Asymptotic behavior of a generalized TCP congestion avoidance algorithm

Teunis J. Ott and Jason Swanson

Source: J. Appl. Probab. Volume 44, Number 3 (2007), 618-635.

Abstract

The transmission control protocol (TCP) is a transport protocol used in the Internet. In Ott (2005), a more general class of candidate transport protocols called `protocols in the TCP paradigm' was introduced. The long-term objective of studying this class is to find protocols with promising performance characteristics. In this paper we study Markov chain models derived from protocols in the TCP paradigm. Protocols in the TCP paradigm, as TCP, protect the network from congestion by decreasing the `congestion window' (i.e. the amount of data allowed to be sent but not yet acknowledged) when there is packet loss or packet marking, and increasing it when there is no loss. When loss of different packets are assumed to be independent events and the probability p of loss is assumed to be constant, the protocol gives rise to a Markov chain {W_n}, where W_n is the size of the congestion window after the transmission of the nth packet. For a wide class of such Markov chains, we prove weak convergence results, after appropriate rescaling of time and space, as p → 0. The limiting processes are defined by stochastic differential equations. Depending on certain parameter values, the stochastic differential equation can define an Ornstein-Uhlenbeck process or can be driven by a Poisson process.

Primary Subjects: 60F05

Secondary Subjects: 60G10, 60H10, 60J05

Keywords: Weak convergence; stochastic differential equation; stationary distribution; TCP/IP; congestion avoidance

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Permanent link to this document: http://projecteuclid.org/euclid.jap/1189717533
Digital Object Identifier: doi:10.1239/jap/1189717533
Mathematical Reviews number (MathSciNet): MR2355580

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