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Asymptotic Behaviour of an Integrated Video-Data Network

Published online by Cambridge University Press:  27 July 2009

P. J. Hunt
P. J. Hunt
Affiliation:
Statistical Laboratory University of Cambridge, Cambridge CB2 1SB, England
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Abstract

We consider a communication network that can support both wideband video calls and narrowband data traffic. First we consider a single link and prove a weak convergence result to justify a piecewise-deterministic Markov process approximation to the system. We then generalize this approximation to allow priorities and more than one link. This second approximation is a generalization of the Erlang fixed-point approximation for loss networks and is justified via a diverse routing limit theorem.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 4 , October 1991 , pp. 429 - 447
Copyright
Copyright © Cambridge University Press 1991

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References

Anick, D., Mitra, D., & Sondhi, M.M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell Systems Technical Journal 61: 1871–1894.CrossRefGoogle Scholar
Billingsley, p. (1968). Convergence of probability measures. New York: Wiley.Google Scholar
Costa, O.L.V. (1990). Stationary distributions for piecewise-deterministic Markov processes. Journal of Applied Probability 27: 60–73.CrossRefGoogle Scholar
Davis, M.H.A. (1984). Piecewise-deterministic Markov processes: A general class of non-diffusion stochastic models. Journal of the Royal Statistical Society B 46: 353–388.Google Scholar
Ethier, S.N. & Kurtz, T.G. (1986). Markov processes: Characterization and convergence. New York: Wiley.CrossRefGoogle Scholar
Gaver, D.P. & Lehoczky, J.P. (1982). Channels that cooperatively service a data stream and voice messages. IEEE Transactions on Communications COM-30.CrossRefGoogle Scholar
Hunt, P.J. (1989). Loss networks under diverse routing, II: L-symmetric networks. University of Cambridge, Cambridge, England.Google Scholar
Hunt, P.J. (1990). Limit theorems for stochastic loss networks. Ph.D. thesis, University of Cambridge, Cambridge, England.Google Scholar
Kelly, F.P. (1986). Blocking probabilities in large circuit-switched networks. Advances in Applied Probability 18: 473–505.CrossRefGoogle Scholar
Kraimeche, B. & Schwartz, M. (1985). Analysis of traffic access control strategies in integrated service networks. IEEE Transactions on Communications COM-33: 1085–1093.Google Scholar
Kurtz, T.G. (1989). Averaging for martingale problems and stochastic approximation. University of Wisconsin-Madison.Google Scholar
Leon-Garcia, A., Kwong, R.H., & Williams, G.F. (1982). Performance evaluation methods for an integrated voice/data link. IEEE Transactions on Communications COM-30.CrossRefGoogle Scholar
Parthasarathy, K.R. (1967). Probability measures on metric spaces. New York and London: Academic Press.CrossRefGoogle Scholar
Schwartz, M. (1987). Telecommunication networks. Reading, MA: Addison-Wesley.Google Scholar
Whitt, W. (1980). Some useful functions for functional limit theorems. Mathematics of Operations Research 5: 67–85.CrossRefGoogle Scholar
Whitt, W. (1985). Blocking when service is required from several facilities simultaneously. AT&T Technical Journal 64: 1807–1856.Google Scholar
Yamaguchi, T. & Akiyama, M. (1970). An integrated hybrid traffic switching system mixing preemptive wideband and waitable narrowband calls. Electronics and Communications in Japan 53-A: 43–52.Google Scholar
Ziedins, I. B. (1985). Blocking in queuing and loss systems. Knight Prize Essay, University of Cambridge, Cambridge, England.Google Scholar