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We present an analytical model to compute the blocking probability in channelized cellular systems with dynamic channel allocation. We model the channel occupancy in a cell by a two-dimensional (2D) Markov chain, which can be solved to obtain the blocking probability in each cell. We apply our analytical model to linear highway systems with and without lognormal shadowing and then extend it to 2D cellular systems with lognormal shadowing. We show that, for linear highway systems, distributed dynamic channel-allocation schemes perform similarly to the centralized dynamic channel-allocation schemes in terms of blocking probability. However, for 2D cellular systems, the improvement in the performance is significant and the reduction in the blocking probability in systems with distributed dynamic channel allocation is by almost one order of magnitude, when compared to that in systems with centralized dynamic channel allocation. In practice, our analysis of linear highway systems is applicable to Digital European Cordless Telephony (DECT) and that of 2D cellular systems is applicable to global systems for mobile communications (GSM).