Discrete vs. continuous

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CrbnBlu@aol.com
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Discrete vs. continuous

Post by CrbnBlu@aol.com » Wed Apr 24, 1996 1:56 pm

irt: fnickols@ets.org (fred nickols), Wed, Apr 24, 1996 5:16 AM EST

Fred suggested that I describe the difference between discrete & continuous
simulation, so heres an attempt.

As I understand it, the fundamental difference between discrete and
continuous has to do with how the simulation schedules its run. A discrete
event simulation schedules from event to event and simply skips the time
between events. A continuous simulation considers clock time or step time as
the event which is scheduled so it moves from step time to step time. And the
step time is generally small enough so the simulation appears continuous with
regard to the longer term events happening within the model.

It would seem the only way to do real continuous simulations would be with an
analog machine, and this used to be done but it was most expensive. The
digital computer, which is essentialy a discrete event machine, is made to
mimic analog by using a small step time.

Does this help?
Gene Bellinger
CrbnBlu@aol.com

"David N. Ford"
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Discrete vs. continuous

Post by "David N. Ford" » Thu Apr 25, 1996 6:08 am

To help clarify the differences between discrete and continuous
modeling I see two ways in which models can be considered either
discrete or continuous.

1. Time Handling: If the simulation slices time into evenly sized
pieces and calculates the system conditions at teach timestep it is
continuous. System dynamics uses this method. In contrast, if the
simulation calculates the system conditions only when an event
occurs which will change the condition of the system is can be called
a discrete event or next event simulation.

2. System change: If the simulation assumes and models changes in
parameter values as smooth over time then the change is
continuous. In contrast if the simualtion models parameter changes
with significant jumps in a single timestep than the change can be
considered discrete. In this case system dynamics is continuous. This
description agrees with Dr. Forrester suggestion for formulating
models in Industrial Dynamics (pg. 64) "...we suggest that the system
be treated, at least initially, on the basis of continuous flows and
interactions of the variables. Discreteness of events is entirely
compatible with the concept of information-feedback systems, but
we must be on guard against unnecessarily cluttering our formulation
with the detail of discrete events that only obscure the momentum
and continuity exhibited by our industrial systems." Dr. Forrester
expands this distinction and provides a good example. I believe that
this is the basis of the common admonition to beginning modelers to
avoid IF-THEN statements in equation formulation.

I believe the current discussion is about the second meaning above
and not the first. But SD models do not always have to be
continuous. As suggested by Dr. Forrester, discrete events can be
included in SD models but should not be the focus or initial basis for
those models. In other words, include with caution and careful
thought. In my own work I have found that beginning with an
assumption of continuous change made the relatively few places
where discrete event formulation were appropriate very clear.

Dr. David Ford, Associate Professor
System Dynamics Program
Department of Information Science
University of Bergen
Bergen, Norway
David.Ford@ifi.uib.no



CrbnBlu@aol.com
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Discrete vs. continuous

Post by CrbnBlu@aol.com » Thu Apr 25, 1996 2:38 pm

irt: david.ford@ifi.uib.no (David N. Ford), Thu, Apr 25, 1996 5:35 AM EST

Your description of discrete & continuous from a Time Handling and System
Change perspective adds a dimension I had not considered. My initial question
was posed from a Time Handling perspective, and now I perceieve it as being
relevant also from the System Change perspective. I will have to ponder this
a while.

thanks,
Gene Bellinger
CrbnBlu@aol.com

CrbnBlu@aol.com
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Discrete vs. continuous

Post by CrbnBlu@aol.com » Fri Apr 26, 1996 4:18 am

irt: jimhines@interserv.com (Jim Hines), Thu, Apr 25, 1996 7:43 PM EST

Yes, I would agree that all modeling needs to simplify. I continue to take,
or use, the definition of a model as, "A simplification of reality intended
to promote understanding."

And I agree with your contrast between the pluses for discrete-event modeling
and system dyanmics modeling. The point that continues to confuse me is when
when I misinterpret the character of the environment with the character of
the understanding desired. And Im trying to understand a way to stop doing
this because it gets me in a real bind, meaing all the modeling work doesnt
promote the understanding desired.

I just posted a message that should be in todays set of messages that I
thought I posted yesterday, but sent to the wrong address. This should add
some clarification as to whats confusing me.

thanks,
Gene Bellinger
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"Joel Rahn"
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Discrete vs. continuous

Post by "Joel Rahn" » Fri Apr 26, 1996 10:03 am

On Thu, 25 Apr 1996 10:59:13 +0000,
Jim Hines <
jimhines@interserv.com> wrote:
>
>The plus for system dynamics modelers is that we can more easily
>represent the fact that things are continually changing and
>influencing eachother. I think this probably helps with the
>representation of feedback.
>
My colleagues and many students (I am in an OR-Decision Sciences
department) have a lot of trouble with the "continually changing" aspect of
SD. They see things in terms of discrete decisions. I have always found it
interesting that SD clearly emphasises the distinction between material and
information flows and the sources of decisions, whereas no discrete
simulation approach or package (that I am aware of) deals explicitly with
either of these as part of model conceptualisation.

