Framework based on stochastic L-Systems for modeling IP traffic with multifractal behavior

This paper presents and compares a set of traffic models, and associated parameter fitting procedures, based on so-called stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. Starting from an initial symbol, an L-System generates iteratively sequences of symbols, belonging to an alphabet, through successive application of production rules. In a traffic modeling context, the symbols are interpreted as packet arrival rates or mean packet sizes, and each iteration is associated to a finest time scale of the traffic. These models are able to capture the multiscaling and multifractal behavior sometimes observed in Internet traffic. We describe and compare four traffic models, one characterizing the packet arrival process, and the other three characterizing both the packet arrival and the packet size processes. The models are tested with several measured traffic traces: the well-known pOct Bellcore, a trace of aggregate WAN traffic and two traces of specific applications (Kazaa and Operation Flashing Point). We assess the multifractality of these traces using Linear Multiscale Diagrams. The traffic models are evaluated by comparing, for the measured traffic and for traffic generated according to the inferred models, the probability mass function, the autocovariance function and the queuing behavior. Our results show that the L-System based traffic models that characterize both the packet arrival and packet size processes can achieve very good fitting performance in terms of first- and second-order statistics and queuing behavior.