A hybrid approach for generating fractional Brownian motion

Abstract

Self-similar traffic models have been found to be more appropriate for the representation of bursty telecommunication traffic. The fractional Brownian motion (FBM) processes is one of the two most commonly used traffic models to interpret self-similarity. The discrete fractional Gaussian noise (dFGN) and random midpoint displacement (RMD) algorithms have been used to synthesize self-similar sample paths. However, the dFGN is very inefficient and the inaccuracy of the RMD is usually unacceptable. In this paper we use the dFGN with interpolated RMD subtraces to get a faster and more accurate algorithm in which the dFGN generates the end points and the RMD produces a subtrace with a level of depth that determines the number of samples for each subtrace. The hybrid algorithm improves the computational time significantly, and still keeps the accuracy of the expected Hurst value.