Modeling network traffic using Cauchy correlation model with long-range dependence. (English) Zbl 1076.90010
Summary: Much attention has been given to the long-range dependence and fractal properties in network traffic engineering, and these properties are also widely observed in many fields of science and technologies. Traffic time series is conventionally characterized by its fractal dimension $D$, which is a measure for roughness, and by the Hurst parameter $H$, which is a measure for long-range dependence. Each property has been traditionally modeled and explained by self-affine random functions, such as fractional Gaussian noise (FGN) and fractional Brownian motion (FBM), where a linear relationship between $D$ and $H$, say $D=2-H$ for one-dimensional series, links the two properties. The limitation of single parameter models (e.g., FGN) in long-range dependent (LRD) traffic modeling has been noticed. Hence, models which can provide good fitting of LRD traffic for both short-term lags and long-term ones are worth studying due to the importance of accurate models of traffic in network communications. This letter utilizes a statistical model called the Cauchy correlation model to model LRD traffic. This model characterizes $D$ and $H$ separately, and it allows any combination of two within the constraint of LRD condition. It is a new power-law correlation model for LRD traffic modeling with its local and global behavior decoupling. Its flexibility in data modeling in comparison with a single parameter model of FGN is briefly discussed, and applications to LRD traffic modeling demonstrated.