lacatos, “On a simple continuous cyclic-waiting problem." Ann. Univ. Sci.. Budapest Sect. Comp., no. 14, pp. 105–113, 1994.

B. V. Gnedenko and I. N. Kovalenko, An Introduction to Queuing Theory, Komkniga, Moscow, 2005. [in Russian]

P.P. Bocharov and A. V. Pechenkin, Queueing Theory, Izd. RUDN. Moscow, 1995. [in Russian]

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Issue

Vol. 1 No. 47 (2016)

Section

MATHEMATICAL MODELING OF PROCESSES AND SYSTEMS

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