How to split a stock variable?

[jmu]

Hi,
due to my lack of knowledge I run into a problem. Maybe someone could give my an advise.

I have a stock variable A. There is one input (a constant!) and there are two outputs. The outputs depend on the value of A.

A holds the amount the people from age 0 to age 9 (example). The input is a constant birth rate (100 per year), the first output is 1/10 ... so every year 1/10 of the people leave the stock and move to a second stock. The second output is k*A where k is some factor (people moveing to another location). So far, so good.


Now I would like to split the stock variable A into to new stocks (named C and D). The reason: the modelling of ages range from 0 to 9 is too big. I want an age range from 0 to 3 and from 4 to 9.

The input to C is the same as to A (constant birth rate).
The first output from C to D is 1/4 (every year a quarter leaves this stock and moves the the next stock).
The output from D is 1/6 (a sixth leaves the stock every year)

But how to calculate the second output from C (say k1*C) and the second output from D (say k2*D)?

A reasonable assumption is, that k1 = 2*k2 - so actually I only need to find k1 or k2.

All in all the first system (only A) should behave like the second system (C and D) if I only regard the input / output.

Any help is appreciated!

Thanks,
jmu

[LAUJJL]

Hi

First you cannot split an exponential delay, like the one you represent, this way. In fact you change a first order exponential delay into a second order that does not behave the same way even if the value of K is equal to zero.
See model joined where K is equal to zero.
Even if you do not split A, representing an aging chain like this, only works if the input is constant.
It seems logical that once you have solved the first problem
the problem with splitting k is evident. K2=K1=K unless the probability of moving to another location is depending on the age.
If you want to split A you have to represent it as an aging chain. See the examples of aging chain in the samples joined with the Vensim documentation.
There was a short thread on this subject some time ago on the 22/8/2009 called 'aging chain model discussed at the SDS forum' on the same system dynamics discussion forum.
Regards.
JJ

[Edited on 14-3-2010 by LAUJJL]

[jmu]

thanks for the insights,
jmu

[LAUJJL]

I have found a way to split the stock but that will work only with a stable input and output, so that the system may reach an equilibrium or stay in equilibrium with the right initialisation.
See the model joined. It has four parameters the input, the output, how you want to split, the ratio 4,6,10 ratios and the coefficient K. It calculates the initial stock A to start in equilibrium, and how to split the constant k in kc and kd.
You can too work with a determined initial stock A, the system will then reach an equilibrium progressively and you will have only to optimize the parameters kc and kd.
I have choosed a very long horizon, to make it possible for the model to reach a good optimum even with a determined initial value of A.
But is is still safer to use a classical aging chain.
Regards
JJ

[Edited on 15-3-2010 by LAUJJL]