Maximum weight matching with hysteresis in overloaded queues with setups

We consider a system of parallel queues where arriving service tasks are buffered, according to type. Available service resources are dynamically configured and allocated to the queues to process the tasks. At each point in time, a scheduler chooses a service configuration across the queues, in response to queue backlogs. Switching from one service configuration to another incurs a setup time, during which idling occurs and service bandwidth is lost. Such setup times are inherent in manufacturing and computer systems. Frequent switchings can significantly compromise the service capacity of such systems. A maximum weight matching (MWM) scheduler, which is known to maximize throughput in the absence of setups, can easily become unstable with setups, even under low load. To remedy this problem, we propose a new MWM-H scheduler which utilizes a controller introduced hysteresis and achieves maximum throughput even with setups, without requiring knowledge of arrival rates and average traffic loads. During prolonged traffic bursts, the queues may become overloaded and the issue becomes how to reasonably distribute the growing backlog under MWM-H. It is shown that by appropriately selecting the MWM-H parameters, one can control the backlog among the individual queues in order to achieve a desired balance.