On the topic, the four-point check mentioned by Gene(? - sorry if the
credit is misplaced; my e-mail is so deficient I cant check it right now)
sums up the criteria for deciding which approach to use pretty well. I tell
my students that if they have to know what each item in a system is doing
at any time, use a discrete, stochastic simulation; if they need only to
deal with the overall flow of items, a continuous (SD) or
fixed-time-advance (time-series) approach is best, and if they need to deal
with the overall flow of items and decisions, SD is best.
R. Joel Rahn
Dipartement OSD
Faculti des sciences de ladministration
Universiti Laval
Ste-Foy, Quibec
G1K 7P4 CANADA
til.: 418 656 7163 fax: 418 656 2624
e-mail: Joel.Rahn@fsa.ulaval.ca

jimhines@interserv.com
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Discrete vs. continuous

Post by jimhines@interserv.com » Sun Apr 28, 1996 6:55 pm

"The point that continues to confuse me is when when I misinterpret the
character of the environment with the character of the understanding desired."

You may be trying to express what confuses you, but your statement is clarifying
for me: What determines the choice of SD vs. Discrete Event is the character of
the understanding desired.

Now, we need to get a little sharper on the character of the understanding that
Discrete Event modeling produces. I said earlier that it has to do with
variability within a population of entities. Im not sure about that, because
people sometimes give results of discrete event simulations sometimes as just
the mean (I think). So ... suggestions?

Jim Hines
jimhines@interserv.com

jimhines@interserv.com
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Discrete vs. continuous

Post by jimhines@interserv.com » Sun Apr 28, 1996 8:03 pm

On Fri, 26 Apr 96, "Joel Rahn" <rahnj@fsa.ulaval.ca> wrote in SD0069:
I tell
>my students that if they have to know what each item in a system is doing
>at any time, use a discrete, stochastic simulation; if they need only to
>deal with the overall flow of items, a continuous (SD) or
>fixed-time-advance (time-series) approach is best, and if they need to deal
>with the overall flow of items and decisions, SD is best.

Joel: two questions
1) What is "fixed-time-advance" approach?
2) What about feedback as a criterion? When your students want to investigate
feedback, does it matter whether they go SD or discrete?

Jim Hines
jimhines@interserv.com

"Joel Rahn"
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Discrete vs. continuous

Post by "Joel Rahn" » Mon Apr 29, 1996 3:53 pm

On Sun, 28 Apr 1996 20:03:33 -0700,
jimhines@interserv.com <jimhines@interserv.com> wrote:
>Joel: two questions
>1) What is "fixed-time-advance" approach?

It is the discrete time step approach beloved of econometricians and time
series mavens. Their observable variables are generally aggregates or
averages over a time period.

>2) What about feedback as a criterion? When your students want to investigate
>feedback, does it matter whether they go SD or discrete?

Yes indeed. I should have added in the last sentence "...and decisions and
feedback, SD is best". I guess I have internalized the idea that if you
have flows of decisions, you generally have feedback (otherwise you are
modeling irrational decision-making)... Hmmm, maybe that is why there are
so few models of political processes, or why we usually dont deal with
decision processes having a large component of irrationality. Why do I
feel I have just stepped in a cow-pie of gargantuan dimension?
R. Joel Rahn
Dipartement OSD
Faculti des sciences de ladministration
Universiti Laval
Ste-Foy, Quibec
G1K 7P4 CANADA
til.: 418 656 7163 fax: 418 656 2624
e-mail: Joel.Rahn@fsa.ulaval.ca

"Joel Rahn"
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Discrete vs. continuous

Post by "Joel Rahn" » Mon Apr 29, 1996 4:20 pm

On Sun, 28 Apr 1996 18:55:42 -0700,
jimhines@interserv.com <jimhines@interserv.com> wrote:

>for me: What determines the choice of SD vs. Discrete Event is the
>character of the understanding desired.... So ... suggestions?

Yes, the results of discrete event simulations are sometimes given as the
means of various measures of performance (queue lengths, time in system,
utilization percentages) but a complete study should also report estimated
confidence intervals for these measures and control for correlation and
confounding effects.

