ofMultiple Time - Scale Markov Streams

We study the problem of statistical multiplexing of cell streams which have correlations at multiple timescales. Each stream is modeled by a singularly perturbed Markov-modulated process with some state transitions occurring much more infrequently than others. One motivation of this model comes from variable-rate compressed video, where the fast timescale dynamics may correspond to correlations between adjacent frames while the slow timescale dynamics may correspond to correlations within the same scene of a video sequence. Another motivation is to use the model to study situations when dynamics of diierent traac streams occur at diierent timescales. We develop a set of large deviations results to estimate the buuer overrow probabilities in various asymptotic regimes in the buuer size, rare transition probabilities and the number of streams. Using these results, we characterize the multiplexing gain in both the channel capacity and the buuering requirements, and highlight the impact of the slow timescale of the streams. It is also shown that while a recently proposed eeective bandwidth concept generalizes naturally to multiple timescale streams in some parameter regimes, in regimes where there are many statistically simliar sources, it becomes overly conservative and has to be replaced by better estimates.