Modeling video traffic using M/G/∞ input processes: a compromise between Markovian and LRD models
Marwan Krunz, Armand M. Makowski · IEEE Journal on Selected Areas in Communications · 1998
Statistical evidence suggests that the autocorrelation function p(k) (k=0,1,...) of a compressed-video sequence is better captured by p(k)=e/sup -/spl beta//spl radic/k/ than by p(k)=k/sup -/spl beta//=e/sup -/spl beta/logk/ (long-range dependence) or p(k)=e/sup -/spl beta/k/ (Markovian). A video model with such a correlation structure is introduced based on the so-called M/G//spl infin/ input processes. In essence, the M/G//spl infin/ process is a stationary version of the busy-server process of a discrete-time M/G//spl infin/ queue. By varying G, many forms of time dependence can be displayed, which makes the class of M/G//spl infin/ 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/sup -/spl beta//spl radic/k/. Though not Markovian, this model is shown to exhibit short-range dependence. Poisson variates of the M/G//spl infin/ 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//spl infin/ 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//spl infin/ 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//spl infin/ trace of length n, compared to O(n/sup 2/) for an F-ARIMA trace.