因特网数据包传输：从全局拓扑到局部拓扑动态
Internet data packet transport: from global topology to local queueing dynamics
摘要：
我们在自治系统的层次上研究互联网的结构特征和演化。提取相关参数的互联网拓扑结构的增长动力学，我们构建了一个玩具模型的互联网进化，其中包括乘法随机演化的节点和边缘和自适应重布线的边缘的成分。该模型成功地再现了互联网的基本结构特征。我们还引入了一个称为负载的量，作为处理通信流量所需的节点容量，并研究了其随时间变化的行为，在枢纽跨年。集线器处的负载随着网络大小$N$增加为$\sim N^{1.8}$。最后，我们研究了微观尺度下的数据包流量。计算了到达信道数为无标度时，数据包在排队系统中的平均时延。我们发现，当到达的数据包的数量遵循幂律分布，$\sim n^{-λ}$，队列长度分布衰减为$n^{1-λ}$和平均延迟时间在枢纽发散为$\sim N^{(3-λ)/(γ-1)}$在$N \to \infty$限制时，$2 < λ< 3$，$γ$是网络度指数。
英文摘要：
We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes the ingredients of multiplicative stochastic evolution of nodes and edges and adaptive rewiring of edges. The model reproduces successfully structural features of the Internet at a fundamental level. We also introduce a quantity called the load as the capacity of node needed for handling the communication traffic and study its time-dependent behavior at the hubs across years. The load at hub increases with network size $N$ as $\sim N^{1.8}$. Finally, we study data packet traffic in the microscopic scale. The average delay time of data packets in a queueing system is calculated, in particular, when the number of arrival channels is scale-free. We show that when the number of arriving data packets follows a power law distribution, $\sim n^{-λ}$, the queue length distribution decays as $n^{1-λ}$ and the average delay time at the hub diverges as $\sim N^{(3-λ)/(γ-1)}$ in the $N \to \infty$ limit when $2 < λ< 3$, $γ$ being the network degree exponent.
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