A REGULATOR STABILIZATION TECHNIQUE - KUMAR-SEIDMAN REVISITED

We discuss the stability of a class of models applicable to manufactur ing systems consisting of several machines, producing many types of pa rts, sharing resources, under dynamical decentralized scheduling. Kuma r and Seidman have shown the role of ''cycles'' of material dow as a s ource of instability, presented sufficient conditions for stability an d also presented a general supervisory mechanism to ensure stability. In this note, we exploit the hereditary properties of the sufficient c onditions for stability (hereditary in the connection graph that model s the interconnections), relax this condition and also present a regul ator based stabilization technique, easily implementable in distribute d fashion. Besides that, as a corollary, we give an upper bound for th e number of regulatory mechanisms to be used in a given system. This u pper bound is also valid for previous stabilization techniques like di stributed CAF policies with backoff and for the universally stabilizin g supervisory mechanism.