In this paper we study the properties of the Barabasi model of queuing under the hypothesis that the number of tasks is steadily growing in time. We map this model exactly onto an invasion percolation dynamics on a Cayley tree. This allows us to recover the correct waiting time distribution P(W)(tau) similar to tau(-3/2) at the stationary state (as observed in different realistic data) and also to characterize it as a sequence of causally and geometrically connected bursts of activity. We also find that the approach to stationarity is very slow.
Gabrielli, A., Caldarelli, G. (2009). Invasion percolation and the time scaling behavior of a queuing model of human dynamics. JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT, 2009(2), P02046 [10.1088/1742-5468/2009/02/P02046].
Invasion percolation and the time scaling behavior of a queuing model of human dynamics
Gabrielli A.
;
2009-01-01
Abstract
In this paper we study the properties of the Barabasi model of queuing under the hypothesis that the number of tasks is steadily growing in time. We map this model exactly onto an invasion percolation dynamics on a Cayley tree. This allows us to recover the correct waiting time distribution P(W)(tau) similar to tau(-3/2) at the stationary state (as observed in different realistic data) and also to characterize it as a sequence of causally and geometrically connected bursts of activity. We also find that the approach to stationarity is very slow.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
