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.
