Abstract
A two-parameter, probabilistic growth model for partition polygon clusters is introduced and exact results obtained relating to the area moments and the area probability distribution. In particular, the scaling behaviour in the presence of asymmetry between growth along the two principal axes is discussed. Variants of the model are also examined, including the extension to rooted stack polygons. An interesting application relates to characterizing the asymptotic behaviour of the cumulative customer waiting time distribution in a particular discrete-time queue.
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