Modeling Network Traffic with Multifractal Behavior

The traffic engineering of IP networks requires accurate characterization and modeling of network traffic, due to the growing diversity of multimedia applications and the need to efficiently support QoS differentiation in the network. In recent years several types of traffic behavior, that can have significant impact on network performance, were discovered: longrange dependence, self-similarity and, more recently, multifractality. The extent to which a traffic model needs to incorporate each of these characteristics is still the subject of much research. In this work, we address the modeling of network traffic multifractality by evaluating the performance of four models, which cover a wide range of traffic types, as mathematical descriptors of measured traffic traces showing multifractal behavior. We resort to traffic traces measured both at the University of Aveiro and at a Portuguese ISP. For the traffic models, we selected a Markov modulated Poisson process as an example of a Markovian model, the well known fractional Gaussian noise model as an example of a self-similar process and two examples of models that are able to capture multifractal behavior: the conservative cascade and the L-system. All models are evaluated comparing the density function, the autocovariance and the loss ratio queuing behavior of the measured traces and of traces synthesized from the fitted models. Our results show that the fractional Gaussian noise model is not able to perform a good fitting of the first and second order statistics as well as the loss rate queuing behavior, whereas the Markovian, the conservative cascade and the L-system models give similar and very good results. The cascade and the L-system models are intrinsically multifractal in the sense that they are able to capture and synthesize traffic multifractality, thus the obtained results are not surprising. The good performance of the Markovian model can be attributed to the parameter fitting procedure, that aggregates distinct sub-processes operating in different time scales, and matches closely both the first and second order statistics of the traffic. The poor performance of the self-similar model can be explained mainly by its lack of parameters.