We investigate the performance of channel assignment policies for cellular networks. The networks are given by an interference graph which describes the reuse constraints for the channels. In the first part, we derive lower bounds on the expected (weighted) number of blocked calls under any channel assignment policy over finite time intervals as well as in the average case. The lower bounds are solutions of deterministic control problems. As far as the average case is concerned, the control problem can be replaced by a linear program. In the second part, we consider the cellular network in the limit, when the number of available channels as well as the arrival intensities are linearly increased. We show that the network obeys a functional law of large numbers and that a fixed channel assignment policy which can be computed from a linear program is asymptotically optimal. Special networks like fully connected and star networks are considered.