Joint Characterization of the Packet Arrival and Packet Size Processes of Multifractal Traffic based on Stochastic L-Systems

Multifractal behavior was recently observed in several traces of IP WAN traffic. This paper proposes a novel multifractal traffic model, which characterizes the joint process of packet arrivals and packet sizes. The construction of the traffic process is based on stochastic L-Systems, which were introduced by biologist A. Lindenmayer as a method to model plant growth. We work with a single L-System alphabet and production rule, where the alphabet is a set of pairs, and each pair element represents a packet arrival rate and a packet mean size. In this way, the traffic model is able to capture correlations between arrivals and sizes, leading to an accurate prediction of the queuing behavior. We provide a detailed comparison with a related multifractal model based on conservative cascades. Our results, that include applying the fitting procedure to real observed data with multifractal scaling behavior on both the packet arrival and packet size processes, show that our L-System based model can achieve excellent fitting performance in terms of first and second order statistics and queuing behavior.