In this paper we study the properties of the Barabsi 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 PW(τ) ∼τ-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. © 2009 IOP Publishing Ltd.
Invasion percolation and the time scaling behavior of a queuing model of human dynamics
Caldarelli G.
2009-01-01
Abstract
In this paper we study the properties of the Barabsi 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 PW(τ) ∼τ-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. © 2009 IOP Publishing Ltd.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
