We consider the following queueing system which arises as a model of a wireless link shared by multiple users. Multiple ows must be served by a \channel" (server). The channel capacity (service rate) changes in time randomly and asynchronously with respect to di erent ows. In each time slot, a scheduling discipline (rule) picks a ow for service based on the current state of the channel and the queues. We study a scheduling rule, which we call the exponential rule, and prove that this rule is throughput-optimal, i.e., it makes the queues stable if there exists any rule which can do so. In the proof we use the uid limit technique, along with a separation of time scales argument. Namely, the proof of the desired property of a \conventional" uid limit involves a study of a di erent uid limit arising on a \ ner" time scale. In our companion paper 12] it is demonstrated that the exponential rule can be used to provide Quality of Service guarantees over a shared wireless link.
Another example of the throughput optimal control is the exponential rule proposed in REF .
Scheduling for Multiple Flows Sharing a Time-Varying Channel: The Exponential Rule
American Mathematical Society Translations, Series
Computer Science