Modeling video traffic using M/G/∞ input processes: a compromise between Markovian and LRD models

Statistical evidence suggests that the autocorrelation function p(k) (k=0,1,...) of a compressed-video sequence is better captured by p(k)=e^{-β√k} than by p(k)=k^-β=e^-βlogk (long-range dependence) or p(k)=e^-βk (Markovian). A video model with such a correlation structure is introduced based on the so-called M/G/∞ input processes. In essence, the M/G/∞ process is a stationary version of the busy-server process of a discrete-time M/G/∞ queue. By varying G, many forms of time dependence can be displayed, which makes the class of M/G/∞ input models a good candidate for modeling many types of correlated traffic in computer networks. For video traffic, we derive the appropriate G that gives the desired correlation function p(k)=e^{-β√k}. Though not Markovian, this model is shown to exhibit short-range dependence. Poisson variates of the M/G/∞ 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/G/∞ model, the fractional ARIMA model (which exhibits LRD), and the DAR(1) model (which exhibits a Markovian structure). Our results indicate that only the M/G/∞ model is capable of consistently providing acceptable predictions of the actual queueing performance. Furthermore, only O(n) computations are required to generate an M/G/∞ trace of length n, compared to O(n²) for an F-ARIMA trace