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Outline

Title
Abstract
Introduction
Empirical Results
Numerical Results for L > 2
Comparison with the Empirical Data
Discussion
Appendix A: Preferential Selection Protocol
References
All Topics
Mathematics
Probability

Modeling bursts and heavy tails in human dynamics

Profile image of Imre KondorImre Kondor

2006, Physical Review E

Abstract

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. 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. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, 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. In contrast, priority blind execution is well approximated by uniform interevent statistics. 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 hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution P (τw) ∼ τ −α w with α = 3/2. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by α = 1. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display α = 1, the surface mail based communication belongs to the α = 3/2 universality class. Finally, we discuss possible extension of the proposed queueing models and outline some future challenges in exploring the statistical mechanisms of human dynamics. These findings have important implications not only for our quantitative understanding of human activity patterns, but also for resource management and service allocation in both communications and retail.

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  • Engineering
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  • Queueing theory
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