Mohammad Hadi Zibaeenejad
Analysis of Parameterized Networks
Networks with arbitrarily large numbers of isomorphic subprocesses appear in areas such as computer software and hardware, transportation networks and manufacturing systems. Parameterized discrete event systems (PDES) provide a framework for modeling these networks. This modeling is specifically useful when the number of subprocesses is arbitrary, unknown or time-varying. Unfortunately, some key properties of these networks, such as nonblocking and deadlock-freedom, are undecidable. To support the analysis of nondeterministic PDES, we introduce a novel mathematical tool: weak invariant simulation. We use this simulation relation to define a tractable subclass of parameterized ring networks of isomorphic subprocesses in which all the reachable deadlocked states can be calculated. Two examples is given to illustrate the usage of the proposed framework.