Left panels: distribution of the avalanche duration f(T). Central panels: distribution of the avalanche size f(S). The gray points are the original distribution function, and the black points mark the distribution logarithmically binned. Right panels: average avalanche size ⟨S⟩ vs. avalanche duration T. Upper panels: setup 1, similar to the original simulation of Mineshige et al. (1994a,b). Central upper panels: setup 2, including a link between mass accretion and wind mass outflow as in MCDW models. Central lower panels: setup 3, including a link between mass accretion and wind mass outflow as in MCDW models and an Eddington-like limit on the mass-accretion rate due to the wind thrust that contrasts the accretion flow at the first radius. Bottom panels: setup 4. This is the same as setup 1, but includes a threshold on the disk luminosity above which the accretion is halted (similar to an Eddington limit). The red lines in the left and central panels are best-fit models. The red lines in the right panels bridge the interval of allowed α.