Deadlock analysis and routing on free-choice multipart reentrant flow lines using a matrix-based discrete event controller

We present an analysis for deadlock avoidance in manufacturing free-choice multipart reentrant flow-lines (FMRF). In FMRF, shared resources are not dedicated for certain jobs; some jobs have multiple resource choices in reentrant flow lines, i.e. routing decisions to be made. A discrete event (DE) supervisor for deadlock avoidance dispatching, which framework uses a rule-based matrix formulation, is used for routing/dispatching FMRF systems. The development of deadlock-free dispatching rules is derived from circular wait (CW) analysis for possible blocking situations. We analyze the so-called critical siphons, and certain critical subsystems on FMRF systems to develop deadlock-free dispatching. The DE controller guaranties deadlock avoidance by limiting the work-in-progress in the critical subsystems associated with each CW. This is the least-restrictive dispatching policy that avoids deadlock. In this paper, we calculate in matrix form all constructions needed for implementation of DE controllers using online-deadlock-free dispatching rules, for the case of regular FMRF systems.