Algebraic deadlock avoidance policies for conjunctive/disjunctive resource allocation systems

Operational flexibility of deadlock avoidance policies (DAPs) is an essential requirement for achieving high resource utilization of the underlying deadlock-prone resource allocation system. The paper presents computational methods for synthesizing highly flexible DAPs for the class of conjunctive/disjunctive resource allocation systems (CD-RAS), which generalizes the resource allocation model that has been typically studied in the past, by allowing multiple resource acquisitions and flexible routings. Specifically, a linear programming method to compute DAPs for CD-RAS is developed, and subsequently a series of computational tools are provided to enhance the policy permissiveness/flexibility. These methods are based on: (i) the pertinent exploitation of the policy parameterization, (ii) the observation that the considered class of policies is closed under policy disjunctions, and (iii) the systematic relaxation of the policy-imposed constraints through Petri net structural analysis. The presented results are demonstrated through an example modeling an agile automation system.