Asymptotic Approximations for TCP Compound

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.Comment: Longer version for NCC 201

How Fast Can Dense Codes Achieve the Min-Cut Capacity of Line Networks?

In this paper, we study the coding delay and the average coding delay of random linear network codes (dense codes) over line networks with deterministic regular and Poisson transmission schedules. We consider both lossless networks and networks with Bernoulli losses. The upper bounds derived in this paper, which are in some cases more general, and in some other cases tighter, than the existing bounds, provide a more clear picture of the speed of convergence of dense codes to the min-cut capacity of line networks.Comment: 15 pages, submitted to IEEE ISIT 201