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Invasion percolation on a tree and queueing models

Gabrielli, Andrea and Caldarelli, Guido Invasion percolation on a tree and queueing models. Physical Review E, 79 (4). ISSN 1539-3755 (2009)

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We study the properties of the Barabási model of queuing [ A.-L. Barabási Nature (London) 435 207 (2005); J. G. Oliveira and A.-L. Barabási Nature (London) 437 1251 (2005)] in the hypothesis that the number of tasks grows with time steadily. Our analytical approach is based on two ingredients. First we map exactly this model into an invasion percolation dynamics on a Cayley tree. Second we use the theory of biased random walks. In this way we obtain the following results: the stationary-state dynamics is a sequence of causally and geometrically connected bursts of execution activities with scale-invariant size distribution. We recover the correct waiting-time distribution PW(τ)∼τ−3/2 at the stationary state (as observed in different realistic data). Finally we describe quantitatively the dynamics out of the stationary state quantifying the power-law slow approach to stationarity both in single dynamical realization and in average. These results can be generalized to the case of a stochastic increase in the queue length in time with limited fluctuations. As a limit case we recover the situation in which the queue length fluctuates around a constant average value.

Item Type: Article
Identification Number: 10.1103/PhysRevE.79.041133
Additional Information: © 2009 American Physical Society
Uncontrolled Keywords: PACS: 02.50.Le, 89.75.Da, 05.45.Tp, 89.65.Ef
Subjects: Q Science > QC Physics
Q Science > QH Natural history
Research Area: Economics and Institutional Change
Depositing User: Ms T. Iannizzi
Date Deposited: 26 Jan 2012 14:23
Last Modified: 18 Dec 2014 15:38
URI: http://eprints.imtlucca.it/id/eprint/1087

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