1 Neural Network Modeling of a Class of ON-OFF Source Models with Self-Similar Characteristics Homayoun Yousefi’zadeh Center for Pervasive Communications Electrical and Computer Engineering Department University of California, Irvine Irvine, CA 92697 hyousefi@uci.edu Abstract— The significant characteristic of bursty traf- fic is self-similarity. Self-similarity is the main reason for observing the burst within burst patterns across a wide range of time scales. This is one of the unique charac- teristics of nonlinear systems with fractal nature. Percep- tron neural networks, because of their nonlinear nature and simple method of learning, provide a powerful tool to model such kind of traffic patterns. In this paper, we intro- duce a novel scheme for the modeling task of source- and aggregated-level self-similar traffic patterns relying on the prediction power of perceptron neural networks. We also present and discuss some of the experimental findings. In- dex Terms— Perceptron Neural Networks, Back Propaga- tion Algorithm, Packet Network, Bursty Traffic, ON-OFF Source, Self-Similarity, Traffic Modeling. I. I NTRODUCTION T ELETRAFFIC analysis of of computer commu- nication networks is one of the most important applications of mathematical modeling and queuing theory. This is mostly because of the widespread de- ployment of packet switching, specifically, services from Ethernet LANs, Variable Bit Rate (VBR) video, ATM, and ISDN. Modeling of bursty traffic patterns is among the most challenging problems in teletraffic analysis. Although, numerous models of packet ar- rival processes were proposed by Ramaswami et al. [8], Hellstern et al. [9], Sriram et al. [10], Heffes et al. [11], it seems that there is still a number of packet traffic features not being understood perfectly. This is partly due to uncertainties in the traffic characteris- tics and to the difficulties in characterizing the traffic arrival models. Adas [17] provided a survey of dif- ferent teletraffic models in his paper. Analysis of traffic data from networks and services such as Ethernet LANs [7], Variable Bit Rate (VBR) video [12], ISDN traffic [9], and Common Channel Signaling Network (CCNS) [14], have all convinc- ingly demonstrated the presence of features such as self-similarity, long range dependence, slowly de- caying variances, heavy-tailed distributions and frac- tal dimensions which are among the characteristics of fractal processes. Leland and Wilson from Bell- core research center presented a statistical analysis of Ethernet traffic, on the presence of ”burstiness” across a wide range of time scales [7] in which traf- fic spikes ride on the longer term ripples, that in turn ride on longer term swells, so on and so forth. This phenomenon is explained in terms of self-similarity, i.e., self-similar phenomena show structural similar- ities across all or a very wide range of time scales. This burst within burst structure not only captures the fractal properties observed in actual traffic data but also explains why measurements show no actual burst length for the packet traffic pattern despite pre- diction of conventional models. Chaos is a phenomenon observed in nonlinear dy- namical systems and may be described as a situation in which a low order system is able to exhibit a very complicated behavior. For this reason, chaos used to be called deterministic noise. Since the trajectories of chaotic systems are mostly fractals, they may be used as very suitable generators of fractals. From the modeling point of view, the challenge is to capture the complexity of bursty traffic pattern with a small number of parameters of a chaotic map. Erramilli et al [3] used a number of simple nonlinear maps in or- der to capture some of the real traffic patterns char- acteristics. Giovanardi et al. [15] used self-similar