电子邮件通信中重尾现象的泊松解释
A Poissonian explanation for heavy-tails in e-mail communication
摘要：
在疾病传播、资源分配和应急响应等不同领域，人类活动和行为的模式都至关重要。由于其广泛的可用性和使用，电子邮件通信提供了一个有吸引力的代理研究人类活动。最近，据报道，连续发送的电子邮件之间的事件间时间$τ$的概率密度渐近衰减为$τ^{-α}$，其中$α\approx 1$。事件间时间分布比指数衰减慢，这表明有意识的人类活动本质上是非泊松的。在这里，我们证明了近似幂律缩放的事件间的时间分布是人类活动的昼夜节律和每周周期的结果。我们提出了一个级联的非齐次泊松过程，明确集成这些周期性的模式，在活动与个人的倾向，继续参与活动。使用标准的统计技术，我们表明，我们的模型与经验数据是一致的。我们的研究结果也可能提供洞察重尾分布在其他复杂系统的起源。
英文摘要：
Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides an attractive proxy for studying human activity. Recently, it was reported that the probability density for the inter-event time $τ$ between consecutively sent e-mails decays asymptotically as $τ^{-α}$, with $α\approx 1$. The slower than exponential decay of the inter-event time distribution suggests that deliberate human activity is inherently non-Poissonian. Here, we demonstrate that the approximate power-law scaling of the inter-event time distribution is a consequence of circadian and weekly cycles of human activity. We propose a cascading non-homogeneous Poisson process which explicitly integrates these periodic patterns in activity with an individual's tendency to continue participating in an activity. Using standard statistical techniques, we show that our model is consistent with the empirical data. Our findings may also provide insight into the origins of heavy-tailed distributions in other complex systems.
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