Stability of scheduling policies for processing networks

This paper considers the stability of a network of processors executing a set of tasks on orders that arrive either externally or from other processors in the network. These orders wait at each task until a control policy assigns the processor to execute the orders for that task. We consider a class of control policies, work-conserving control policies, that consider look-ahead of workload from existing orders. These policies are shown, in general, to ensure that work accumulation in the system is bounded and thus the system is stable. We then consider the class of apparently-work-conserving controllers, which operate on task-level information instead of global information. By adding supplemental information dynamics, it is shown that these apparently-work-conserving controllers can be made equivalent to work-conserving and thus ensure stability.