Statistical Multiplexing of Multiple Time-Scale Markov Streams

We study the problem of statistical multiplexing of cell streams which have correlations at multiple time-scales. Each stream is modeled by a singularly perturbed Markovmodulated process with some state transitions occurring much more infrequently than others. We develop a set of large deviations results to estimate the buffer overflow probabilities in various asymptotic regimes in the buffer size, rare transition probabilities and the number of streams. Using these results, we characterize the multiplexing gain in both the channel capacity and the buffering requirements, and highlight the impact of the slow time-scale of the streams. It is also shown that while a recently proposed effective bandwidth concept generalizes naturally to multiple time-scale streams in some parameter regimes, in other regimes it breaks down and has to be replaced by better estimates.