Asymptotic Approximations for TCP Compound

TL;DR

This paper develops an asymptotic approximation for TCP Compound throughput under random packet losses, validating a deterministic model and deriving a limit process for small error rates that matches simulation results.

Contribution

It introduces a novel asymptotic approximation method for TCP Compound throughput under random losses, extending deterministic models with a limit Markov chain analysis.

Findings

The deterministic window evolution is periodic and initial-independent.

The scaled window process converges to a unique stationary distribution.

The approximation closely matches ns2 simulation results.

Abstract

In this paper, we derive an approximation for throughput of TCP Compound connections under random losses. Throughput expressions for TCP Compound under a deterministic loss model exist in the literature. These are obtained assuming the window sizes are continuous, i.e., a fluid behaviour is assumed. We validate this model theoretically. We show that under the deterministic loss model, the TCP window evolution for TCP Compound is periodic and is independent of the initial window size. We then consider the case when packets are lost randomly and independently of each other. We discuss Markov chain models to analyze performance of TCP in this scenario. We use insights from the deterministic loss model to get an appropriate scaling for the window size process and show that these scaled processes, indexed by p, the packet error rate, converge to a limit Markov chain process as p goes to 0. We show the existence and uniqueness of the stationary distribution for this limit process. Using the stationary distribution for the limit process, we obtain approximations for throughput, under random losses, for TCP Compound when packet error rates are small. We compare our results with ns2 simulations which show a good match.