What is
simulation?
Simulation is used to
study systems and thus obtain insight into the behavior of such a system.
However, often there are other ways to obtain that insight. So, when is this
study called simulation? When we are talking about imitating a system.
Definition of simulation:
Simulation is the imitation of a system, based on the knowledge or
assumptions regarding the behavior of parts of that system, with the purpose of
obtaining insight in the behavior of that system as a whole.
Using a simple example, we shall now discuss three ways to solve a
problem.
Situation
At a certain time, a vessel contains 100 litres. We know the contents flow
from the vessel with a speed of 1 litre per minute.
Purpose
We wish to know how long it takes before the vessel is empty.
Methods of solving the problem
a.
Calculation
If 1 litre pours out of the vessel per minute and there are 100 litres in
the vessel, a simple calculation shows that the vessel will be empty in 100
minutes.
b.
Measuring
Assume we don't know how to calculate, but have learnt to tell time. We can
then stand next to the vessel with a stopwatch and wait till the vessel is
empty. If we then press the button immediately, we read: 100 minutes
c.
Simulation
If we don't have a vessel to stand next to, we could decide to put 100
grams of sugar in a cardboard box and then cut a hole in the box so that 1 gram
of sugar pours out per minute.
We measure the time it takes for the box to empty and conclude that the
same is probably valid for the vessel.
Four questions arise from these three methods:
1. Does one
only simulate when one can't calculate?
2. Is the
experiment with the box not a lot of work for such a simple question?
3. Can we
simply assume that the box is a good representation of the vessel?
4. Is
simulating also measuring?
To start with the last question: yes, simulating is measuring
(registering), with, as a specific characteristic, that we do not measure
reality, but a model of reality. Thus, simulation is not a mathematical method.
Simulation does use mathematical techniques (especially statistical), but merely
as a tool for measuring.
The third question hides an aspect to which we will dedicate an entire
chapter, namely verification and validation (Chapter 9) or: does the behavior of
the model correspond with reality?
The second question contains the aspect of purpose. If we know that
simulation is the only way to solve a problem, we will also have to ask
ourselves if the costs of the experiment weigh up to the extra information the
experiment will provide.
The first question touches the problem: when do we simulate? In general,
there are two ways to solve a problem: analytically and experimentally. The
first solution was analytical, the second and third were both experimental.
Analytical methods often give an optimum solution, experimental methods often
lead to a good, but not necessarily optimum solution (of heuristic
nature).
Solving a problem experimentally without simulation, requires that the
system to be studied exists and is available.
That is not always the case. Often one wants to know things about a system
which does not yet exist or about the consequences of a change in a system
without first having to build the new system. In that case, two possibilities
remain: simulation or an analytical solution.
Solving a problem analytically requires that we be able to describe the
whole system, including the relation between the subsystems, mathematically.
This is not always possible. This has two main causes: complexity and
uncertainty.
Complexity
A system can be so complex, with so many mutual influences of the
subsystems, that it is simply not possible (or extremely difficult) to describe
the system in terms of mathematical relations. Say the speed of the flow of the
above described vessels is dependent on the amount of fluid still in the vessel
and also on the size of the opening and that, on top of that, the opening is
enlarged 10% every 4 minutes.
It will be clear that the mathematical (analytical) solution becomes more
difficult and that most of us will choose to stand next to the vessel to
measure. Now imagine a batch of vessels that all influence each other. It now
becomes a lot easier to realize that there is a point at which the preference
goes towards a non-analytical approach, because this is cheaper (measuring is
cheaper/easier than calculating), or because the analytical approach is
impossible.
Uncertainty
Describing a system in mathematical terms can also be difficult, if we are
considering a simple (not complex) system and are faced with uncertainty.
Imagine again the simple vessel with, as a special characteristic, the fact that
the opening blocks up sometimes. We don't know when it happens, we just know it
happens. This makes it impossible to solve the initial problem (either
analytically or non-analytically): when is the vessel empty (we could measure
it, but who says the next result will be the same?). We have to formulate the
problem differently: when do we expect the vessel to be empty? Then, this
problem can only be solved if we know a little more about the blocking up, for
example: how often is there a blockage and how long, on an average, does such a
blockage last? If we have statistical information, for example a probability
distribution of the blockage behavior, then we essentially have a solvable
problem. The question now is: do we choose an analytical or non-analytical
method of solution? The characteristic of processes in which uncertainty plays a
role, is that they easily become analytically unsolvable. Only systems
containing few uncertainties can sometimes be approached mathematically (see
Chapter 4).
We have now seen how a choice is made between analytical and non-analytical
methods. The choice between the two experimental methods (experiment in reality
or experiment with a model) needs some explanation.
In general, you will choose simulation (model experiment) if:
- the
experiment in reality is not possible (what happens to the weather when the
ice-cap melts?)
- the experiment
in reality is not safe (think of the flight simulator)
- the experiment
in reality is too expensive (building a new factory and discovering the design
is not right)
The process of choosing simulation as a method of solution is shown in the
following illustration: