Scaling of Fluctuations in Internet - the State States Perspective

M. Bigus-Kwiatkowskaa, A. Fronczaka, P. Fronczaka, G. Siudema, M. Thelwallb aFaculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland bStatistical Cybermetrics Research Group, School of Mathematics and Computing, University of Wolverhampton, Wulfruna Street, Wolverhampton WV1 1SB, United Kingdom

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Taylor's law of fluctuation scaling is a power-law relationship between a variance and a mean. It has been observed in a wide range of disciplines, ranging from population dynamics through the Internet to the stock market. To explain origins of the law, a number of theoretical approaches have been proposed. Here, we discuss applicability of one of them, the maximum entropy-based formalism, to non-equilibrium stationary states. In addition to analyzing several real time series, we show that a simple model of transport of packets in communication networks also exhibits Taylor's law and could serve as a good testbed for verification of the formalism. We draw attention of the complex system community to the Bell polynomials that turn out to be very well suited for studying systems that exhibit Taylor's law.

DOI:10.12693/APhysPolA.138.14 topics: Taylor law, scaling fluctuation, Bell polynomials, density of states