网络流的波动与伪长程相关：一个非平稳Poisson过程模型
Fluctuations and Pseudo Long Range Dependence in Network Flows: A Non-Stationary Poisson Process Model
摘要：
在复杂网络（系统）的研究中，流量波动的标度现象是指第n个节点的平均流量（活动）$i$与其方差$σ_i$之间的某种幂律为$σ_i \propto < F_{i} > ^α$。人们发现这种标度律在自然和人造网络系统中都很普遍，但我们对其起源的了解仍然有限。本文提出了一个非平稳泊松过程模型，对非普适标度现象给出了解析解释：指数$α$在1/2和1之间变化，取决于采样时间窗的大小和系统内外驱动力的相对强弱。该模型还解释了交叉行为和涨落标度与伪长程相关的关系。数值实验表明，该模型可以恢复多尺度现象。
英文摘要：
In the study of complex networks (systems), the scaling phenomenon of flow fluctuations refers to a certain power-law between the mean flux (activity) $<F_i>$ 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.
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