  This paper reports simulations allowing for stochastic accretion and mass
loss within closed and open systems modeled using a previously developed
multi-population, multi-zone (halo, thick disk, thin disk) treatment. The star
formation rate is computed as a function of time directly from the model
equations and all chemical evolution is followed without instantaneous
recycling. Several types of simulations are presented here: (1) a closed system
with bursty mass loss from the halo to the thick disk, and from the thick to
the thin disk, in separate events to the thin disk; (2) open systems with
random environmental (extragalactic) accretion, e.g. by infall of high velocity
clouds directly to the thin disk; (3) schematic open system single and multiple
collision events and intracluster stripping. For the open models, the mass of
the Galaxy has been explicitly tracked with time. We present the evolution of
the star formation rate, metallicity histories, and concentrate on the light
elements. We find a wide range of possible outcomes, including an explanation
for variations in the Galactic D/H ratio, and highlight the problems for
uniquely reconstructing star forming histories from contemporary abundance
measurements.
