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

Yudong Chen; Li Li; Yi Zhang; Jianming Hu

doi:10.1088/1674-1056/18/4/015

paper

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

arXiv:0806.0206 · doi:10.1088/1674-1056/18/4/015

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 $σ_{i}$ as $σ_{i} \propto< F_{i} >^{α}$ . 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 $α$ 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.

There is a mistake in the previous axiv post (indeed the scaling law holds for both Δt > τand Δt < τ)

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

Abstract

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