A priority queue model of human dynamics with bursty input tasks

Jin Seop Kim*, Naoki Masuda, Byungnam Kahng

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


The physics of human activities recently has been studied in the view point that they are dynamic processes of a complex system. The studies reveal that the human activities have bursty nature - occasional abrupt bursts of activity level for short periods of time, along with long periods of inactivity. Quantitative studies show that the distribution of the time, t, between two consecutive activity events exhibits a power-law behavior with universal exponents ∼τ-1.5 or ∼τ-1.0. Such universal behaviors were explained by the universality in the waitingtime distribution of tasks in model queue systems, which operate based on priority. In the models, the rates of task input are presumed to follow a Poisson-type distribution. An empirical observation of human activities, however, shows that the task arriving rate for some people also has bursty nature - the number of tasks arrive to the people follows a power-law distribution. In this paper, a new model queue system for this case is introduced and studied by analytic and numerical methods. The waiting-time distribution for the new model is found also to follow a power law, but the exponent varies according to the parameters of the model and takes other values than 1.5 or 1.0. The analytic solution is obtained via the generating function formalism, different from the biased random walk approach used in the previous studies.

Original languageEnglish
Title of host publicationComplex Sciences - First International Conference, Complex 2009, Revised Papers
Number of pages9
EditionPART 2
Publication statusPublished - 2009
Externally publishedYes
Event1st International Conference on Complex Sciences: Theory and Applications, Complex 2009 - Shanghai, China
Duration: 2009 Feb 232009 Feb 25

Publication series

NameLecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering
NumberPART 2
Volume5 LNICST
ISSN (Print)1867-8211


Conference1st International Conference on Complex Sciences: Theory and Applications, Complex 2009


  • Complex systems
  • Generating function
  • Human dynamics
  • Modelling
  • Power law
  • Priority queue

ASJC Scopus subject areas

  • Computer Networks and Communications


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