Discrete and continuous

[George Richardson]

Ive been holding back on this discussion, but finally feel that I have to
point out that there is a lot of literature on this topic. The topic
emerged naturally in my study of the history of feedback thought -- the
index of Feedback Thought contains the entries - continuity and
discreteness - continuous point of view - difference equations -
differential equations - discreteness - events - message loops each of
which has references to at least ten places in the text, and some to a lot
more. Some of the stuff covered here shows how smart people got confused
about dynamic feedback systems by using difference equations instead of
differential equations, and some shows how different the contributions are
when one is thinking in terms of discrete events and decisions and when
one is thinking in terms of policy structure and dynamics. Some of it
shows how many in one line of feedback thought in the social sciences came
to center on discrete events and messages, thus drifting away from ideas
like loop polarity, which peopl in the other thread seem to emphasize so
much. I think we need more data for this discussion.

Weve been tending to discuss this topic on the list as an issue of
"representation" -- the choice of differential or difference equations,
or event-oriented simulation packages or whatever. But fundamentally the
topic is about how we are trying to think about the system. The choice
of how we are trying to think about the system has a lot to do with our
purpose -- we might think that electricity is fundamentally (really) a
discrete thing (electrons or smaller bits) but we might know that we can
do wonders designing electronic circuits if we think of electricity as a
flow. Same goes for population or inventory, at some sufficient level of
aggregation and conceptual distance. Our simulations are tools for our
thinking, so we should push the discrete/continuous questions in the
direction of thinking and away from representation.

To bring the matter close to home: The article by R.G. Coyle ("A System
Dynamics Model of Aircraft Carrier Survivability", SDR 8,3(fall 1992):
193-212) is, in my view a discrete model, formulated that way because the
author was intentionlly thinking in discrete event terms when he built
it. He used COSMIC/COSMOS, a DYNAMO-like language intended for system
dynamics modeling. One can imagine a continuous representation of that
dynamic system, where aircraft carriers and planes ebb and flow on
continuous paths rather than steps from 6 to 7 or 583 to 584. To help
focus our discussion on discrete and continuous, we might well ask what
does one learn in each repsentation? Are there differences in what one
learns? Rod MacDonald is addressing just that question. We might help
our list discussion along if more of us tackled such a question.

...Geo

-----------------------------------------------------------------------------
George P. Richardson G.P.Richardson@Albany.edu
Rockefeller College of Public Affairs and Policy Phone: 518-442-3859
University at Albany - SUNY, Albany, NY 12222 Fax: 518-442-3398
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[CrbnBlu@aol.com]

irt: gr383@cnsvax.albany.edu (George Richardson), Fri, Apr 26, 1996 6:11 PM
EST

George, thanks for the reference. I have a copy of your book on reserve which
Ill pick up as soon as I can get to the library.

You make the comment:

Weve been tending to discuss this topic on the list as an issue of
"representation" -- the choice of differential or difference equations,
or event-oriented simulation packages or whatever. But fundamentally the
topic is about how we are trying to think about the system. ...

Which evoked the following thoughts:

Yes, I would agree that purpose must come first and should guide a
determination of how we think about the system. And I find CLDs a convenient
representation for thinking about the system independent of implementation.
And with an awareness that implmentation will happen, specific representation
continues to creep back into my thoughts. I found this same difficulty quite
evident for years when doing application software design and development.
Althought I could think about the application in terms of structured system
design diagrams and structured english, independent of programming language,
knowing that sooner or later I would have to write the program caused
implementation specifics to creep back into my thoughts. This same thought
creep seems to happen when thinking about systems in a CLD representation.

Based on your comments I guess I would now phrase my confusion in terms of,
"Once I understand the purpose for considering the system, and have thought
about it in an implementation independent representation, how do I consider
the appropriate factors to determine the most appropriate implementation
representation?"

Gene Bellinger
CrbnBlu@aol.com

[jimhines@interserv.com]

On Fri, 26 Apr 1996, George Richardson <gr383@cnsvax.albany.edu> wrote in
SD0074:
>Some of it
>shows how many in one line of feedback thought in the social sciences came
>to center on discrete events and messages, thus drifting away from ideas
>like loop polarity, which people in the other thread seem to emphasize so
>much.

