  Stability with respect to a given scheduling policy has become an important
issue for wireless communication systems, but it is hard to prove in particular
scenarios. In this paper two simple conditions for stability in broadcast
channels are derived, which are easy to check. Heuristically, the conditions
imply that if the queue length in the system becomes large, the rate allocation
is always the solution of a weighted sum rate maximization problem.
Furthermore, the change of the weight factors between two time slots becomes
smaller and the weight factors of the users, whose queues are bounded while the
other queues expand, tend to zero. Then it is shown that for any mean arrival
rate vector inside the ergodic achievable rate region the system is stable in
the strong sense when the given scheduling policy complies with the conditions.
In this case the policy is so-called throughput-optimal. Subsequently, some
results on the necessity of the presented conditions are provided. Finally, in
several application examples it is shown that the results in the paper provide
a convenient way to verify the throughput-optimal policies.
