A sequential approach for optimal broadcast scheduling in packet radio networks

An important problem that arises in the design of packet radio networks is that of scheduling access to the high speed communications channel in such a way as to avoid interference while keeping the frame length to a minimum. The broadcast scheduling problem is known to be NP-hard and to date, this problem has been formulated as a nonlinear discrete optimization problem for a given frame length, and solved via heuristic approaches by parametrically varying the length of the frame. This paper presents a linear integer programming formulation for the composite problem of maximizing channel utilization while minimizing the length of the frame. It then introduces a solution approach based on solving two relatively easier (though still NP-complete) integer programs in succession. Computational experiments are conducted on a set of benchmark cases and additional randomly generated problem instances. Results show that this sequential integer programming approach is very effective, solving all the problems optimally within a few seconds. These results imply that optimal solutions can be identified in very little time for problems of realistic size, and that heuristic approaches will be needed only when problems get much larger than those considered in the literature to date.