Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems

Manufacturing systems consisting of many machines and producing many types of parts are considered. Each part type requires processing for a specified length of time at each machine in a prescribed sequence of machines. Machines may require a setup time when changing between part types, and parts may incur a variable transportation delay when moving between machines. The goal is to schedule all the machines dynamically so that all the part types are produced at the desired rates while maintaining bounded buffer sizes at all machines. A previously open problem is resolved by exhibiting the instability of all clearing policies for some nonacyclic manufacturing systems. Surprisingly, such instabilities can occur even when all setup times are identically zero, and they are induced purely by starvation of machines. Sufficient conditions on the system topology and processing and demand rates which ensure the stability of distributed clear-a-fraction policies are shown. A general distributed supervisory mechanism which will stabilize any policy is studied.<<ETX>>