Markov models of internet traffic and a new hierarchical MMPP model

Abstract

The first part of this paper gives a short tutorial survey of Internet traffic modeling, focusing on recent advances in Markov models showing pseudo-LRD (Long Range Dependence) characteristics that match those measured on the Internet. The interest in Markov models of Internet traffic, in spite of the impossibility to achieve true LRD or Self-Similarity, lies in the possibility of exploiting powerful analytical techniques to predict the network performance, which is the ultimate goal when adopting models to either study existing networks or design new ones. Then, the paper describes a new MMPP (Markov Modulated Poisson Process) traffic model that accurately approximates the LRD characteristics of Internet traffic traces over the relevant time scales. The heart of the model is based on the notion of sessions and flows, trying to mimic the real hierarchical generation of packets in the Internet. The proposed model is simple and intuitive: its parameters have a physical meaning, and the model can be tuned with only a few input parameters. Results prove that the queuing behavior of the traffic generated by the MMPP model is coherent with the one produced by real traces collected at our institution edge router under several different traffic loads. Due to its characteristics, the proposed MMPP traffic model can be used as a simple and manageable tool for IP network dimensioning, design and planning: the paper provides examples of its application in both simulative and theoretical analysis.