Self-similar traffic generation: the random midpoint displacement algorithm and its properties

Recent measurement studies have shown that the burstiness of packet traffic is associated with long-range correlations that can be efficiently described in terms of fractal or self-similar models e.g., fractional Brownian motion (FBM). While FBM models are an attractive alternative to traditional models in terms of parsimony, comprehensive queueing solutions of these models are lacking at present. For this reason, simulation studies that make use of synthetically generated traces from FBM-based traffic processes become crucially important for gaining a better understanding of queueing and network-related performance issues. To this end, 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 known as the random midpoint displacement (RMD) algorithm and perform extensive statistical analyses on a variety of traces generated via RMD. Our analysis indicates that (i) RMD is attractive for qualitative studies (ii) for quantitative studies the parameters of the generated traces may differ from their target values. Such discrepancies can partly be explained by the natural variability of the FBM process, and parameter estimation errors. The approximation to FBM can be improved by using aggregated versions of the traces generated by RMD. We also discuss the application of RMD to traffic interpolation, i.e., inferring traffic measurements on fine time scales from actual measurements made over coarse time scales