Discrete and Continuous Simulation

[gsimpso4@csc.com]

I am involved in a discussion in which there are proponents of both
discrete and continuous simulation. I have come to the tentative
conclusion that discrete simulation has an important role to play in
process optimisation, while continous simulation is the appropriate tool
for consideration of business-level alternatives. And (even more
tentatively) that neither tool is appropriate in the others domain.

I am dissatisfied with this formulation; it seems to me that there must be
more precise statements that could be made.

Can anyone offer more insight into this topic, or direct me to resources
that bear on this question?

...george...
From: gsimpso4@csc.com

[=?iso-8859-2?Q?Andrej_=A9kraba?=]

I suppose that there was once a discussion on the SD list about
Discrete Vs continuous simulation, it should be checked in the archive.

In my opinion, simulation methodology should connect the discrete and
continuous models. There some efforts put in this manner from the
Powersim.

We have made some efforts at the interconnection of both methodologies
at the modeling of the business system where production process was
modeled
by the discrete model and the financial flows were modeled by the SD
approach. The idea of interconnection is presented in the following
paper:

Kljajic M, Bernik I, Skraba A. 2000. Simulation Approach to Decision
Assessment in Enterprises, Simulation 75: 199-210

Hypothetically (and technically to some limitations) you could model any
system by continuous or discrete approach, which is, for example,
demonstrated by some discrete models done in Powersim, but proper
approach at the solving of certain problem leads us to more elegant
solutions. The approaches should be integrated in order to benefit from
both worlds.

Best regards, Andrej Skraba.

-------------------------------------------------------------
University of Maribor
Faculty of Organizational Sciences
Cybernetics and DSS Laboratory
Kidriceva cesta 55a
SI-4000 Kranj
Slovenia
E-mail: andrej.skraba@fov.uni-mb.si
-------------------------------------------------------------

["Raymond T. Joseph"]

Both modeling architectures may be applicable in either or both domains
depending upon the relationships between the components in each system and
the operational and simulation time scales of each system.

All physical processes are discrete in nature. But this may be down at the
atomic level. Aggregation of behavior is a tool to turn this atomic,
discrete nature into a continuous view. Such a process may be a chemical
reaction which occurs to individual molecules. The statistical nature of
the process lends itself to viewing this more simply as an ensemble of
actions. The chemical process make take several batch processes to sequence
into a final product. The batch mode suggests discrete events, but if the
observation time interval is sufficiently long, the batch processing may be
looked at as a continuous process.

A similar view could be developed for business process. Thus there is no
clear line between business and physical processing architectures. The
considerations are:
1. There under-lying physical process
2. The physical processing time intervals
3. The simulation/observation time intervals
4. The simulation/observation duration (relative to intervals)
5. The required accuracy.

Ray
From: "Raymond T. Joseph" <rtjoseph@ev1.net>

["Jim Hines"]

Raymond,

I was curious about one thing you said: Im not sure that all physical
processes are discrete in nature -- even at the sub-atomic level. At
the sub-atomic level some people visualize an electron as forming a
cloud, dont they? And a photon can be considered (and "physically"
viewed) as either a particle or a wave. Is this correct?

Note, I do agree with you that often in social systems the more detailed
processes are often viewed as being discrete. But, I dont know if this
is due to any underlying "reality" of discrete events vs. continuous
events. Franco Modigliani who was a smart guy (Nobel laureate), but not
a physicist, made the retort to me (when I was arguing in favor of
continuity) that the world was neither continuous nor discrete -- I
didnt believe him at the time, but I think I do now.

Jim Hines (obviously, not a physicist either)
jhines@mit.edu

["Anibal Porro"]

Dear Jim and Raymond,

Let me do a simple question?
Are you talking about processes or entities (particles)?

>From a physical point of view there is no doubt that
physical entities are discrete but, as far as we know,
time and space are continuous.

So particles are discrete but processes are continuous.
... and an event is a process that happens in a short
period of time (for the observer).

The discrete nature of the matter and energy was the
great discovery of the science at the beginning
of the 20th century.

You can visualize the density distribution on an electron
around the nucleus as a cloud but it doesnt mean that one
specific electron is a cloud. The cloud is only the probability
of finding it in one specific location.
Also when you perform dispersion experiments with one photon
you always "see" a particle. The wave phenomenon appears when
you involve millions of them.


My best regards,

Anibal Porro
From: "Anibal Porro" <aporro@infovia.com.ar>

["Raymond T. Joseph"]

Jim,

Yes, this is fun!

