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A Markovian analysis of additive-increase multiplicative-decrease algorithms

Part of: Special processes Computer system organization Operations research and management science

Published online by Cambridge University Press:  19 February 2016

Vincent Dumas ,
Fabrice Guillemin  and
Philippe Robert
Vincent Dumas*
Affiliation:
Université Bordeaux
Fabrice Guillemin*
Affiliation:
France Télécom
Philippe Robert*
Affiliation:
INRIA
*
∗ Postal address: INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France.
∗∗ Postal address: France Télécom R&D, DAC/CPN, 2, Avenue Pierre Marzin, 22 300 Lannion, France.
∗ Postal address: INRIA, Domaine de Voluceau, BP 105, 78153 Le Chesnay Cedex, France.
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Abstract

The additive-increase multiplicative-decrease (AIMD) schemes designed to control congestion in communication networks are investigated from a probabilistic point of view. Functional limit theorems for a general class of Markov processes that describe these algorithms are obtained. The asymptotic behaviour of the corresponding invariant measures is described in terms of the limiting Markov processes. For some special important cases, including TCP congestion avoidance, an important autoregressive property is proved. As a consequence, the explicit expression of the related invariant probabilities is derived. The transient behaviour of these algorithms is also analysed.

Keywords

TCPconvergence of invariant probabilitiesautoregressive processeshitting timesnetwork protocols

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 90B18: Communication networks 68M12: Network protocols

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 1 , March 2002 , pp. 85 - 111
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Partly supportedby contract 00-1B320 with France Télécom andthe Future andEmer ging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT).

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