Journal
ADVANCES IN APPLIED PROBABILITY
Volume 34, Issue 1, Pages 85-111Publisher
APPLIED PROBABILITY TRUST
DOI: 10.1239/aap/1019160951
Keywords
TCP; convergence of invariant probabilities; autoregressive processes; hitting times; network protocols
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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.
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