Optimal Control Based on a General Exponential Scheduling Rule for a Generalized Switch

We design a general exponential scheduling rule for a generalized switch system, which includes many systems as special cases such as the system of multiuser data scheduling over a wireless medium, the input-queued cross-bar switch and a discrete time version of a parallel server queueing system. Multiple flows must be served by the switch and the switch state changes in time randomly and asynchronously for different users. The designed scheduling rule picks flows for service based on the current state of the switch and the queues explicitly, which avoids any knowledge requirements of input rates and switch statistics and hence overcomes the disadvantage of existing Max Weight scheduling rule. Moreover, we prove that this rule is throughput-optimal (i.e., it makes the queues stable if there exists any rule which can do so) and is to minimize certain form of workload (i.e., minimize certain form of queue-lengths or delays).