中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1373-1379.doi: 10.1088/1674-1056/18/4/015

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Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model

陈煜东, 李力, 张毅, 胡坚明   

  1. Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100084, China
  • 收稿日期:2008-10-30 修回日期:2008-11-14 出版日期:2009-04-20 发布日期:2009-04-20
  • 基金资助:
    Project supported in part by National Basic Research Program of China (973 Project) (Grant No 2006CB705506), Hi-Tech Research and Development Program of China (863 Project) (Grant No 2007AA11Z222), National Natural Science Foundation of China (Grant Nos 6

Fluctuations and pseudo long range dependence in network flows: A non-stationary Poisson process model

Chen Yu-Dong(陈煜东), Li Li(李力)†, Zhang Yi(张毅), and Hu Jian-Ming(胡坚明)   

  1. Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Automation, Tsinghua University, Beijing 100084, China
  • Received:2008-10-30 Revised:2008-11-14 Online:2009-04-20 Published:2009-04-20
  • Supported by:
    Project supported in part by National Basic Research Program of China (973 Project) (Grant No 2006CB705506), Hi-Tech Research and Development Program of China (863 Project) (Grant No 2007AA11Z222), National Natural Science Foundation of China (Grant Nos 6

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摘要： In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) < Fi> of the i-th node and its variance σi as Fi ∝ <Fiα. Such scaling laws are found to be prevalent both in natural and man-made network systems, but the understanding of their origins still remains limited. This paper proposes a non-stationary Poisson process model 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 behaviour 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.

关键词: scaling, long range dependence, non-stationary Poisson process

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) $\langle F_i \rangle$ of the $i$-th node and its variance $\sigma_i$ as  $\sigma_i \propto \langle F_{i} \rangle ^ {\alpha}$. Such scaling laws are found to be prevalent both in natural and man-made network systems, but the understanding of their origins still remains limited. This paper proposes a  non-stationary Poisson process model 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 behaviour 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.

Key words: scaling, long range dependence, non-stationary Poisson process

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
89.75.Da (Systems obeying scaling laws) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 02.50.Ey (Stochastic processes)