# American Institute of Mathematical Sciences

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August  2005, 5(3): 543-564. doi: 10.3934/dcdsb.2005.5.543

## Asymptotic properties of a TCP model with time-outs

 1 Department of Mathematics, Åbo Akademi University, 20500 Åbo, Finland, Finland

Received  February 2004 Revised  August 2004 Published  May 2005

We examine a simple discrete time Markov model of TCP congestion control, which contains congestion avoidance, fast retransmit and time-out, and we prove that it has a unique invariant measure. If the process is scaled by a factor $\sqrt{p}$, then the invariant measures converge as $p \to 0$, where $p$ is the probability of error in any given data packet. This is the $1/\sqrt{p}$-behavior of TCP throughput.
If the scaled process is transformed to continuous time, we show that it converges to a piecewise linear limit process. The unique invariant measure of the limit process coincides with the limit of the invariant measures above and can be easily computed.
Finally, we examine a slightly more sophisticated way of modelling time-outs.
Citation: Niclas Carlsson, Göran Högnäs. Asymptotic properties of a TCP model with time-outs. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 543-564. doi: 10.3934/dcdsb.2005.5.543
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