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 sources are ON-OFF type with exponential ON and OFF times, then, under a certain scaling, the steady-state distribution of the number of active sources can be described by a combination of two appropriately truncated and renormalized normal distributions, For the case where the source arrival process is Poisson and the service times are exponential, the steady-state distribution 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-tine distributions that are phase type, and show the impact of these distributions on the steady-state distribution of the number of sources in the system. We also establish an insensitivity to ser,ice-time distribution when the arrival process is Poisson, 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.