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Asymptotic Behavior of a Generalized TCP Congestion Avoidance Algorithm

Part of: Limit theorems Markov processes Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Teunis J. Ott  and
Jason Swanson
Teunis J. Ott*
Affiliation:
Rutgers University
Jason Swanson*
Affiliation:
University of Wisconsin-Madison
*
∗Postal address: WINLAB, Rutgers University, New Brunswick, NJ 07930, USA. Email address: ott@winlab.rutgers.edu
∗∗Postal address: Mathematics Department, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI 53706-1388, USA. Email address: swanson@math.wisc.edu
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Abstract

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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.

Keywords

Weak convergencestochastic differential equationstationary distributionTCP/IPcongestion avoidance

MSC classification

Secondary: 60F05: Central limit and other weak theorems 60G10: Stationary processes 60H10: Stochastic ordinary differential equations 60J05: Discrete-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 618 - 635
Copyright
Copyright © Applied Probability Trust 2007 

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