Statistical multiplexing of regulated sources having deterministic subadditive envelopes

We study a single-server queue fed by various kinds of sources, each of which is constrained by a deterministic regulator, e.g., a token bucket. In particular, we derive bounds of virtual-waiting-time distribution only assuming that sources are stationary, statistically independent from each other, and have deterministic subadditive envelopes without using a specific traffic pattern. Based on the derived bounds, we investigate how large statistical multiplexing gain can be achieved when regulated sources share a common network resource. Numerical examples reveal that the regulated sources are more advantageous than Markov arrival processes or long-range-dependent sources with respect to the statistical multiplexing gain.