Distributed scheduling of flexible manufacturing systems: stability and performance

We consider a manufacturing system producing several part{types on several machines. Raw parts are input to the system. Each unit of a given part{type requires a predetermined processing time at each of several machines, in a given order. A setup time is required whenever a machine switches from processing one part{type to another. For a single machine system with constant demand rates, we present a class of Generalized Round Robin scheduling policies for which the buuer level trajectory of each part{type converges to a steady state level. Furthermore, for all small initial conditions, we show that these policies can be Pareto{eecient with respect to the buuer sizes required. Allowing the input streams to have some burstiness, we derive upper bounds on the buuer levels for small initial conditions. For non{acyclic systems, we consider a class of policies which are stable for all inputs with bounded burstiness. We show how to employ system elements, called regulators, to stabilize systems. Using the bounds for the single machine case, we analyze the performance of regulated systems implementing Generalized Round Robin scheduling policies.