Notes

The general process of analytical modeling involves mapping the behavior of a complex system onto a relatively simpler system, solving the simpler system for the measures of interest, and then extrapolating the results back to the complex system.

As with other performance evaluation methods, analytic studies of computer systems yield only approximations to the solutions we desire. In analytic modeling several distinct types of compromises can be made:

1) In the abstraction of the real world to a mathematical model. Examples here include assumptions of certain arrival processes, service time distributions, and idealized service disciplines.

2) In an approximate analysis of the mathematical model. The diffusion approximation is an example of an approximate solution technique.

3) In settling for a less complete solution, e.g., mean response time rather than the distribution of the response time, or equilibrium distributions rather than transient solutions

4) In settling for a less convenient form of solution, e.g., a Laplace Transform or a computational procedure is obtained rather than an explicit solution.

It should be pointed out that the real question is whether analysis yields results which are valid in a practical sense and not whether the model appears 'over simplified'. The art of where to apply compromises in modeling is an exceedingly difficult question and can really only be determined by experience in applying analysis.

We are faced with the problem of determining what characteristics of a system must be included in a model to get reasonably accurate results. The question is what all can be excluded to produce reasonable approximation of reality rather than what all to include: since simpler models are easier to build, maintain, and analyze.