But is it the messages or the discrete events that makes people move away from
loop polarity (and loops)? Messages obviously move away from loop polarity,
because you dont know what is IN the messages, and hence what the direction of
influence will be.

Discrete event seems more subtle. I suspect its not well suited to
investigating feedback. But, why? (one of us should do the workforce/inventory
oscillator in discrete event terms and report back to the group!).

Regards,
Jim Hines
jimhines@interserv.com

[Jack Homer <70312.2217@CompuServ]

Jim Hines writes:

>Discrete event seems more subtle. I suspect its not well suited to
>investigating feedback. But, why?

And in another message:

>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?

These are two good leading comments for a recent modeling project I want to
describe a bit. (The work is company private, so all I can do here is give a
sketchy description.) I was working with an oil exploration company that wanted
to assess the value of various types of data collection activities at different
stages during the exploration process. Individual prospects within a given
region are evaluated seismically, and decisions are made about whether or not to
proceed with drilling. More pre-drill data means better estimates of whether
anything is down there and how big it is if its there. More post-drill data,
on the other hand, further improves size estimates, and also helps refine
understanding of the whole region, which is helpful for assessing subsequent
prospects.

When modeling this issue, it is important to capture its stochastic nature and
to provide information on the full distribution of outcomes (not just means)
under different assumptions. Consequently, one must track individual prospects
and their attributes, which requires a discrete Monte Carlo approach. This is
something I was able to do using ithink software, with its conveyors and
queues, using lots of co-flows to track prospect size attributes, and with
carefully specified random number generators.

But this is also a system with feedback loops, the most important of which is
the influence of current drilling data on the reliability of subsequent prospect
estimates. So one ends up with a discrete-element model with feedback,
operating in continuous time. It works just fine technically, once you get a
handle on those tricky conveyors and queues.

The only problem with this kind of modeling is that it can take hundreds of
simulations to get a good solid sense of how different assumptions affect the
outcomes. Unlike most SD modeling, where we almost always deal with
distribution means, discrete-element simulation often aims to provide statistics
on the full distribution of outcomes. As a result, getting from model to
insights can be a real chore, and requires careful up-front design of
experiments.

The problem here is mainly one of software. Specifically, ithink allows for the
discrete element simulation, but does not provide summary statistics (like 75%
confidence intervals) for a series of simulations. Conversely, Vensim does
provide such summary statistics, but does not support discrete element
simulation.
I should add that in my years as an SD modeler, the oil exploration model is the
first time Ive done a discrete-element simulation with feedback, and I dont
expect to be doing another one soon. Nonetheless, it is important to note that
the modeling project bogged down and became something that the client could not
support to its logical conclusion, in part because of the shortcomings of the
software. It sure would have been nice if one of the SD software packages had
allowed me to do discrete-element simulation with automated summary statistics.
Oh well, you cant always get what you need at the time.

Jack Homer
70312.2217@compuserve.com

["Joel Rahn"]

On 29 Apr 96 11:03:35 EDT,
Jack Homer <70312.2217@compuserve.com> wrote:


>
>But this is also a system with feedback loops, the most important of which is
>the influence of current drilling data on the reliability of subsequent prospect
>estimates. So one ends up with a discrete-element model with feedback,
>operating in continuous time.

This looks like a Bayesian model with the revision of probabilities
occurring as new data arrives. Are the times at which (or the sequence in
which) new data arrives important for the results (i.e., does it matter if
datum A arrives before datum B, in the sense that you will try to get datum
A before datum B)? If not, maybe a Monte Carlo approach would be adequate.
And if not, maybe neither ithink nor Vensim would be the best tool.
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

[Jim Hines]

Jack Homer describes a very interesting project in SD0091 that promises
to shed light on this discussion.

Just to check my understanding, Jack: Youre saying that the stochastic
nature of the problem means that you have to track individuals (as
opposed to central tendencies of populations) and that this means you
need to take a discrete event approach. Right?

Feedback was a property of the continuous-time portion of the model,
right?

