In a dual band personal communications services (PCS) network, heavy traffic areas are covered by microcells which overlay macrocells. In such a network, microcells and macrocells utilize different frequency bands. We propose an analytic model to study the performance of a dual band PCS architecture. Our model assumes that a PCS subscriber has a general residence time distribution in a microcell and the macrocell residence time distribution is derived from the microcell residence time distribution. An iterative algorithm is used to compute the overflow traffic from a microcell to its overlaid macrocell. Then, the call incompletion probability is computed by a macrocell model based on the overflow traffic. Our study indicates that the variance of the microcell residence time distribution and the number of microcells covered by a macrocell have significant effects on the call incompletion probability.