The colloquial cloud image is intended to describe the electrons wave
function. Even at this point, the wave/particle duality has proponents
polarized. At one end, the wave function describes the particles
probability distribution in space - its actual location being unobservable
until measured. At the other end, the wave function describes the actual
electron distributed through space as a standing wave. In either case,
there is still a mixture of continuous and discrete models and tools to
explain/predict their behavior. For example, to calculate the energy of an
electron in an atom, the quantum mechanic calls upon the continuous
relationships of the attractive force between the nucleus and the electron
and the repulsive force of the electrons momentum driving it from a fixed
position. This results in a set continuous partial differential equations.
That is, the problem is set up in a continuous space. The solution(s) to
the problem are a set of wave equations whose parameters must be identified
through the problems boundary conditions. Application of the boundary
conditions produce the discrete result of quantized energy states.

So what do we have here? We have a set of relationships that are continuous
in nature and produce a result that are discrete. So is the system
continuous or discrete? It depends upon what system is being described.
The forces and masses are all continuous in an open system. As soon as
there is a physical constraint added (the electron bound to the neighborhood
of the nucleus), the behavior of the atomic system is discrete. Photon
studies produce similar results.

I would only have a little difficulty with Franco Modiglianis comment that
the world was neither continuous or discrete. But this is only due to
semantics. The world is both, depending upon how one looks at it.

Please let me apologize for my brash statement: "All physical processes are
discrete in nature."
My intent was to convey that in chemical reactions, each reaction is at the
atomic or molecular level and involve a small number of components -
discrete. Macroscopically, these produce a bulk product that may more
easily be viewed as continuous. As most all processes of interest (e.g.
people shuffling paper) involve some material, the laws of chemistry and
thus QM are thus involved.

Note 1: The discrete states of electrons in atomic orbital are steady state
values. The actual transitions from one state to the other may be described
through continuous dynamics.

Note 2: Although A. Einstein has been quoted to denying quantum mechanics
interpretation of the bound electrons wave function as a probability
distribution ("God doesnt roll dice"), he did understand the discrete
nature of QM solutions. Also, he pointed out (1950s) that he was
reconsidering his previous belief of natures fundamental continuity; he was
open to the possibilities that the substances of nature may have both
discrete and continuous properties.

Ray
From: "Raymond T. Joseph" <rtjoseph@ev1.net>

["chariya"]

Andrej,
I am more familia with the discrete vs continuous modeling form
Estimation/Control theory point of view. Not sure how these two concepts
defined in SD.

Continuous model is basically, mathematical modeling using continuous
functions of some sort to represent the system, while discrete modeling is
basically, a rule-based system. As you said, both types of modeling work
together, doing what each can do best. For instance, to steer a ship around
an obstacle from point A to point B, the trajectory is partitioned into
sections (based on the sensor observations as the obstacle unfolded),
Discrete algorithm would select appropriate continuous algorithm / function
to represent each section, and continuous algorithm is used to steer the
ship within that section. Good discussion for htis treatement is in the
"Ingelligent Control Systems: Theory and Application" by Madan M. Gupta
and Naresh K. Sinha.

My guess is that is is probably similar idea in SD. Would love to read that
paper you mentioned. Unfortunately, I am house-bounded currently.
chariya

From: "chariya" <Chariya.Peterson@verizon.net>

["Raymond T. Joseph"]

Chariya made a very good presentation pointing out that discrete and
continuous systems may be architected in a variety of fashions. The ship
example can be viewed as the ship being a continuous plant with a continuous
controller. The continuous controller uses some of the plants output as
its input, and the continuous controllers output goes to the plants input -
it is a feedback controller. The discrete controller observes the plants
state (location) presumably by reading the plants input and determines the
parameters needed by the continuous controller to best perform in the
current state. The discrete controller adjusts the continuous controllers
parameters, which could be considered as the discrete controllers output
feeding to some of the continuous controllers input.

DC - discrete controller transfer function
CC - continuous controller transfer function
CP - continuous plant transfer function

-----------
--->---| DC |----------->----------------
| ----------- |
| |
| |
| ----------- |
| | |---<--
^ ----<----| CC |---<--
| | ----------- |
| | |
| / |
| | |
| | ----------- |
--o----------->------+-| CP | ---->-------
-----------



We have the plant with a continuous controller and a supervisory controller
managing the continuous controller. Masons gain formula can be used to
condense the graphic:

-----------
-->--| DC |- >-
| ----------- |
| |
| |
| |
| | -----------
| | CP |
--o----------->---------+-| ------- | ---->-------
| 1+CP*CC |
-----------

Now there are two systems in cascade: a discrete system and a continuous
system. This may undergo further contraction to produce a single block
system:

---------------
| CP |
-------->-------| DC * ------- | ---->-------
| 1+CP*CC |
---------------


In general, any combination of discrete and continuous subsystems (feedback,
parallel, cascade) can be combined to describe a target system.

Ray
From: "Raymond T. Joseph" <rtjoseph@ev1.net>