Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for 5 human activity patterns the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity.

We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times.

We discuss two queueing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can handle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution with exponent alpha=3/2. The second model imposes limitations on the queue length, resulting in alpha=1.

We provide empirical evidence supporting the relevance of these two models to human activity patterns. Finally, we discuss possible extension of the proposed queueing models and outline some future challenges in exploring the statistical mechanisms of human dynamics.

…Supercritical regime, ρ > 1: Given that in this regime the arrival rate exceeds the response rate, the average queue length grows linearly as 〈l(t)〉 = (λ − μ)t. Therefore, a 1 − 1/ρ fraction of the letters is never responded to, waiting indefinitely in the queue. Given Darwin, Einstein and Freud’s small response rate, this regime captures best their correspondence pattern. We can measure the waiting time for each letter that is responded to. In Figure 5 we show the waiting time probability density obtained from numerical simulations, indicating that it follows a power law with exponent α = 3⁄2. Thus the supercritical regime follows the same scaling behavior as the critical regime, but only for the letters that are responded to. The rest of the letters wait indefinitely in the list (τ_w = ∞).

While the discussed model can indeed generate power law waiting time distributions, a critical comparison with the empirical datasets reveals some notable deficiencies. First, a power law distribution emerges only in the critical (ρ = 1) and the supercritical (ρ > 1) regimes. The critical regime requires a careful tuning of the human execution rate, so that the execution and the arrival rates are exactly the same. In contrast, for ρ > 1 no tuning is necessary, but the number of tasks on the list increases linearly with time, thus many tasks are never executed. This limit is probably the most realistic for human dynamics: we often take on tasks that we never execute, and technically stay on our priority list forever. As we discussed above, this is documentedly the case for Einstein, Darwin and Freud, who answer only a fraction of their letters.

However, we must not overlook the second important feature of the discussed model: the only exponent it can predict is α = 3⁄2, rooted in the fluctuations of the queue length. While this fully agrees with the correspondence patterns of Einstein, Darwin and Freud, it is substantially higher than the values observed in the empirical data discussed in §III A on web browsing, email communications or library visits, which we found to be scattered around α = 1.

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