Note on blockage in manufacturing systems

Blockage is a known and highly undesirable phenomenon in manufacturing systems. In certain situations the processing or motion of parts becomes impossible due to cyclic resource requests in some portion of the system, leading eventually to zero throughput. This phenomenon is similar to deadlock which is encountered in computer systems in which concurrent activities can take place. However hardly any theoretical study of this phenomenon in manufacturing systems has been carried out. In this paper we study a general manufacturing system in which a finite number of machines process parts or pieces which are trasported by AGVs (automated guided vehicles) moving independently from each other. We first model the manufacturing system as a discrete event state transition system. We then illustrate blockage using a set of simulations, and show how the size of the mnufacturing system can affect its onset. In particular, we relate blockage to system throughput, and show that it leads to eventually zero throughput. We then present a theoretical explanation of the phenomenon, showing that under mild conditions blockage will "almost surely" occur. We then discuss sufficient conditions under which it will not occur.