Analysis of Deadlock and Circular Waits Using a Matrix Model for Flexible Manufacturing Systems

The problem of deadlock in a large class of reentrant flowline systems is analysed based on a Petri net model. The relation between deadlock and circular waits is established by rigorously defining the situation of circular blocking. Deadlock analysis is then performed in terms of circular waits and their associated structures, the so-called critical siphons and critical subsystems. A dynamical system representation obtained by coupling the Petri net marking transition equation with the matrix rule-based controller equations is adopted. The task of computing the Petri net structures of deadlock analysis is largely simplified (operations involved are of polynomial complexity) by using the matrices of this system description. An on-line maximally permissive control policy for deadlock avoidance (MAXWIP) is then devised. This can be efficiently implemented by incorporating the ''outer-loop'' control decisions via certain dispatching control inputs. The result is a dispatching control with deadlock avoidance, which is a generalized kanban scheme.