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Lecture Series |
How should flows through a network be organized, so that the system responds sensibly to differing user requirements and to failures and overloads? The question is currently of considerable technological importance for communication networks, while in various other forms it has a long history in the fields of physics and economics. In all of these areas there is interest in how simple, local rules, often involving random actions, can produce coherent and purposeful behaviour at the macroscopic level. The first lecture describes some examples from these various fields, and indicates how analogies with fundamental concepts such as energy and price can provide powerful insights into the design of communication networks.
Network routing.
Philosophical Transactions of the Royal Society A337 (1991) 343-367.
Work on large deviations has
provided an elegant means to summarize the statistical haracteristics of
sources over different time and space scales, in terms of an effective
bandwidth. We discuss the use of the theory, in a connection-oriented network,
as a basis for simple tariffing and connection acceptance control mechanisms
for poorly characterized traffic.
Notes on effective
bandwidths. In Stochastic Networks: Theory and Applications (Editors
F.P. Kelly, S. Zachary and I.B. Ziedins) Royal Statistical Society Lecture
Notes Series, 4. Oxford University Press, 1996. 141-168.
This lecture will discuss
the stability and fairness of rate control algorithms for communication
networks. Additive increase/multiplicative decrease schemes are shown to be
stable about a system optimum characterized by a proportional fairness
criterion. Stability is established by showing that an appropriate formulation
of an overall optimization problem provides a Lyapunov function for the
dynamical system defined by the rate control algorithm. The optimization
problem may be cast in primal or dual form: this leads to two classes of
algorithm, which may be interpreted in terms of either congestion indication
feedback signals or explicit rates based on shadow prices. Both classes of
algorithm provide natural implementations of proportionally fair pricing, and
can be viewed as "charge-aware" developments of, respectively,
Jacobson's TCP algorithm and ATM available bit rate algorithms.
Rate control in
communication networks: shadow prices, proportional fairness and stability.
Frank P. Kelly, Aman Maulloo and David Tan. Journal of the Operational
Research Society 49 (1998) 237-252.
As an application of the
earlier theory, the final lecture will discuss ways in which the transmission
control protocol of the Internet may evolve to support heterogeneous
applications. The claim will be made that by appropriately marking packets at
overloaded resources and by charging a fixed small amount for each mark
received, end-nodes are provided with the necessary information and the correct
incentive to use the network efficiently.
Resource pricing and the
evolution of congestion control.
R.J. Gibbens and Frank P. Kelly. Automatica 35 (1999) 1969-1985.
Global Optimization with End-to-End
Congestion Control: Pointers to the Literature. Sally Floyd and Jeonghoon Mo
Congestion
Pricing and a Distributed Game.
Peter Key