Statistical analysis of RMD method for generating fractional Brownian motion sample paths

Fractional Brownian Motion (FBM) has emerged as a powerful traffic model, able to fit the long-term correlations of actual network traffic flows with a limited number of parameters. An open research issue is the fast generation of FBM sample paths to be used in network simulations, which might require a large number of samples in case rare events are involved. In this paper we analyse the statistical behaviour of the well-known Random Midpoint Displacement algorithm, an approximate generation algorithm whose complexity is linear with the simulation length, taking into account marginal distribution as well as correlation structure.