Abstract

Self similar models capture the stochastic fractal nature of Variable Bit Rate (VBR) sequences which exhibit both long memory and short memory. Long Range Dependence (LRD) has been found to be much significant if the system operates in relatively large time scales whereas Short Range Dependence (SRD) seems to be more prominent when the system has short memory with small buffer sizes of till about 1000 cells. Long memory results into a familiar burstiness, even at low resolutions, thus, having consequences to loss probability and to mean queuing delay. The best models for LRD include the Deterministic Chaotic maps, Fractional Gaussian Noise, as well as models of ON/OFF sources. These are either aggregated or with ON and OFF periods distributed according to heavy tailed marginals. On the other hand, the best models for SRD include most classical models such as the Markovian and autoregressive/moving average models and their combinations. Models are now needed that are parsimonious yet capturing the intrinsic properties of multimedia traffic. To the best of our knowledge there are no models that capture both LRD and SRD. This work, therefore, aimed at deriving a marginal probability distribution of packet sizes of VBR video sequences which exhibit both long range and short range dependencies of typical video sequences. An extensive study of the statistical properties of packet sizes of VBR video sequences coupled with the application of the Principle of Maximum Entropy and Stochastic Programming were employed where two important results were obtained. Firstly, the data was found to assume a Product Log (Lambert W) probability distribution. Secondly, the derived probability distribution suggests that the sequences are intrinsically fractal in nature, complex stochastic processes, and possibly, more amenable to circular statistics.