Matching Multi - Fractal Process Parameters Against Real Data

Recent analyses of real data/internet tra c indicate that data tra c exhibits long-range dependence as well as self-similar or multi-fractal properties. By using mathematical models of Internet tra c that share these properties we can perform analytical studies of network tra c. This gives us an opportunity to analyse potential bottlenecks and estimate delays in the networks. Processes with multi-fractal properties can be modeled by multiplying the output of Markov Modulated Rate Processes (MMRP) [1] each de ned by four parameters. The MMRP are easily used in stochastic uid ow modeling. This model is also suited for analysis of other tra c types e.g. VoIP and thus, it allows for integration of di erent tra c types, i.e. time-sensitive voice tra c with best-e ort data trafc. Using this model we can calculate performance parameters for each individual stream that enters the system/model. In this paper we show how to construct a multifractal process that is matched to measured data from MMRP sub processes.