Fractional Brownian Motion Modeling Self-Similar Network Traffic

The last decade has seen an enormous increase in studies of data network, which describe pertinent statistical characteristics, Long-Range Dependence and Self-Similarity, and influence the landscape of network exploitation. These characteristics are in sharp contrast to what one observes in the traditional models for network traffic, models that are based on an exponentially fast decaying correlation function, implying that time-aggregation time series quickly results in white noise traffic characterized by the absence of any temporal correlations. Fractional Brownian motion plays an important role in the studies mentioned above. This paper reviews the history of research of long-range dependence and self-similarity in data network traffic, introduces the related concepts and discusses the physical interpretation of long-range dependence and self-similarity along with Fractional Brownian motion. Finally, a method for generating Fractional Brownian motion random series is analyzed.