The important variability in discrete-event simulations is the variability
in time between successive events (between arrivals, service starts and
finishes) since it is this variability that explains the creation of
queues, as well as their variability, and thus explains the variability of
time-in-system and in utilization rates. Other variability may be
important (type of product to be produced, service priorities, alternate
routings through the system) but without the time-interval variability,
you could just do a Monte Carlo evaluation of the distribution function of
a performance measure (using something like @RISK, for example), no
simulation (as understood here, involving change of state over time) would
be required.
R. Joel Rahn
Dipartement OSD
Faculti des sciences de ladministration
Universiti Laval
Ste-Foy, Quibec
G1K 7P4 CANADA
til.: 418 656 7163 fax: 418 656 2624
e-mail: Joel.Rahn@fsa.ulaval.ca

CrbnBlu@aol.com
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Discrete vs. continuous

Post by CrbnBlu@aol.com » Tue Apr 30, 1996 10:28 am

irt: jimhines@interserv.com, Mon, Apr 29, 1996 5:31 AM EST

Jim made the comment, "What determines the choice of SD vs. Discrete Event is
the character of the understanding desired," and although I think this has
passed by several times, finally it caught me. I have continued to perceive
my confusion in terms of implementation, and as such I continued to search
for an understanding in the wrong place. My repeated implementation
difficulties have been the result of not having a clear distinction of the
character of understanding desired. I guess as Covey said in "The 7 Habits,"
"begin with the end in mind," yet "the end" is not the implementation and
simulation but "the understanding."

So I guess Im now at the point of asking what is the different character of
understanding provided by discrete and continuous considerations of a
particular situation?

The current thought, which Im not quite comfortable with yet is that I would
look to a continuous perspective to provide insight into the transition of
one or more variables over time. I would then look to a discrete perspective
to provide me with an insight as to possible distribution of values for one
or more values at some point in time. So I now see one as providing variable
transitions while the other provides value probablilities (developed over
multiple runs).

Gene Bellinger
CrbnBlu@aol.com

William Steinhurst
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Discrete vs. continuous

Post by William Steinhurst » Tue Apr 30, 1996 5:06 pm

IRT: CrbnBlu@aol.com Wed, 24 Apr 1996
>
> It would seem the only way to do real continuous simulations would be with an
> analog machine, and this used to be done but it was most expensive. The
> digital computer, which is essentialy a discrete event machine, is made to
> mimic analog by using a small step time.

The Euler method used in DYNAMO, etc., is a discrete numerical
solution method that is applied to continuous differential equations.
In other words the model is continuous in time and "simulating" it
digitally means finding a solution to the continuous problem using
discrete numerical methods. I hope this is not a nit pick, but I feel
there is an important difference between a numerical approximation to
a continuous solution and the simulation of a discrete model.

BTW there is now a third method in principle: symbolic math programs
(Mathematica, Maple, etc.) can solve *some* systems of ODEs that
would be beyond any pencil and paper work. Has anyone tried them on
classic SD problems?

William Steinhurst
wsteinhu@psd.state.vt.us

"CDH"
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Discrete vs. continuous

Post by "CDH" » Sun Nov 30, 2003 12:11 pm

Hi group and Raymond.

My name is Rainer Uwe Bode and I work in Brazil at a consulting firm. I do
SD modeling since 1996.

I have been accompanying this discussion for the last two weeks, and I must
say that in case I had some certainties before, they are all gone now.

Raymond says:

If a process converts a single object at a time,
> it is a discrete-event process. If the process works on a continuous
> stream, it is a continuous process. If a system is composed of one or
more
> discrete-event processes, it must be a discrete-event system. If a system
> is composed of one or more continuous processes, it must be a continuous
> system.

So, if you have pieces on an assembly line, lets say bars of steal,
managing one at a time, you willl have, accordingly, discrete time events.
But, if you convert all the bars into weight and process them at tons/ hour,
you will have a continuous process in continuous time.

So, the same event can be addressed and modeled in two different ways.

Then, the problem is not the one-at-a-time, since you can convert almost all
intire units into averaged pieces processed continuously, like envelopes.

The problem in deciding what method to use seems more to be one of deciding
wether you want to accompany the variations of a stream of items, or if you
want to accompany a single object from start to finish.

So, if you want to see, in a set of bars, bar 37 travel through the system,
you would want to use a discrete-event-modeling.
If tou prefer to analyse the journey of the bundle of bars, the bottlenecks
and the supply-chain, SD would be more than adequate.

Still, the specs of the flow of time seem to be of minor importance when
comparing dicrete and SD modeling: to me, the basic criterium for choice
seems to be the necessity of considering the more complex phenomena, like
feedbacks and non-linearities.

To me, with SD ou are able to address a lot more broader spectrum of
problems, whereas discrete-event-modeling seems to be useful in a more
limited order.

Rainer Uwe Bode
CDH- Recife
cdeh@hotlink.com.br

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