IMCS/Publications/CSJM/Issues/CSJM v.12, n.2 (35), 2004/

On the Chaotic Behavior of Variable-Bit-Rate Video and Its Application in Traffic Modeling

Authors: Marwan Krunz, Ahmad Alkhatib
Keywords: Chaos theory, traffic analysis, variable-bit-rate video, embedding dimension.


Nonlinear chaos-based modeling offers an alternative approach to stochastic (typically, linear) approaches, with the advantages of lower dimensionality and more determinism. In this paper, we investigate the presence of chaos in variable-bit-rate (VBR) video and explore its application in traffic synthesis and forecasting. We provide statistical evidence that points to the potential chaoticity of VBR video time series. Our evidence is based on the sensitivity of the trajectories to initial conditions, the correlation coefficient between the transformed video sequence (after filtering out any apparent autocorrelations) and a predicted version of it, and the estimated value of the maximum Lyapunov exponent. Accurate forecasting of the future values of a presumably chaotic time series requires good estimation of the embedding dimension. We present a novel approach for estimating the embedding dimension of a suspectedly chaotic time series that is modeled according to the nonlinear functional relationship of Farmer and Sidorowich [10]. Our approach indicates that the minimum embedding dimension in video sequences is seven. Using this estimate along with a modified forecasting approach of the one in [10], we generate synthetic video sequences and show that they exhibit chaotic behavior.

Marwan Krunz, Ahmad Alkhatib
Department of Electrical and Computer Engineering,
University of Arizona, Tucson, AZ 85721,
Phone: (520) 621-8731
E-mail :


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