Introduction to Modeling and Simulation

SYSTEMS AND EXPERIMENTS
What is a system? We have already mentioned some systems such as
the universe, a space shuttle, and the like. A system can be almost anything.
A system can contain subsystems that are themselves systems.
A possible definition of system might be:
• A system is an object or collection of objects whose properties
we want to study.
Our wish to study selected properties of objects is central in this definition.
The “study” aspect is fine despite the fact that it is subjective.
The selection and definition of what constitutes a system is somewhat
arbitrary and must be guided by what the system is to be used for.
What reasons can there be to study a system? There are many
answers to this question but we can discern two major motivations:
• Study a system to understand it in order to build it. This is the
engineering point of view.
• Satisfy human curiosity, for example, to understand more about
nature—the natural science viewpoint.
THE MODEL CONCEPT
Given the previous definitions of system and experiment, we can now
attempt to define the notion of model:
• A model of a system is anything an “experiment” can be applied
to in order to answer questions about that system.
This implies that a model can be used to answer questions about a
system without doing experiments on the real system. Instead we
perform simplified “experiments” on the model, which in turn can
be regarded as a kind of simplified system that reflects properties of
the real system. In the simplest case a model can just be a piece of
information that is used to answer questions about the system.
Given this definition, any model also qualifies as a system.
Models, just like systems, are hierarchical in nature. We can cut out
a piece of a model, which becomes a new model that is valid for a
subset of the experiments for which the original model is valid. A
model is always related to the system it models and the experiments
to which it can be subjected. A statement such as “a model of a
system is invalid” is meaningless without mentioning the associated
system and the experiment. A model of a system might be valid
for one experiment on the model and invalid for another. The term
model validation, see Section 1.5.3, always refers to an experiment
or a class of experiment to be performed.
We talk about different kinds of models depending on how the
model is represented:
• Mental model—a statement like “a person is reliable” helps us
answer questions about that person’s behavior in various situations.
• Verbal model—this kind of model is expressed in words. For
example, the sentence “More accidents will occur if the speed
limit is increased” is an example of a verbal model. Expert
systems is a technology for formalizing verbal models.
• Physical model—this is a physical object that mimics some
properties of a real system, to help us answer questions about
that system. For example, during design of artifacts such as
1.3 Simulation 7
buildings, airplanes, and so forth, it is common to construct
small physical models with the same shape and appearance as
the real objects to be studied, for example, with respect to their
aerodynamic properties and aesthetics.
• Mathematical model—a description of a system where the relationships
between variables of the system are expressed in mathematical
form. Variables can be measurable quantities such as
size, length, weight, temperature, unemployment level, information
flow, bit rate, and so forth. Most laws of nature are
mathematical models in this sense. For example, Ohm’s law
describes the relationship between current and voltage for a
resistor; Newton’s laws describe relationships between velocity,
acceleration, mass, force, and the like.
The kinds of models that we primarily deal with in this book are
mathematical models represented in various ways, for example, as
equations, functions, computer programs, and the like. Artifacts represented
by mathematical models in a computer are often called virtual
prototypes. The process of constructing and investigating such models
is virtual prototyping. Sometimes the term physical modeling is
used also for the process of building mathematical models of physical
systems in the computer if the structuring and synthesis process is the
same as when building real physical models.
1.3 SIMULATION
In the previous section we mentioned the possibility of performing
“experiments” on models instead of on the real systems corresponding
to the models. This is actually one of the main uses of models, and
is denoted by the term simulation, from the Latin simulare, which
means to pretend. We define a simulation as follows:
• A simulation is an experiment performed on a model.
Analogous to our previous definition of model, this definition of simulation
does not require the model to be represented in mathematical
or computer program form. However, in the rest of this text we
will concentrate on mathematical models, primarily those that have
8 CHAPTER 1 Basic Concepts
a computer-representable form. The following are a few examples of
such experiments or simulations:
• A simulation of an industrial process such as steel or pulp manufacturing,
to learn about the behavior under different operating
conditions in order to improve the process.
• A simulation of vehicle behavior, for example, of a car or an
airplane, for the purpose of providing realistic operator training.
• A simulation of a simplified model of a packet-switched computer
network, to learn about its behavior under different loads
in order to improve performance.
It is important to realize that the experiment description and model
description parts of a simulation are conceptually separate entities. On
the other hand, these two aspects of a simulation belong together even
if they are separate. For example, a model is valid only for a certain
class of experiments. It can be useful to define an experimental frame
associated with the model, which defines the conditions that need to
be fulfilled by valid experiments.
If the mathematical model is represented in executable form in
a computer, simulations can be performed by numerical experiments,
or in non numeric cases by computed experiments. This is a simple
and safe way of performing experiments, with the added advantage
that essentially all variables of the model are observable and controllable.
However, the value of the simulation results is completely
dependent on how well the model represents the real system regarding
the questions to be answered by the simulation.
Except for experimentation, simulation is the only technique that is
generally applicable for analysis of the behavior of arbitrary systems.
Analytical techniques are better than simulation, but usually apply
only under a set of simplifying assumptions, which often cannot be
justified. On the other hand, it is not uncommon to combine analytical
techniques with simulations, that is, simulation is used not alone but
in an interplay with analytical or semi-analytical techniques.