A Priority Queue Model of Human Dynamics with Bursty Input Tasks

  • Jin Seop Kim
  • Naoki Masuda
  • Byungnam Kahng
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 5)

Abstract

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, τ, 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 waiting-time 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.

Keywords

complex systems human dynamics modelling priority queue power law generating function 

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Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2009

Authors and Affiliations

  • Jin Seop Kim
    • 1
  • Naoki Masuda
    • 2
  • Byungnam Kahng
    • 1
  1. 1.FPRD, Department of Physics and AstronomySeoul National UniversitySeoulKorea
  2. 2.Graduate School of Information Science and TechnologyThe University of TokyoTokyoJapan

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