Wavelet Based Estimators of Long-range Dependencies in Traffic Traces

It has been shown that Internet traffic possesses a high degree of self-similarity and long-range dependency. Hence, classical statistical models cannot adequately model the fundamental properties of such traffic. The degree of long-range dependency is captured by the Hurst parameter. Various statistical estimators can be used to estimate the long-range dependency and consequently, the Hurst (H) parameter. Such estimation is always based on o bserving mostly the second moment of the processes on various time scales. Wavelets are a mathematical technique that can be used to observe an arbitrary signal on various time scales. In the first part of this project, we applied wavelet based monofractal and multifractal estimators to long-range dependent video traffic traces in order to evaluate the performances of the estimators. In the second part, the same video traces were used as an input to ns-2 simulator in order to observe the packet loss processes. By analyzing the results obtained we are able to conclude that both wavelet estimators provide consistent and useful graphical output. By observing the graphical output we could determine the time scale in the trace, where long range dependency is present. However, the values of H produced by estimator are somewhat unreliable and need to be compared to values of H obtained by other means. By examining the algorithms and procedures used in estimators, we conjecture that the iv underlying assumptions of Gaussian distribution of wavelet coefficient may be the cause of the unstable performance of the estimator. Also, by considering the multifractal properties of the traces, we conjecture that there is a possibility that a single H parameter may not be sufficient to fully describe the self-similarity of a statistical process In the case of the loss process we shown that the loss process, being strongly influenced by the traffic, also possesses a strong degree of self-similarity and long-range dependency. Such long-range dependant behaviour remains unchanged regardless of the buffer size.