Simulation of fractional Brownian motion with conditionalized random midpoint displacement

Recent measurement studies have shown that the burstiness of packet traffic is associated with long-range correlations that can be efficiently modeled by terms of fractal or self-similar processes, e.g., fractional Brownian motion (FBM). To gain a better understanding of queuing and network-related performance issues based on simulations as well as to determine network element performance and capacity characteristics based on load testing, it is essential to be able to accurately and quickly generate long traces from FBM processes. In this paper, we consider an approximate FBM generation method based on the concept of bisection and interpolation, which is an improvement of a much used but inaccurate method known as the random midpoint displacement (RMD) algorithm. We further extend our new algorithm (referred to as RMDmn) to be able to generate FBM traces without a priori knowledge of the length of the simulation (i.e., on--the-fly generation), instead of being a pure top-down generation (that is, the entire trace has to be generated first before it can be used) like the original RMD) algorithm. We present the mathematical and numerical aspects of the RMDmn algorithm as well as compare it with two other widely favored FBM generation methods, i.e., the fast Fourier transform (FFT) method.