Barabasi人体动力学模型的精确结果
Exact results for the Barabasi model of human dynamics
摘要：
人类活动模式显示出突发性的动态，与interevent时间遵循重尾分布。这种行为最近已经被证明是植根于这样一个事实，即人类为他们的活动任务分配不同的优先级，这个过程可以被建模为优先级分配系统[A. L. Barabasi，Nature 435，207（2005）]。在这项工作中，我们得到了精确的结果，Barabasi模型与两个任务，计算优先级和等待时间分布的活动任务。我们证明了该模型具有奇异行为的极值动力学极限，当最高优先级的任务被选中。我们发现，独立的选择协议，平均等待时间小于或等于活动任务的数量，并讨论了等待时间分布的渐近行为。这些结果对于理解具有极值动力学的复杂系统具有重要意义。
英文摘要：
Human activity patterns display a bursty dynamics, with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabasi, Nature 435, 207 (2005)]. In this work we obtain exact results for the Barabasi model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.
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