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

Statistical evidence suggests that the autocorrelation function rho(kappa) (kappa = 0, 1, ...) of a compressed-video sequence is better captured by rho(kappa) = e(-beta root kappa) than by rho(kappa) = kappa(-beta) = e(-beta log kappa) (long-range dependence) or rho(kappa) = e(-beta kappa) (Markovian). A video model with such a correlation structure is introduced based on the so-called M/G/infinity input processes. In essence, the M/G/infinity process is a stationary version of the busy-server process of a discrete-time M/G/infinity queue. By varying G, many forms of time dependence can be displayed, which makes the class of M/G/infinity 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 rho(kappa) = e(-beta root kappa). Though not Markovian, this model is shown to exhibit short-range dependence, Poisson variates of the M/G/infinity 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/infinity 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/G/infinity 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/infinity trace of length n; compared to O(n(2)) for an F-ARIMA trace.