grantor:
University of TorontoWe propose a new model for network heavy-traffic approximation) based on Ã-Stable self-similar processes, namely the skewed Linear Fractional Stable Noise. The model is long-range dependent and demonstrates more flexibility than existing models in fitting different levels of burstiness and dependence in the data. Nonetheless, it is parsimonious in the number of parameters, which have a direct physical meaning. The marginal distribution of the model is Ã-Stable, and therefore the Generalized Central Limit Theorem can be applied to provide a physical interpretation on how aggregate effects in traffic appear as a superposition of traffic from independent sources. We present an algorithm for the estimation of the model parameters, which is based on properties of the Totally Skewed Ã-Stable distribution. We investigate the implications of our proposed modeling on the estimation of bandwidth allocation and admission control of bursty, long-range dependent sources. Analytic formulas for the overflow probability bounds of a constant service rate buffer are derived, and they are used to provide bounds of the required bandwidth allocation of Ã-Stable self-similar sources, for which the general theory of effective bandwidths does not apply. Extensive simulations are presented, where the new model is fitted to bursty Ethernet and variable-bit-rate video data. Furthermore, new measurements of aggregate web and web-casting traffic are introduced along with traffic generated by the fitted new model. Queueing simulations with real traffic support our analytical results for the overflow probability. The expression of the upper bandwidth allocation bound is simple and allows quick computation of admissible regions for multiplexed homogeneous or heterogeneous sources entering the network. Our analytical results for the equivalent rate bounds are verified with extended simulation studies with real and model generated traffic. In the context of predicting rare events, such as cell losses in networks, more efficiently, we present a new method for fast simulation of rare events which follow an Ã-Stable distribution. The proposed method provides considerable reduction in the number of samples required for accurate estimation, compared to a Monte-Carlo simulation. Furthermore, the variance of the estimator can be three orders of magnitude smaller than the traditional Mean-Translation method in the Importance Sampling framework.Ph.D
