| Network traffic analysis and modeling play a major role in charactering network performance, so it has been a focus of many researches. Models that accurately capture the salient characteristics of the traffic is useful for analysis and simulation, and they further our understanding of network dynamics, so it has a fundamental meaning for many network designs and engineering problems, e.g., the traffic balance scheme, router, switcher designing, the manage devices and its support software developing.Recently, communication and network technologies are developing rapidly, it brings the traffic characteristics to change greatly, and the main changes are shown as follow:(1) The drastic increasing of the amount of the data-The Internet has beengrowing exponentially. This growth has occurred both in the number of hosts connected to Internet, and the amount of traffic produced by each host.(2) The changing of the service functions-Recently, more and more.differentiated services such as multi-media and VOD are widely deployed in Internet.(3) The development of mobile and wireless technology-The access ofmany wireless users has changed the original characteristics of the traffic.The development of network technology has brought many new problems for the network researches. As for the traffic characterization and modeling, the problems are as follow:(1) The high link capacity of the network will allow us to zoom into small-time scale (below 100ms) and middle-time scale (100ms—1s) and perform reliable data analysis. This is different from the traditional analysis method at the large-time scale (1s and above).(2) Video and audio traffic has their own characteristics which are different from the Internet traffic, so the widely deployed multi-media technology will lead new problems to traffic characterization and modeling. The traditional analysis method and models need to be modified.(3) The access of many mobile and wireless users will lead some new problems such as multi-path shading and frequency selecting. Wavelet transform is a time-scale analysis method which has a multi-resolution analysis function. It can capture the local behaviors of the signal both in time and frequency fields. The method can change its window's shape while hold the window's size the same, and it can also change the time window and frequency window at the same time. It is a time-frequency localization analysis method, i.e., at the part of low frequency, it has higher frequency resolution and lower time resolution, and at the part of high frequency, it has lower frequency resolution and higher time resolution. So it is suitable for detecting the burst phenomena in the signal. It is a microscope for signal analysis.Based on wavelet analysis method and multi-fractal theory, we have done some research works on traffic characterization and modeling. They are as follow:(1) The performance of several Hurst parameter estimate algorithms is studied and the influence of SRD to these algorithms is analyzed.(2) The behaviors of MPEG-4 video traces are studied, and based on the results, the video traces are simulated using multi-fractal wavelet model. The performance of the model is evaluated and the influence of mother wavelet selection and vanishing moment selection to the performance of the model is also studied.(3) Multi-scale analysis is done to the network traffic. The stationary, Poisson, Gaussian, LRD, and multi-fractal behaviors of the traffic at the small-time scale are studied in detail. Based on the Alpha, Beta separation scheme, some research works are done to identify the potential causing factors of the non-stationary and non-LRD behavior of the traffic at the small-time scale.The research results can be summarized in following:(1) The robustness of 5 Hurst parameter estimate algorithms is studied and the principle which we should obey when using these methods to study the LRD behavior of traffic is presented.(2) The influence of SRD to the performance of 5 Hurst parameter estimate algorithms is studied and a method which can eliminate this influence is presented. The method is called aggregate analysis method.(3) The LRD behavior of MPEG-4 video traces is studied and the results show that the burstiness is the main causes. Based on the results, the MPEG-4 video trace is simulated using multi-fractal wavelet model and its performance is evaluated. The results show that multi-fractal wavelet model is a good model for characterizing MPEG-4 video trace. It can capture the global behavior of the traffic perfectly, but its ability to capture the local behavior of the traffic become weaker when the burstiness of the traffic become stronger.(4) The influence of mother wavelet selection and vanishing moment selection to the performance of the MWM model is studied. The results show that they both have influence to the performance of MWM model. The influence of mother wavelet selection is the bigger.(5) The stationary, Poisson, Gaussian, LRD, and multi-fractal behaviors of the traffic at the small-time scale are studied. The results show that the traffic exhibits non-stationary, non-Gaussian, non-LRD and Poisson distribution behaviors at the small-time scale. The results also show that the multi-fractal behavior is not uniform, for the relatively low capacity link (several kbps), the traffic exhibits multi-fractal behavior, but for the high capacity link (several Gbps), the traffic exhibits mono-fractal behavior.(6) The non-stationary and non-LRD causing factors are studied at the small-time scale, the results show that Dense flow is the main causing factor of the non-LRD. From the global view, the Dense flow is the main causing factor of non-stationary, but from the local view, the Alpha flow is the main causing factor of non-stationary.In this dissertation, combined with the fractal theory, the wavelet is used as a tool, to make a detailed analysis to the traffic. Based on the results, the traffic simulation is made using MWM model. This study provides a useful way for the traffic characterization and modeling. Especially in this dissertation, much more researches are done to the small-time scaling (1s and down) behaviors of the traffic, which is differ from the conventional works which focus on the large-time scaling (1s and above) behaviors, and the non-stationary and non-LRD behaviors causing factors at the small-time scale were found. This study is helpful for the recently construction works of the high-speed network. Finally, the dissertation summarizes the to-be-resolved problems and point out the emphasis of the further research.
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