Introduction to Modeling
- What is a Model? Webster's dictionary provides 25 definitions for the word "model". This is a good indication of generality of the term and one cause of great
misunderstanding. We begin with the definition that a model is "a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs" (Webster definition #13). From that foundation we can begin to
understand how to use a model.
- How is a Model Used? A model captures the
relevant information and behavior of a system. Therefore, it can be used to study, understand,
dissect, and communication information about that system.
- How Does a Model Become a Simulation? A simulation is a group of models tied together with software and hardware that make the model useful for some purpose. Simulations often require a standard set of components to active the models within them.
Philosophy of Modeling
- Abstraction. A modeler is in the business of abstraction. In the words of Paul Fishwick (University of Florida), "To model is to abstract from reality a description of a dynamic system." The real world is much to
complex to capture in its entirety,
therefore, we abstract reality and distill it down to its most essential content.
- Purpose. We create models so we can understand the behavior of some part of the world around us. Simulations active these models to allow us to see and understand the world in its
dynamic form. Other disciplines limit themselves to the static side of the world.
- Advantages. Modeling and Simulation has many advantages over other approaches to studying or experiencing the world. Six categories of advantages have been identifies. Two of the most valuable are (1) a model can explore the world much more cheaply than other methods (e.g. flight simulation), and (2) it is much safer to experiment with models than with real situations (e.g. nuclear explosions).
Principles of Modeling
- Voices of Experience. This section explores the important lessons learned by some of the leaders of the modeling field. These include Grady Booch, Phil Kiviat, Paul Fishwick, Averill Law, Alan Pritsker, and Robert Shannon.
- First Principle. In 1975 Robert Shannon identified the most important principle of modeling - "The tendency is nearly always to simulate too much detail rather than too little. Thus, one should always design the model around the questions to be answered rather than imitate the real system exactly ...".
- This section
includes similar key
principles from leaders in the field.
Products of Modeling
- Categories. A simulation contains many different models of an object and its relationships with other objects. We use Phil Kiviat's definitions of the categories of models that must be created to completely capture the state and behavior of a system.
- Formal Model Structure. Many people create models are ad hoc representations of the real world. However, some formalism can help to design models that cover all of the bases. This section introduces Bernard Zeigler's concepts of a modeling formalism.
Process of Modeling
- Problem Statement. The most important step in creating a model is defining a clear problem statement. This is the basis from which most modeling decisions
- Ordered Creation of Products. This section provides an ordered process for creating the products described in the previous section.
Practice of Modeling
- Hands On. The course provides ample opportunities to practice using the ideas presented. There are several hands-on sections that allow participants to create models of every type and to apply the principles that have been learned.
- Software Implementation. Most of the participants in the course intend to apply these principles in the construction of software models. Therefore, we close with some directions on creating a software product from the models that have been designed.