These problems representing the characterization of a phenomenon or process could be modelled at an abstract level by extracting common qualities from specific examples.The process of formulating generalized concepts enables a better understanding of complex issues and, consequentially, the resolution of complex problems.
Therefore, modelling starts with the use of abstraction for the understanding of the problem and the use of methodologies and techniques for the implementation aspects.
A model has three essential parts:
(i) a process or phenomenon which is to be modeled,
(ii) a mathematical structure capable of expressing the important properties of the process to be modeled, and
(iii) an explicit correspondence between the two.
(iii) an explicit correspondence between the two.
The first part of a model is a phenomenon or a process which is to be characterized mathematically. For example the execution of a program, the allocation of resources of a computation center, and the flow of information in a computer network. The real world component is described quantitatively by such things as parameters values each times the event occur.
The second part of a model is an abstract mathematical structure. The structure has no intrinsic relation to the real world. However, because of its abstractness, the structure can be used to model many different phenomena. Therefore, if the mathematical model is successful, the language of its mathematical structure can be used to make assertions about the object being modeled.
The third part of a model is a specification of the way in which the real world is represented by a mathematical structure, i.e., a correspondence between the elements of the first component and those of the second. Parameters, relationships, and occurences in the real world will be associated with such variables, equations, and operations in the mathematical structure. This correspondence makes possible the use of the mathematical structure to describe those facets of the real world which are of interest.
