Extremal traffic and bounds for the mean delay of multiplexed regulated traffic streams

In this paper, we present simple performance bounds for multiplexed regulated traffic streams, which are leaky-bucket regulated with peak, mean rate and burst size constraints. We consider independent, heterogeneous streams, which are multiplexed in a common buffer. We derive bounds on the mean delay in the deterministic context and we then obtain a simple stochastic bound, which is exact when the number of sources increases. A byproduct is a characterization of the worst case sources for mean delay, when they are leaky bucket regulated.