Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T20:59:21.589Z Has data issue: false hasContentIssue false

Overflow Asymptotics for large Communications Systems with General Markov Fluid Sources

Published online by Cambridge University Press:  27 July 2009

Michel Mandjes
Affiliation:
Department of Econometrics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands

Extract

This paper is concerned with overflows in queues fed by Markov fluid input. The results are asymptotic in the number of sources; that is, we let the number of users grow large. The main objectives of this study are to characterize both overflow probability and the “most probable way” in which overflow occurs. Applying large deviations techniques, known results (Weiss, 1986, Advances in Applied Probability 18: 506–532) for exponential on-off sources are extended to general Markov fluid input. Successively, zero, small, and large buffers are treated. Finally, results for multiclass input are given.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Anick, D., Mitra, D., & Sondhi, M.M. (1982). Stochastic theory of data-handling system with multiple sources. Bell System Technical Journal 61: 18711894.CrossRefGoogle Scholar
2.Bucklew, J.A. (1990). Large deviation techniques in decision, simulation, and estimation. New York: Wiley.Google Scholar
3.Dembo, A. & Zeitouni, O. (1993). Large deviations techniques and applications. Boston: Jones and Bartlett.Google Scholar
4.Ellis, R.S. (1985). Entropy, large deviations, and statistical mechanics. Berlin: Springer-Verlag.CrossRefGoogle Scholar
5.Elwalid, A., Heyman, D., Lakshman, T.V., Mitra, D., & Weiss, A. (1995). Fundamental bounds and approximations for ATM multiplexers with applications to videoconferencing. IEEE Journal on Selected Areas in Communications 13: 10041016.CrossRefGoogle Scholar
6.Elwalid, A.I. & Mitra, O. (1993). Effective bandwidth of general Markovian traffic sources and admission control of high speed networks. IEEE/ACM Transactions on Networking 1: 329343.CrossRefGoogle Scholar
7.Freidlin, M.I. & Wentzell, A.D. (1984). Random perturbations of dynamical systems. New York: Springer-Verlag.CrossRefGoogle Scholar
8.Gelfand, I. & Fomin, S. (1963). Calculus of variations. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
9.Hirsch, M.W. & Smale, S. (1974). Differential equations, dynamical systems, and linear algebra. San Diego: Academic Press.Google Scholar
10.Kelly, F.P. (1979). Reversibility and stochastic networks. New York: Wiley.Google Scholar
11.Kesidis, G. & Walrand, J. (1993). Quick simulation of ATM buffers with on-off multiclass Markov fluid sources. A CM Transactions on Modeling and Computer Simulation 3: 269276.CrossRefGoogle Scholar
12.Kesidis, G., Walrand, J., & Chang, C.S. (1993). Effective bandwidths for multiclass Markov fluids and other ATM sources. IEEE/ACM Transactions on Networking 1: 424428.CrossRefGoogle Scholar
13.Kosten, L. (1986). Liquid models for a type of information buffer problem. Delft Progress Report 11.Google Scholar
14.Mandjes, M. & Ridder, A. (1995). Finding the conjugate of Markov fluid processes. Probability in the Engineering and Informational Sciences 9: 297315.CrossRefGoogle Scholar
15.O'Reilly, P. & Ghani, S. (1987). Data performance in burst switching when the voice silence periods have a hyperexponential distribution. IEEE Transactions on Communications 35: 11091112.CrossRefGoogle Scholar
16.Schassberger, R. (1973). Warteschlangen. Berlin: Springer-Verlag.CrossRefGoogle Scholar
17.Shwartz, A. & Weiss, A. (1993). Induced rare events: Analysis via large deviations and time reversal. Advances in Applied Probability 25: 667689.CrossRefGoogle Scholar
18.Shwartz, A. & Weiss, A. (1995), Large deviations for performance analysis, queues, communication, and computing. New York: Chapman and Hall.Google Scholar
19.Tijms, H.C. (1994). Stochastic models, an algorithmic approach. New York: Wiley.Google Scholar
20.Weiss, A. (1986). A new technique of analyzing large traffic systems. Advances in Applied Probability 18: 506532.CrossRefGoogle Scholar