A Fundamental Characterization of Stability in Broadcast Queueing Systems

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.