## Negative Levels, furnaces

Tom Fiddaman
Junior Member
Posts: 14
Joined: Fri Mar 29, 2002 3:39 am

### Negative Levels, furnaces

Guenther Ossimitz wrote (edited for brevity):

>4) Wayne Wakelands binary "furnace on-off 0-1 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"

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. Higher-order 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 multiplier-accelerator 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 stock-flow distinctions and
units of measure in general, which eliminates an important tool for
understanding and error-checking.
-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.

****************************************************
Thomas Fiddaman, Ph.D.
Ventana Systems http://www.vensim.com
8105 SE Nelson Road Tel (253) 851-0124
Olalla, WA 98359 Fax (253) 851-0125