Exact results for the Barabasi model of human dynamics

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  • 15 June 2005
Abstract
Empirical evidence shows that the human activity patterns display a bursty dynamics, with interevent times following a heavy tailed distribution. Recently it was proposed that this behavior is rooted in the fact that humans assign their active tasks different priorities, helping them to decide what to do next. This process has been modeled as a queuing system with a fix number of active tasks [A.-L. Barabasi, Nature 435, 207 (2005)]. In this work we obtain exact results for the Barabasi model of human dynamics by calculating the priority distribution of active tasks and the task waiting time distribution for the case of two tasks. Using these results we prove that the model has a singular behavior in the limit of a highest priority first selection protocol, and derive the scaling behavior in this limit. We also show that, independently of the selection protocol, the average waiting time is smaller or equal than the number of active tasks, and discuss the possible asypmtotic behavior of the waiting time distribution.

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