MODELS

SOME BASIC CONCEPTS

Sistem concept have diferents definitions among which are:

-Components collection organized to accomplish a function or set of functions [1].

-Set of cohesive entities pursuing a specific goal [2].

-Entity that maintains its existence through the interaction of its parts [3].

Model definition has multiple references about them too, among which are:

-Physic representation, mathematic or about logic type, from system, entity, phenomena or process [1].

-Representation of a real system that is equivalent to this system in all aspects respects [2]

-Simplified representation of a system from a particular viewpoint in time and space to provide an understanding of the real system [3]

-Representation of the construction and operation of some system of interest [4]

-Description logic of how a system, process or component works [5].

The models maybe physics, when show at scale the physic properties from the real system, graphics, when build graphics diagrams that describe the structure high level about system operation, or mathematics, when a set of mathematical or logical expressions which express the relations between the entities of the system.

A simple mathematical model can be defined as a formulation or equation that expresses the essential characteristics of a physical system or process in mathematical terms.
Can be represented by a functional relationship of the form:

Dependent Variable = f (independent variables, parameters, depending on strength)

In where:


· The dependent variable is: a feature that reflects the state or system behavior.

· The independent variables are generally as space and time dimensions, through which the system behavior will be determined.

·Parameters: they are reflections of the properties system or system composition.

·The force functions: the external influences acting on the system.

·The f function: can be an algebraic expression or a huge and complicated set of differential equations.*

It should be noted that mathematical models can be solved by analytical methods or numerical methods. The analytic solution of a mathematical model consists in obtaining an expression which can be calculated to obtain exact values of the output variables that interest us. The numerical methods of solving mathematical models are based on the discretization and approximation of the numerical values of model variables, generally conditioned by the discretization of the independent variables (usually time and or space).

MODELS TIPES

Mathematical models of any system can be:

-Static or dynamic.
-Continuous or discrete.
-Deterministic or random.

Static models are those time-invariant and dynamic, by contrast, considered the temporal variation of the state of the modeled system.

Continuous models work in the system state variables modeled as continuous variables in terms of working time or performance of the system while discrete models (or discrete event models) consider only actions or events characteristic of the simulated system for those who do not take into account their evolution, but only the moment of its consummation.

REFERENCES

1.- DoD Glossary of M&S Terms. (DoD 5000.59-M). December 1997.
2.- Cunningham, Conrad H. “Lecture Notes of CSci405: Computer Simulation”. Department of Computer and Information Science, University of Mississippi, 2000.
3.- Bellinger, Gene. “Modeling & Simulation”. Outsights Corp., 1997.
4.- Maria, Anu. “Introduccion to Modeling and Simulation”. State University of New York at Binghamton. Proceeding of the 1997 Winter Simulation Conference.
5.- Diamond, Bob. “Concepts of Modeling and Simulation”, Imagine That Inc., 1997.

Prof. Dr. J. A. Capote; Dr. D. Alvear; Dr. O. Abreu; Ing. Ind. M. Lázaro; Ing. Ind. P. Espina.
“Algunos Conceptos y Definiciones del Modelado y Simulación Computacional de Incendios” Grupo GIDAI – Seguridad contra Incendios – Investigación y Tecnología. UNIVERSIDAD DE CANTABRIA, 2006.

*Jorge Icaro Condado Jauregui. “Modelos métodos numéricos y computadoras”, Notas del instituto de investigación en ciencias matemáticas, 2010.