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This paper presents an analytical model that evaluates the performance of the Maximum Packing channel allocation technique on linear and planar cellular systems. The main innovations introduced by this model are the deterministic identification of the system space-state SMP and its application to a multi-dimensional Markov chain. The model was thereafter applied to several cellular systems with different characteristics: number of cells, number of channels, interference constraints and offered traffic values. Simulation results have validated the model and shown that Maximum Packing technique provides the best performance among all the available algorithms.