Dependency graph: An algorithm for analysis of generalized parameterized networks

In areas such as computer software and hardware, manufacturing systems and transportation, engineers encounter networks with arbitrarily large numbers of isomorphic subprocesses. Parameterized discrete event systems (PDES) provide a framework for modeling such networks. The analysis of PDES is a challenge as some key properties such as nonblocking and deadlock-freedom are undecidable. Previously we have established a procedure for deadlock analysis of a parameterized ring network of isomorphic subprocesses. Here we consider a network consisting of several parameterized sections with a more general topology. To model these networks we introduce Generalized Parameterized Discrete Event Systems (GPDES). The difficulty in analysis of a GPDES is the fact that some of the subprocesses interact with several parameterized sections of the network. Hence the analysis proposed in this paper involves careful study of interaction among different branches of the network. We investigate interactions among different components of the network, using a dependency graph. The dependency graph is a directed graph developed to characterize reachable deadlocks of proposed GPDES.