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In this paper, we present a model of a shingled magnetic recording system, where Voronoi regions are used to model the grains of the magnetic medium. A probabilistic model is used to represent imperfections in the write process, i.e., the head failing to write some grains correctly. A two-dimensional model of the head response is used to calculate the signal read back by the head over any place on the medium, thereby including both intertrack and intersymbol interference effects in the model. We also present simulation results from tests of this model using a multitrack detector and an intertrack interference canceller and give performance results of the channel/detector combination for various track offsets.