Motivated by the need to introduce design improvements to the Internet network to make it robust to high traffic volume anomalies, we analyze statistical properties of the time separation between arrivals of consecutive anomalies in the Internet2 network. Using several statistical techniques, we demonstrate that for all unidirectional links in Internet2, these interarrival times have distributions whose tail probabilities decay like a power law. These heavy-tailed distributions have varying tail indexes, which in some cases imply infinite variance. We establish that the interarrival times can be modeled as independent and identically distributed random variables, and propose a model for their distribution. These findings allow us to use the tools of of renewal theory, which in turn allows us to estimate the distribution of the waiting time for the arrival of the next anomaly. We show that the waiting time is stochastically substantially longer than the time between the arrivals, and may in some cases have infinite expected value. All our findings are tabulated and displayed in the form of suitable graphs, including the relevant density estimates.

由于需要对Internet网络进行设计改进以使其对高流量异常具有鲁棒性，因此我们分析了Internet2网络中连续异常到达之间时间间隔的统计属性。使用几种统计技术，我们证明对于Internet2中的所有单向链接，这些到达时间具有分布，其尾部概率像幂定律一样衰减。这些重尾分布具有变化的尾部索引，这在某些情况下表示无穷大的方差。我们建立了到达间隔时间可以建模为独立且均匀分布的随机变量的模型，并提出了其分布模型。这些发现使我们能够使用更新理论的工具，这又使我们能够估计下一个异常到达的等待时间的分布。我们显示，等待时间随机地比到达之间的时间长得多，并且在某些情况下可能具有无限的期望值。我们所有的发现都以表格的形式列出，并以适当的图表形式显示，包括相关的密度估算值。