| Rapid advances in computer and telecommunication technologies in the past decade have created the possibility of merging digital telephony, data communication and multimedia applications services into a single integrated services digital network. To efficiently utilize the network, traffic modeling and queueing analysis for various types of traffic are crucial. Recent statistical analysis on various types of network traffic has revealed that network traffic has long-range dependence and a non-Gaussian marginal distribution. These characteristics invalidate traditional traffic models and analysis which are usually for short-range dependent and Gaussian marginally distributed traffic. Therefore, open questions include (1) how to model long- and short-range dependent network traffic accurately and efficiently, (2) how to model higher-order statistics in non-Gaussian traffic, and (3) how to analyze the buffer overflow probability for non-Gaussian traffic. In this thesis, we present models and analysis to tackle these open problems.;To accurately model and efficiently synthesize network traffic, we present wavelet models in the first part of the thesis. As opposed to existing methods which model network traffic in the time domain, we model network traffic in the wavelet domain. We demonstrate that the strengths of wavelet models are: (1) wavelet models have the ability to reduce temporal dependence so significantly that either independent or Markov models in the wavelet domain can be used to model long- and short-range dependent network traffic, (2) wavelet models provide a unified approach to modeling both long-range and short-range dependence in network traffic simultaneously, (3) wavelet models result in computationally efficient methods to generate high quality synthesized traffic, (4) wavelet models make it feasible to analyze modeling performance, and (5) wavelet models can provide time-scale modeling for non-Gaussian network traffic. Specifically, we show the correlation structure of the wavelet coefficients of long- and short-range dependent Gaussian traffic, and demonstrate experimentally the strengths of wavelet models through modeling well-known long-range and short-range dependent Gaussian processes. Then we analyze the performance of the wavelet models and show analytically that a simple wavelet model based on independent wavelet coefficients yields sufficient accuracy in predicting the buffer overflow probability and modeling the auto-correlation function. Any other wavelet model which captures additional correlations in the wavelet domain only improves the performance marginally. Finally, we develop algorithms for the wavelet models to model non-Gaussian network traffic and periodic MPEG video traffic accurately.;To analyze theoretically how non-Gaussian distributed traffic affects the buffer overflow probability, we propose a gamma model and derive the buffer overflow probability for the gamma model in the second part of the thesis. We demonstrate how the non-Gaussian model influences the estimated buffer overflow probability compared with the Gaussian model. We show that the gamma model significantly improves the estimation accuracy of the concerned network resources for real network traffic. |
