Tra c Using M jGj 1 Input Processes : A Compromise Between Markovian and LRD

Statistical evidence suggests that the autocorrelation function (k) (k = 0; 1; : : :) of a compressed-video sequence is better captured by (k) = e ? p k than by (k) = k ? = e ? log k (long-range dependence) or (k) = e ?k (Markovian). A video model with such a correlation structure is introduced based on the so-called M jGj1 input processes. In essence, the M jGj1 process is a stationary version of the busy-server process of a discrete-time M jGj1 queue. By varying G, many forms of time dependence can be displayed, which makes the class of M jGj1 input models a good candidate for modeling many types of correlated traac in computer networks. For video traac, we derive the appropriate G that gives the desired correlation function (k) = e ? p k. Though not Markovian, this model is shown to exhibit short-range dependence. Poisson variates of the M jGj1 model are appropriately transformed to capture the marginal distribution of a video sequence. Using the performance of a real video stream as a reference, we study via simulations the queueing performance under three video models: our M jGj1 model, the fractional ARIMA model 9] (which exhibits LRD), and the DAR(1) model (which exhibits a Markovian structure). Our results indicate that only the M jGj1 model is capable of consistently providing acceptable predictions of the actual queueing performance. Furthermore, only O(n) computations are required to generate an M jGj1 trace of length n, compared to O(n 2) for a F-ARIMA trace.