Performance Evaluation Of Network Traffic Based On FBM

Over the last ten years many studies have shown that no matter what topology and traffic, statistics behavior of self-similarity and long-range dependence could be found in all network traffic. The, discovery of the self-similarity of network traffic strongly influence the network traffic modeling, performance evaluation and network control. The results of these studies also show that traditional traffic models, such as Poisson or Markov models, cannot capture the observed features of telecommunication traffic. It is quite necessary to establish new model to reflect the characteristics of self-similar traffic.This thesis firstly introduces the basic concepts of self-similarity and long-range dependence. Several mathematical definitions of self-similarity are given. Some mathematical and physical features describing the self-similar processes are described. Several methods to estimate Hurst parameter are studied. Among the existing traffic models, Fractional Brownian Motion process is the simplest self-similar traffic model. Several mathematical definitions of FBM are given. Some features describing the FBM and algorithms of generating FBM data are described.There are only few results about the performance of FBM model, and lots of problems are still not well solved. In the thesis the problems of FBM-based traffic modeling and performance analysis are deeply studied. Based on the buffer overflow probability given by Norros, the formulas for computing the average queue length, the variance of queue length, average delay, the variance of the delay and the effective bandwidth, under the conditions of infinite buffers are derived. Based on these formulas and the formulas for computing these network performances index under the conditions of finite buffers given by literature [29], the theoretical analysis of network performance is performed through MATLAB.In order to analyze the queuing performance of self-similar traffic and verify the theoretical analysis, a simulation model of FBM-based self-similar traffic network is established. We analyze four algorithms of generating FBM data which all based on the fast Fourier converse transforms of FGN spectral density. The results show that making all negative data be zero can capture the observed features of the real telecommunication traffic very well. Based on the FGN data and the real telecommunication traffic, the simulation analysis of network performance is performed through the simulation model.Finally, the comparison between theoretical analysis of network performance and simulation analysis of network performance is performed. The correctness of the formulas for computing these network performances index is further confirmed. The variance of the system performance indices, such as packet loss probability, average delay, the variance of the delay and the effective bandwidth, with the model parameters, namely Hurst index, buffer size and utilization of the traffic, are studied through theoretical analysis and simulation. The results show that beside Hurst index, several other factors, such as buffer size and utilization strongly influence the system performances. The traditional concept which only consist the influence of Hurst index is not overall, and it may be sometimes misleading.