Assuming I did understand, would it be possible to explain a little more
about the stochastic nature of the problem, and particularly why it
wasnt possible to simply have stochasticness in the "policies" of a SD
model. Also, I didnt understand the central feedback loop that you
needed to capture. I think the answers to these questions will further
pin down for all of us what the nature of the problem is that discrete
event modeling can help out with and where continuous simulation
modeling is key.

And now two comments: Jack says that discrete event modeling "is
something I was able to do using ithink software, with its conveyors
andqueues, using lots of co-flows to track prospect size attributes
..."

The necessity of using lots of coflows is a big drawback, necessitated
by ithinks lack of a built-in way of tracking indivivuals and their
characteristics. Discrete event simulators (like that written by
Goldberg and Robson in smalltalk) make tracking characteristics of
individuals easy.

The second comment: Jack says
"I should add that in my years as an SD modeler, the oil exploration
model is the first time Ive done a discrete-element simulation with
feedback, and I dont expect to be doing another one soon" I am
confident that this corresponds to the experience of most other people
who have been in the SD field for a decade or more.

This means (1) discrete-event extensions to the system dynamics
simulation environments are probably low-priority extensions for the
system dynamics community. (2) This discussion-thread of discrete-event
modeling probably will not convince us to go out there and do discrete
event modeling, but rather will sharpen our understanding of what is
unique and valuable about what we do in continuous-time modeling.

Jim Hines
<jimhines@interserv.com>

[Jack Homer <70312.2217@CompuServ]

Re: Joel Rahn, Mon, 29 Apr 96 16:39:59 CST

>This looks like a Bayesian model with the revision of probabilities
>occurring as new data arrives. Are the times at which (or the sequence in
>which) new data arrives important for the results (i.e., does it matter if
>datum A arrives before datum B, in the sense that you will try to get datum
>A before datum B)? If not, maybe a Monte Carlo approach would be adequate.
>And if not, maybe neither ithink nor Vensim would be the best tool.

Yes, indeed, the situation is a fascinating case of Bayesian estimation
occurring in continuous time, with gradual improvement in the reliability of
estimates of oil presence (0 or 1) and amount for a given prospect. The
determinant of reliability is the pooled accumulation of drilling data, without
regard to the order in which it arrives.

The big question in the study was: Should standards for drilling be purposely
low toward the beginning of a regional program, resulting in more early drilling
than otherwise would be done, so that later prospects are better estimated?
Would this approach result in fewer errors (accepting bad prospects, rejecting
good ones) being made overall, due to the strength of the learning effect?

The approach was to build a feedback model with both discrete and continuous
elements, and with prospect sizes (both actual and estimated) being generated
Monte Carlo-style with specified probability distributions.

The client had previously built a spreadsheet model using Crystal Ball software,
which, like @Risk, handles the stochastic stuff nicely, but could not handle the
effects of learning (feedback) and bottlenecked capacity (thus, queues) that we
wanted to capture in the dynamic model.

Jack Homer
70312.2217@compuserve.com

[Jack Homer <70312.2217@CompuServ]

Re: Jim Hines, SD0111, April 30

Forgive me if I did not make myself clear. The oil exploration model is
continuous-time in its entirety, all done within ithink. Individual prospects
(along with attributes of actual and estimated size) are generated Monte
Carlo-style at regular intervals, and they immediately get on a sequence of
conveyors and queues that take them through the exploration process. At
evaluation junctures, a prospect faces certain hurdles or requirements, and
either passes (on to the next stage) or fails (does not proceed to the next
stage). Constraints on drilling capacity may occasionally bring certain
conveyors to a halt, causing the prospects behind to pile up in queues until the
capacity frees up. Drilling experience is accumulated, and feeds back to affect
the co-flows of estimated, as opposed to actual, prospect size.

Re: Gene Bellinger, SD0091, April 30

Yes, Ive seen Extend but never modeled with it. Id be interested to get
confirmation on Extends ability to handle the model Ive described, and deliver
summary statistics and tolerance intervals (a la Vensim).

Jack Homer
70312.2217@CompuServe.COM