STATISTICAL MULTIPLEXING OF MULTIPLE TIME-SCALE MARKOV STREAMS

We study the problem of statistical multiplexing of cell streams that have correlations at multiple time-scales. Each stream is modeled by a singularly perturbed Markov-modulated process with some state transit ions occurring much less frequently than others. One motivation of thi s model comes from variable-rate compressed video, where the fast time -scale dynamics may correspond to correlations between adjacent frames , while the slow time-scale dynamics may correspond to correlations wi thin the same scene of a video sequence. We develop a set of large dev iations results to estimate the buffer overflow probabilities in vario us asymptotic regimes in the buffer size, rare transition probabilitie s, and the number of streams. Using these results, we characterize the multiplexing gain in both the channel capacity and the buffering requ irements and highlight the impact of the slow time-scale of the stream s.