Modelling telecommunications networks

Frank Kelly - Thursday 9 July 1998

14th AUSTRALIAN STATISTICAL CONFERENCE

This talk will describe work on the stochastic modelling of communication networks. Throughout the century problems from this field have provided an impetus to the development of probability theory, pure and applied. The emergence of the Internet and the current deployment of broadband networks are just the latest examples where the pace of technological change is generating exciting challenges for mathematical modellers.

The talk will discuss two specific topics. First, I plan to outline the idea of an effective bandwidth, describing how the theory of large deviations has provided a concept that summarizes the statistical characteristics of traffic streams over different time and space scales, and simplifies the modelling of statistical multiplexing under quality of service constraints. Secondly, I shall describe very recent work on the modelling of elastic traffic, rate control algorithms, charging and proportional fairness.

References:

Loss networks .
Annals of Applied Probability, 1 (1991), 319-378.
Notes on effective bandwidths .
In "Stochastic Networks: Theory and Applications" (Editors F.P. Kelly, S. Zachary and I.B. Ziedins) Oxford University Press, 1996. 141-168.
Rate control in communication networks: shadow prices, proportional fairness and stability.
Frank Kelly, Aman Maulloo and David Tan
Journal of the Operational Research Society 49 (1998) 237-252.
Resource pricing and the evolution of congestion control .
Richard Gibbens and Frank Kelly

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