Multiscale network processes: fractal and p-adic analysis

Computer scientists have been raising a number of original methodological questions which, while being common to many fields of technology, have thus far remained completely unexplored even by mathematicians. Among such questions of fundamental importance are what is the nature of multiscale processes in computer networks and how to quantify the fractal properties of packet flow. This paper begins with an experimental analysis of the property of burstiness and statistical operation with network traffic. The proposed approach offers hope that one can find simple enough adequate models and combine the concept of distance in normalized space with number theory. This is followed by some technical details concerning real analysis of fractional measure, and a calculus formalism that could be employed to describe network traffic models. The paper concludes with a wavelet and p-adic spectral analysis, which can be used to investigate multiscale fractal features of network traffic.