Graphical model structures for discrete event simulation

Several different graphical techniques for specifying models for discrete event systems are reviewed including process networks, generalized stochastic Petri nets, stochastic state diagrams, and event graphs. This paper presents a brief summary of these modeling approaches and highlights some of their similarities and differences. 1. BACKGROUND AND DEFINITIONS A system is defined as a set of entities that interact for shared purposes according to sets of common laws and policies for an interval of time. A system can be either real or hypothetical. The interval of time for which the system is defined is called its llfietime; this is the amount of time we are interested in studying the system. The entities in a system are either resident, remaining in the system for its entire lifetime, or transient, entering and exiting the system as time passes. A model is simply a system that is used for a surrogate of another system. A simulation is a computer program used as a model for some other system of interest. In a simulation model the entities are described by numerical (coded) attributes. The state of the simulation includes the values for all of its attributes as well as what is known about the future. We define an event as any situation where the state of the system might possibly change. In a discrete event dynamic system all changes in state occur at discrete instants of time. A discrete event system is typically an idealized or abstract system that is used as a model for a more complex system. In this paper, we concentrate on tools for specifying the behavior of discrete event systems that are complete graphical representations. That is, a directed graph can be drawn with labeled edges (arrows) and vertices (balls or blocks) forming a network that completely defines the structure of a specific system. Along with an initial state, stopping conditions, and a specified input process, the graph completely describes a specific model’s behavior. Structural and behavioral properties for simulations have been defined in [Yucesan and Schruben, 1992]. For each graphical model there is a set of implicit rules (e. g., time advance algorithms) that define how the input is processed to produce the model’s output. There are many such graphical procedures; only some of the more popular approaches will be presented. In particular, we will not include the many special-purpose approaches for building simulators, One of the most distinctive features of these modeling methodologies is the number of different types of modeling objects used. Objects are considered to be of a different type if they are defined by different rules of behavior; different types of objects are typically represented in the graphs by different shapes or as having different names. Different types of graphical objects are sometimes referred to as modeling “blocks”. Methodologies that have few types of graphical objects are easier to learn than those with many different types of objects. Methodologies that have many types of objects may be harder to learn but may be easier to use or understand once they are mastered. Surprisingly, having a large number of different types of graphical modeling objects does not imply that the technique is more powerful. If anything, just the opposite tends to be true. This has to do with the modeling philosophy behind each approach. One extreme is to try and identify all of the possible situations that might need to be modeled and define a special macro block or graphical object for each