In this paper we study the properties of the Barabasi model of queueing 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 to recove
r the correct waiting time distribution $P_W(tau)sim tau^{-3/2}$ 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.
