Negative Levels, furnaces

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 Posts: 14
 Joined: Fri Mar 29, 2002 3:39 am
Negative Levels, furnaces
Guenther Ossimitz wrote (edited for brevity):
>4) Wayne Wakelands binary "furnace onoff 01 stock" is
>really a great idea  if you want such a thing at all in a
>SD  model. Of course a flow of 1/DT is the only possiblity
>to maintain such a stock. however, it is easy to prevent
>the 1/DT division of the switching rates if one wants
>to: just create a stock with the levels 0="off" and DT="on"
>instead of 1="on". ...
One thing that helps with situations like this is to define names for
constants  e.g. create a variable called "Off" with the value 0, and a
variable called "On" with the value 1 or DT. Then you can write things like
IF THEN ELSE( Switch = On, ..., ... ), which may help model users interpret
the results.
Creating a stock that takes on a value of 0 or DT doesnt really get you
out of the conceptual bind of avoiding DT on the RHS of equations. The
behavior is identical to the version with the 1/DT flow, just scaled by DT.
Worse, the units are very odd  a dimensionless flow integrated to a stock
with units of time.
Its worth noting that 1/DT tricks dont work unless you use Euler
integration. Higherorder integration methods (e.g. RK4) assume continuous
derivatives and behave much like a smaller time step, so a stock draining
at a rate of stock/dt will never really empty all the way. You may be able
to get around this by using functions (PULSE in Vensim for example) that
hold values constant within a time step regardless of integration method,
but better to carefully consider what youre doing first.
>3) ... There are quite a number of contexts
>where a "natural" DT > 0 is given: consider any deliverance
>models where products are delivered say once a day every
>morning; many production processes have naturally induced cycles
>(eg. in farming, where one cant harvest the apples continually
>over the year), which make it plausible to set DT= 1cycle. ...
This is dangerous ground. When presented with a discrete time model that
aspires to policy relevance, I instinctively reach for the antacid tablets.
I dont want to argue that one cant build a good discrete time model, just
that many people dont.
Theres a long history of discrete time models that mistake the sampling
frequency of a dataset for the relevant time scale of the system.
Samuelsons multiplieraccelerator and the Cobweb pricing model are both
examples of discrete time models that generate economic cycles as an
artifact of their simulation method.
Discrete time models Ive seen tend to neglect stockflow distinctions and
units of measure in general, which eliminates an important tool for
understanding and errorchecking.
Using discrete time (obviously) assumes that nothing of importance happens
on a time scale < DT. In my experience, the reverse is usually true in
strategic models  the important behavior of the system occurs on short
time scales (e.g. weekly sales and production) with measurement processes
layered on top at discrete intervals (e.g. annual revenue reporting).
Using discrete time (less obviously) also complicates the representation
of behavior near the time step. A capital stock with a 15 year lifetime
will not be smoothly integrated in a model with a 10 year time step.
Modelers often account for this by explicitly correcting for compounding
within the time step, but this complicates the model and is seldom done right.
The biggest problem with linking the simulation time step to the freqency
of a process in the model is that it then becomes less meaningful to test
whether the time step matters by changing it.
The approach I would prefer in most circumstances is to build the model
with a smaller time step than whatever discrete behavior is of interest,
and to include a clock mechanism to trigger whatever events do occur at
discrete intervals. This complicates the model somewhat, but allows a high
level of confidence. The (untestable and possible dangerous) alternative I
often select is to ignore the discrete calendar and treat everything as
continuous.
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Thomas Fiddaman, Ph.D.
Ventana Systems http://www.vensim.com
8105 SE Nelson Road Tel (253) 8510124
Olalla, WA 98359 Fax (253) 8510125
Tom@Vensim.com http://home.earthlink.net/~tomfid
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