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This paper reports the results of an investigation of the increase in traffic capacity in a cellular high capacity mobile telecommunications system attainable with dynamic instead of fixed channel assignment. Three dynamic channel assignment algorithms were studied by simulation using a 21-cell hexagonal array as a representative system layout. Detailed results for each algorithm are presented. For the particular system studied, traffic capacity can be increased by approximately 25 percent with dynamic channel assignment. A general upper bound on this increase has been found.