Asymptotic behavior of a generalized TCP congestion avoidance algorithm

Abstract

The Transmission Control Protocol (TCP) is a Transport Protocol used in the Internet. Ott has introduced a more general class of candidate Transport Protocols called "protocols in the TCP Paradigm". The long run objective of studying this larger class is to find protocols with promising performance characteristics. This paper studies Markov chain models derived from protocols in the TCP Paradigm. Protocols in the TCP Paradigm, as TCP, protect the network from congestion by reducing the "Congestion Window" (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 n-th packet. For a wide class of such Markov chains, we prove weak convergence results, after appropriate rescaling of time and space, as p tends to 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.