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Asymptotics of the Exit Distributionfor Markov Jump Processes; Application to Atm

Published online by Cambridge University Press:  20 November 2018

I. Iscoe ,
D. Mcdonald  and
K. Qian
I. Iscoe
Affiliation:
McMaster University, Hamilton, Ontario
D. Mcdonald
Affiliation:
University of Ottawa, Ottawa, Ontario
K. Qian
Affiliation:
University of Ottawa, Ottawa, Ontario
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Abstract

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We approximate the exit distribution of a Markov jump process into a set of forbidden states and we apply these general results to an ATM multiplexor. In this case the forbidden states represent an overloaded multiplexor. Statistics for this overload or busy period are difficult to obtain since this is such a rare event. Starting from the approximate exit distribution, one may simulate the busy period without wasting simulation time waiting for the overload to occur.

Keywords

60J2760K30Exit distributionPerron-FrobeniusDirichlet eigenvalueATMasymptotics

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 6 , 01 December 1994 , pp. 1238 - 1262
Copyright
Copyright © Canadian Mathematical Society 1994

References

[Aldous, D. (1989)] Probability approximations via the Poisson clumping heuristic, Springer-Verlag, New York Inc.Google Scholar
[Iscoe, I. and McDonald, D. (1994)] Asymptotics of exit times for Markov jump processes I, Ann. Probab. (1) 22,372–397.Google Scholar
[Iscoe, I., McDonald, D. and Qian, K. (1993)] Capacity of ATM switches, Ann. Appl. Probab. (2) 3, 277–295.Google Scholar
[Kato, T. (1949)] On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4, 334–339.Google Scholar
[Liggett, T. M. (1989)] Exponential L2 convergence of attractive reversible nearest particle systems, Ann. Prob. (2) 17, 403–432.Google Scholar
[Olver, F. (1974)] Asymptotics and special functions, Academic Press, New York, San Francisco, London.Google Scholar
[Reed, M. and Simon, B. (1978)] Methods of modern mathematical physics Vol. IV: Analysis of operators, Academic Press, New York, San Francisco, London.Google Scholar