eprintid: 1087
rev_number: 14
eprint_status: archive
userid: 6
dir: disk0/00/00/10/87
datestamp: 2012-01-26 14:23:51
lastmod: 2014-12-18 15:38:41
status_changed: 2012-01-26 14:23:51
type: article
metadata_visibility: show
creators_name: Gabrielli, Andrea
creators_name: Caldarelli, Guido
creators_id: 
creators_id: guido.caldarelli@imtlucca.it
title: Invasion percolation on a tree and queueing models
ispublished: pub
subjects: QC
subjects: QH
divisions: EIC
full_text_status: public
keywords: PACS: 02.50.Le, 89.75.Da, 05.45.Tp, 89.65.Ef

note: © 2009 American Physical Society
abstract: 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.
date: 2009-04
date_type: published
publication: Physical Review E
volume: 79
number: 4
publisher: American Physical Society
id_number: 10.1103/PhysRevE.79.041133
refereed: TRUE
issn: 1539-3755
official_url: http://dx.doi.org/10.1103/PhysRevE.79.041133
citation:   Gabrielli, Andrea and Caldarelli, Guido  Invasion percolation on a tree and queueing models.  Physical Review E, 79 (4).   ISSN 1539-3755      (2009)  
document_url: http://eprints.imtlucca.it/1087/1/PhysRevE.79.041133Caldarelli_2009.pdf