Traffic engineering of IP networks requires the characterization and modeling of network traffic on multiple time scales due to the existence of several statistical properties that are invariant across a range of time scales, such as self-similarity, LRD and multifractality. These properties have a significant impact on network performance and, therefore, traffic models must be able to incorporate them in their mathematical structure and parameter inference procedures.

In this work, we address the modeling of network traffic using a multi-time-scale framework. We evaluate the performance of two classes of traffic models (Markovian and Lindenmayer-Systems based traffic models) that incorporate the notion of time scale using different approaches: directly in the model structure, in the case of the Lindenmayer-Systems based models, or indirectly through a fitting of the second-order statistics, in the case of the Markovian models. In addition, we address the importance of modeling packet size for IP traffic, an issue that is frequently misregarded. Thus, in each class we evaluate models that are intended to describe only the packet arrival process and models that are intended to describe both the packet arrival and packet size processes: specifically, we consider a Markov modulated Poisson process and a batch Markovian arrival process as examples of Markovian models and a set of four Lindenmayer-Systems based models as examples of non Markovian models that are able to perform a multi-time-scale modeling of network traffic. All models are evaluated by comparing the density function, the autocovariance function, the loss ratio and the average waiting time in queue corresponding to measured traces and to traces synthesized from the fitted models. We resort to the well known Bellcore pOct traffic trace and to a trace measured at the University of Aveiro.

The results obtained show that (i) both the packet arrival and packet size processes need to be modeled for an accurate characterization of IP traffic and (ii) despite the differences in the ways Markovian and L-System models incorporate multiple time scales in their mathematical framework, both can achieve very good performance.

CEMAT - Center for Computational and Stochastic Mathematics