An Asymptotic Approximation of TCP CUBIC

TL;DR

This paper develops an asymptotic approximation for the average window size of TCP CUBIC under random packet losses, extending previous deterministic models and validating results through simulations.

Contribution

It introduces a novel asymptotic analysis for TCP CUBIC's window size under random losses using Markov chain convergence, which was not previously available.

Findings

Derived an expression for average window size under random losses.

Validated the approximation through simulations.

Connected deterministic and stochastic loss models for TCP CUBIC.

Abstract

In this paper, we derive an expression for computing average window size of a single TCP CUBIC connection under random losses. Throughput expression for TCP CUBIC has been computed earlier under deterministic periodic packet losses. We validate this expression theoretically. We then use insights from the deterministic loss based model to derive an expression for computing average window size of a single TCP CUBIC connection under random losses. For this computation, we first consider the sequence of TCP CUBIC window evolution processes indexed by the drop rate, p and show that with a suitable scaling this sequence converges to a limiting Markov chain as p tends to 0. The stationary distribution of the limiting Markov chain is then used to derive the average window size for small packet error rates. We validate our model and approximations via simulations.