A Multifractal Wavelet Model of Network Traffic

In this paper, a new Multifractal Wavelet Model (MWM) is studied and simulation results are presented. We conclude that MWM has captured most of the properties of network traffic and the computational complexity of MWM is only O(N). The efficiency of MWM makes it possible in the real-time applications. 1.Introduction Network traffic modeling is one of the key topics in the application of network and multimedia. Taking the multimedia download as an example, a well-designed model will help make use of the network efficiently and speed up the transmission of data. One of key issues of multimedia download is how to model the communication channels. This is because after we get the accurate information, like distribution of the network delay, about channel, we may optimally distribute the multimedia data and fetch them by optimal download strategy. The more accurate the information is, the better we may find the strategy. Here we concern the accuracy of the network information in a statistical sense. What we like to know is how to predict the real-time delay of each link over which the data is transmitting, which has the close relation with network traffic modeling. Lots of research that have been done is based on measurement data upon a specific Internet connection [13][14]. They tried to use currently existed models to match measured data, such as AR model, Bernulli model, 2-state Markov chain model, and k-th order Markov chain model. Although these methods give some solutions to prediction of network delay, nobody has concluded whether or not these methods can be generalized to any kinds of Internet situations. Actually we know the Internet channel is so complex that these conventional statistical methods really cannot capture the rich properties of Internet [3]. Nonetheless, a bunch of researchers in Rice University are doing the challenging jobs with excellent insight [1]. By introducing the concepts of multifractal into Internet traffic model, they build a multifractal model that matches the traffic properties, such as Long-range dependency, self-similarity and burstiness, very well. Wavelets are used as a natural tool to analyze and synthesize the model due to its inherent multiscaling property. Based on these ideas, a