The window distribution of idealized TCP congestion avoidance with variable packet loss

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Abstract
This paper analyzes the stationary behavior of the TCP con- gestion window performing ideal congestion avoidance when the packet loss probability is not constant, but varies as a function of the window size. By neglecting the detailed window behavior during fast recovery, we are able to derive a Markov process that is then approximated by a continuous-time, continuous state-space process. The stationary distribution of this process is analyzed and derived numerically and then extrapolated to obtain the stationary distribution of the TCP window. This numerical analysis enables us to predict the behavior of the TCP congestion window when interact- ing with a router port performing Early Random Drop (or Random Early Detection) where the loss probability varies with the queue occupancy. Keywords—TCP, distribution, variable, loss. I. INTRODUCTION In this paper, we present a quantitative analysis of the sta- tionary behavior of the evolution of the TCP congestion window ( ) ((1)) when the packet loss probability is variable and depends on the (instantaneous) window of the TCP connection. It can, thus, be viewed as a generalization of the analysis in ((2)) where the drop probability was assumed constant. The mathe- matical model abstracts TCP behavior into a continuous cycle of "congestion avoidance", packet loss and "fast recovery". We disregard the details of fast recovery ((7)) of TCP and assume an idealized behavior, whereby a packet loss that occurs when the congestion window is MSSs instantaneously reduces the con- gestion window (and the number of unacknowledged packets) to 2 MSSs. The dynamics of window evolution can then be cap- tured by a discrete-time Markov process with state-dependent conditional transition probabilities. Mathematically speaking, we consider the stochastic process 1, where stands for the congestion window just after the good acknowledgement packet (one that advances the left marker of TCP's sliding window) has arrived at the source. By disregarding time-outs and the behavior during fast recovery, this is a discrete-time Markov process with the following behavior: 1 1 1

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