  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.
