Fluctuations and Pseudo Long Range Dependence in Network Flows: A Non-Stationary Poisson Process Model

TL;DR

This paper introduces a non-stationary Poisson process model to explain the varying fluctuation scaling laws in complex network flows, linking them to external/internal forces and pseudo long-range dependence.

Contribution

It provides an analytical framework for understanding non-universal fluctuation scaling and its relation to pseudo long-range dependence in network systems.

Findings

The scaling exponent varies between 1/2 and 1 depending on system factors.

The model captures crossover behavior in fluctuation scaling.

Numerical experiments confirm the model's ability to reproduce multi-scaling phenomena.

Abstract

In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ of the $i$th node and its variance $\sigma_i$ as $\sigma_i \propto < F_{i} > ^{\alpha}$. Such scaling laws are found to be prevalent both in natural and man-made network systems, but our understanding of their origins still remains limited. In this paper, a non-stationary Poisson process model is proposed to give an analytical explanation of the non-universal scaling phenomenon: the exponent $\alpha$ varies between 1/2 and 1 depending on the size of sampling time window and the relative strength of the external/internal driven forces of the systems. The crossover behavior and the relation of fluctuation scaling with pseudo long range dependence are also accounted for by the model. Numerical experiments show that the proposed model can recover the multi-scaling phenomenon.