Negative Levels, furnaces

Tom Fiddaman
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Negative Levels, furnaces

Postby Tom Fiddaman » Sun Oct 31, 1999 12:41 pm

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" >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. 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 8105 SE Nelson Road Tel (253) 851-0124 Olalla, WA 98359 Fax (253) 851-0125 ****************************************************

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