Discrete vs. continuous (or aggregated) representation

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"geoff coyle"
Senior Member
Posts: 94
Joined: Fri Mar 29, 2002 3:39 am

Discrete vs. continuous (or aggregated) representation

Post by "geoff coyle" »

As usual, Jay has hit the nail on the head. Whether one uses one simulation
paradigm or another depends on the nature of the problem, the purpose of the
analysis and, perhaps above all, on the nature of the question to be
answered. I tried to make the same points in my earlier email about
distributions of outcomes versus the dynamics of policy responses. As so
often in these discussions, I conclude that, in order to do good SD, it is
essential to be at least familiar with the other methods of operational
research. Those other methods, such as discrete event simulation, have their
own well-developed and generally accepted terminologies so we do ourselves
no service by trying to have our own debates about what discrete and
event mean.

Of course, even when the problem is essentially continuous and the focus is
policy design - the classical paradigm of SD - it may be necessary to allow
for discrete occurrences within an SD framework. One example which comes to
mind is Juan Regos PhD on the development of Argentinas hydro-electricity
system. There were very clear continuous processes involving the flows of
money etc, and there were some profound policy implications, but the
individual hydro-electric projects differed so enormously in capacity,
capital cost and construction time that they had to be treated as separate
discrete entities within the model. Another case is Eric Wolstenholmes work
on the design of coal-handling facilities for an underground mine. In such a
case, designing the necessary capacity for conveyors, bunkers etc required
to supply the continuous operation of an electricity generating station had
to take account of the random stoppages, of random duration, of the
coal-cutting machines on several production faces in the mine. Both of these
cases involved some tricky modelling but proved to be well within the
capabilities of the DYNAMO-type simulation languages.

I was a bit puzzled by Keith Linards description of a simulation using a
time step of 1 minute over 24 hours (I think it was 24 but I lost the email
in the blizzard of Spam). As I understand SD, the time unit in a model
depends on the nature of the process. In some cases the time unit might be a
year, in others a month, hour, minute or whatever is appropriate. Let us
suppose that in Keiths concrete plant, there are very fast processes and
that a minute is a suitable unit for time (I rather doubt it but lets
accept that for the sake of argument). One would then look for the shortest
delay and let us suppose that the shortest delay is 3 minutes and that that
delay is validly represented as third order. In that case, the standard
texts, going back as far as Industrial Dynamics, imply that the solution
interval, DT, should be not more than 0.5 minutes (Id prefer 0.25). In my
view, the term time step is not appropriate because we are simulating a
set of difference equations that that needs a solution interval, whereas
discrete simulation does use a time step (which may not be constant).

Of the other hand, if it takes, say, 2 hours to mix a batch of concrete, the
time unit should be the hour and DT would become 0.25 (the decimal
equivalent of an exact binary fraction).

In other words, dealing with time in an SD model is not a trivial issue. I
have a student handout which tries to clarify this, though its all in the
standard texts.

I wish you all a joyful Christmas a dynamic New Year.

Geoff
From: "geoff coyle" <
geoff.coyle@btinternet.com>
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