Investigating Multi-Fractality of Network Traffic Using Local Hurst Function

Long-range dependence (LRD) and self-similarity (SS) are two basic properties of network traffic time series. Fractional Brownian motion (fBm) and its increment process fractional Gaussian noise (fGn) are commonly used to model traffic with the Hurst index H that determines both the regularity of the sample paths and the long memory property of traffic. However, it appears too restrictive for traffic modeling since it can only model sample paths with the same smoothness for all time parameterized by a constant H. A natural extension of fBm is multifractional Brownian motion (mBm), which is indexed by a time-dependent Hurst index H(t). The main objective of this paper is to interpret the multi-fractality of traffic using H(t) on a point-by-point basis. The numerically demonstrated results for H(t) of real traffic show that H(t) of traffic is time-dependent, providing an alternative evidence of the multifractal phenomena of traffic.