Transient analysis applied to traffic modeling

Traffic modeling has been an extensive area of research in the last few years, and a lot of modeling effort has been devoted to better understand the issues involved in multiplexing traffic over high speed links. The goals of the performance analyst include the development of accurate traffic models to predict, with sufficient accuracy, the impact of the traffic generated by applications over the network resources, and the evaluation of the quality of service (QoS) being achieved. Performance studies include determining buffer behavior, evaluate cell loss probability, admission control algorithms, and many others.One performance study issue is the calculation of descriptors from different traffic models. In the literature, one can find a large number of models that have been proposed, including Markov and non-Markovian models [1]. Although not possessing the long-range dependence property, Markov models are still attractive not only due to their mathematical tractability but also because it has been shown that long-range correlations can be approximately obtained from certain kinds of Markovian models (e.g. [11]). Furthermore, works such as [8] show that Markov models can be used to accurately predict performance metrics.Once a set of traffic models is chosen, the modeler should obtain the desired performance measures. Hopefully the measures should be calculated analytically using efficient algorithms.The modeling steps briefly outlined above may require the transient analysis of general Markovian models, including Markov reward models. One of the goals of this work is to present new algorithms we developed to obtain efficiently measures such as the transient queue length distribution (and from that, the packet loss ratio as a function of time) directly from the model of the source feeding the queue. We also obtain second order descriptors such as the index of dispersion and the autocovariance from the source models. Using these algorithms the modeler can evaluate the efficacy of different Markovian models to predict performance metrics.