This paper presents a detailed statistical analysis of a 2-hour long empirical sample of VBR video traffic generated by compressing an action movie. The main findings include that the marginal bandwidth distribution has heavy-tailed behavior, and the autocorrelation of the VBR video sequence decays hyperbolically, indicating long-range dependence. These characteristics are modeled using self-similar processes. The study develops a new non-Markovian source model for VBR video and presents an algorithm for generating synthetic traffic. Trace-driven simulations show that statistical multiplexing improves bandwidth efficiency even with long-range dependence. The study also highlights the importance of heavy-tailed marginals and long-range dependence in VBR video traffic models, which are not accounted for in current models. The paper discusses the statistical properties of VBR video traffic, including the distribution of bandwidth, burstiness, autocorrelation, and Fourier spectrum. It shows that the bandwidth distribution follows a heavy-tailed Pareto distribution, and that the time correlation structure exhibits long-range dependence. The study also presents methods for estimating the Hurst parameter H, which quantifies the degree of long-range dependence. The results indicate that H is approximately 0.78 for the VBR video trace. The paper develops a source model for VBR video that incorporates both the heavy-tailed marginal distribution and long-range dependence. The model is used to generate synthetic traffic and is compared to trace-driven simulations. The results show that the model accurately captures the statistical properties of VBR video traffic. The study also discusses the implications of long-range dependence for network performance and resource allocation, and highlights the importance of accurate modeling for efficient network design. The paper concludes that long-range dependence has significant implications for traffic modeling and performance analysis, and that accurate modeling is essential for effective network design.This paper presents a detailed statistical analysis of a 2-hour long empirical sample of VBR video traffic generated by compressing an action movie. The main findings include that the marginal bandwidth distribution has heavy-tailed behavior, and the autocorrelation of the VBR video sequence decays hyperbolically, indicating long-range dependence. These characteristics are modeled using self-similar processes. The study develops a new non-Markovian source model for VBR video and presents an algorithm for generating synthetic traffic. Trace-driven simulations show that statistical multiplexing improves bandwidth efficiency even with long-range dependence. The study also highlights the importance of heavy-tailed marginals and long-range dependence in VBR video traffic models, which are not accounted for in current models. The paper discusses the statistical properties of VBR video traffic, including the distribution of bandwidth, burstiness, autocorrelation, and Fourier spectrum. It shows that the bandwidth distribution follows a heavy-tailed Pareto distribution, and that the time correlation structure exhibits long-range dependence. The study also presents methods for estimating the Hurst parameter H, which quantifies the degree of long-range dependence. The results indicate that H is approximately 0.78 for the VBR video trace. The paper develops a source model for VBR video that incorporates both the heavy-tailed marginal distribution and long-range dependence. The model is used to generate synthetic traffic and is compared to trace-driven simulations. The results show that the model accurately captures the statistical properties of VBR video traffic. The study also discusses the implications of long-range dependence for network performance and resource allocation, and highlights the importance of accurate modeling for efficient network design. The paper concludes that long-range dependence has significant implications for traffic modeling and performance analysis, and that accurate modeling is essential for effective network design.