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Large Deviations of Birth Death Markov Fluids

Published online by Cambridge University Press:  27 July 2009

G. De Veciana ,
C. Olivier  and
J. Walrand
G. De Veciana
Affiliation:
Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, California 94720
C. Olivier
Affiliation:
Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, California 94720
J. Walrand
Affiliation:
Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, California 94720
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Abstract

The asymptotic probability of buffer overflow for a queueing system with a Markov fluid input and deterministic service rate is derived by way of large deviation theory. The equations characterizing the deviant behavior are presented and examples are given for which closed-form solutions may be obtained. An independence result extends the analysis to cases where the input is an aggregate of independent Markov fluids.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 2 , April 1993 , pp. 237 - 255
Copyright
Copyright © Cambridge University Press 1993

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References

1.Anick, D., Mitra, D., & Sondhi, M.M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell System Technical Journal 61: 1871–1894.CrossRefGoogle Scholar
2.Bucklew, J.A. (1990). Large deviation techniques in decision, simulation and estimation. New York: John Wiley and Sons.Google Scholar
3.Cover, T.M. & Thomas, J.A. (1991). Elements of information theory. Wiley Series in Telecommunications.Google Scholar
4.Kesidis, G. (1992). Cell loss estimation in high-speed digital networks. Ph.D. thesis, Department of EECS, University of California, Berkeley.Google Scholar
5.Kesidis, G. & Walrand, J. (to appear). Relative entropy between Markov transition rate matrices. IEEE Transactions on Information Theory.Google Scholar
6.Neuts, M. (1981). Matrix-geometric solutions in stochastic models. Baltimore, MD: John Hopkins University Press.Google Scholar
7.Weiss, A. (1986). A new technique for analyzing large traffic systems. Advances in Applied Probability 18: 506–532.CrossRefGoogle Scholar