Reachability Graph of Finite & Deterministic DEVS Networks

This paper shows how to generate a finite-vertex graph, called a reachability graph for discrete event system specification (DEVS) network. The reachability graph is isomorphic to a given original DEVS network in terms of behavior but the number of vertices as well as the number of edges of the reachability graph are finite. To obtain the finite-vertex reachability graph of a DEVS network, this paper uses a subclass of DEVS, called finite and deterministic DEVS (FD-DEVS). This subclass has been restricted to have (1) finite sets of both events and states, (2) the rational-number time advance function, (3) time independent external transition, and (4) selective reschedule functionality. For abstracting the infinite-state behavior of DEVS network, we use the concept of time zone, invented by Dill [3], that is a conjunction of inequalities of elapsed times. Based-on time zone abstraction, an algorithm for generating the reachability graph of a DEVS network is proposed and its completeness and complexity are addressed. Questions concerning qualitative properties, for examples, “Does this DEVS network have any possibility to reach a bad situation?” or “Will this system repeat a certain pattern forever?” are open problems for more than 30 years. This paper gives an answer about the above questions for the FD-DEVS subclass of DEVS. A reachability graph-based qualitative verification is exemplified with a modular monorail system, so the reader will find the usefulness of the reachability graph. Note to Practitioners— Modular and hierarchical modeling and analysis becomes more important as systems are increasingly complicated [10]. DEVS formalism is a modular and hierarchical formalism in which the user build a system by connecting system components, and the system can be a component in a bigger system. In addition, the practitioners can use the all source codes of the algorithm and the verification example proposed in this paper which are available at http://xsycsharp.sourceforge.net/DEVSsharp.