higher order delays and delyN

[addor]

I construct an aging chain with 3 serial stocks. Every outflow is stock*delaytime, the first inflow is a pulse. Thus the third stock should represent a daly of third order.

Then I compare this last stock with a delayN(inflow,delaytime,0,3).

Both aren't the same. Even if I take another delaytime for the delayN function I cannot define it such that the graph of the third order delay and that one of the delay3 become congruent.

Where is my error in reasoning?

[LAUJJL]

Hi Addor

Can you join a simplistic model to illustrate your problem?
Regards.
JJ

[bob@vensim.com]

Make sure your model passes units checking. The outflow of a stock should be stock/intermediate delay time where

intermediate delay time = delay time/number of stocks

See the DELAY3 documentation in the reference manual for the actual equations for a 3rd order delay.

[addor]

So, you confirm, that a third order delay should be the same as a delay3(...).

I used a delay time of 0.5 for each of 7 stocks but 7*0.5 for the delay3. This should also be valid, shouldn't it?

Strange is, that the delay3 gives "pieces/hour" instead of "pieces" as dimension....

Here is my model

[addor]

I think I should multiply the dealytime in delay3(...) not with 7 but with 3. But then the difference between stock3 and delay3(..) is even greater....

Peter

[bob@vensim.com]

Please read my first response and the reference manual. All exponential delays use level/delay time - multiplying here makes no sense.

[addor]

Of course, Bob, I did it. I attache here the model that uses the intermediate delaytime for the stocks. Still delay3 and stock3 are different, and although the input has the dimension "pieces/hour" and the delaytime has dimension "hour" delay3 get the dimension "pieces/hour".
Also after reading the manual I don't see my error in reasoning. I'm sorry.

Peter

[addor]

Here is the model

[bob@vensim.com]

You are getting closer. The equation should be

flow = level/(delaytime/7) - you forgot the parentheses. It is better to use two variables for delay time (eg "Total Delay Time" and "Per Level Delay Time") to prvent this type of confusion.

[addor]

Of course, Bob, I should know how to handle compound fractions.... it's a shame

Now I have the "total delaytime" and the "delaytime = total delaytime / 7"

But nevertheless delay3 isn't same as stock3

And why gives delay3 as units "pieces/hour" if the input has "pieces/hour" and the "delaytime" has hour?

[addor]

Ok, I built a model once again (only with 3 levels in the aging chain), and now delay3, delayN(...3) and stock3 are indeed same. I don't know what happend in the model before. Somethings went wrong.

But still I get the units/hour as the dimensions of delay...

[bob@vensim.com]

DELAY3 (and DELAYN) have the same units for input and output - the output corresponds to the flow from the last level. So if the input is units/time the output is units/time - while the levels in the ageing chain are have units.