Diffusion approximations for models of congestion control in high-speed networks

We consider simple models of congestion control in high-speed networks and develop diffusion approximations which could be useful for resource allocation. We first show that, if the arrival process is Poisson and the service times are exponential, then, under a certain scaling, the steady-state distribution of the number of sources in the system consists of appropriately normalized and truncated Gaussian and exponential distributions. We then consider the case where the arrival process is a general renewal process with finite coefficient of variation and service-time distributions that are phase-type, and show the impact of these distributions on the steady-state distribution. We use these results to relate the capacity of a bottleneck node to performance measures of interest for best-effort traffic, such as the mean file transfer time or probability of congestion.