Journal of Applied Probability

Asymptotic behavior of a generalized TCP congestion avoidance algorithm

Teunis J. Ott and Jason Swanson

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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 {Wn}, where Wn 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.

Article information

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

First available in Project Euclid: 13 September 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G10: Stationary processes 60H10: Stochastic ordinary differential equations [See also 34F05] 60J05: Discrete-time Markov processes on general state spaces

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


Ott, Teunis J.; Swanson, Jason. Asymptotic behavior of a generalized TCP congestion avoidance algorithm. J. Appl. Probab. 44 (2007), no. 3, 618--635. doi:10.1239/jap/1189717533.

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