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Modelling bursty time series
Title / Series / Name
New Journal of Physics
Publication Volume
15
Publication Issue
Pages
Editors
Keywords
General Physics and Astronomy
Files
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Kertesz-Janos2_2013.pdf
Adobe PDF, 684.07 KB
URI
https://hdl.handle.net/20.500.14018/27223
Abstract
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the non-trivial dynamics of the task list. The model is characterized by a priority distribution as an input parameter, which describes the choice procedure from the list. We give exact results on the asymptotic behaviour of the model and we show that the interevent time distribution is power-law decaying for any kind of input distributions that remain normalizable in the infinite list limit, with exponents tunable between 1 and 2. The model satisfies a scaling law between the exponents of interevent time distribution (β) and autocorrelation function (α): α + β = 2. This law is general for renewal processes with power-law decaying interevent time distribution. We conclude that slowly decaying autocorrelation function indicates long-range dependence only if the scaling law is violated.
Topic
Publisher
Place of Publication
Type
Journal article
Date
2013-10
Language
ISBN
Identifiers
10.1088/1367-2630/15/10/103023