REPLY Age of material in a stock (SD6418)

[SDMAIL Jean-Jacques Laublé]

Posted by  Jean-Jacques Laublé <jean-jacques.lauble at wanadoo.fr>

Hi Jack

You write:
> but not in the
> case of standard bathtub structures in which perfect mixing within the
> stock is implicitly assumed

You are absolutely right and I was wrong.

I was even persuaded that the equation As = To / 2 was true even in a
perfect mixed outflow.

In fact it is not easy to understand that for instance in a 10 people stock
where every day one new person is getting in and one person is getting out,
in the case of a pipeline stock, if you ask anybody how much time he has
been already waiting, the average answer will be 5 days, and in the case of
an outflow where the person getting out is chosen by chance, the answer will
be 10. And in both case that the average To will be the same.

I should have built a co-flow and verified what I said.
In fact I had to build the co-flow to get persuaded of it.
Simulation is sometimes useful.

But I still did not really understand the reason of the difference of the As
in both cases.

In fact when you ask the persons in a pipeline, the sample is complete and
all the persons that have entered the last ten days are there. In the case
of the perfect mix, the only people still there are the unlucky ones, and to
compare both cases, one should too ask the people that had the luck to be
picked up already and who are no more there.

I have added the co-flow to my model in the Vensim Forum.

But when the input and output change as in the case of seasonal variations,
it would be interesting to tell anybody entering the stock, how much time he
will have to wait on average.

Of course one must be able to forecast the inputs and the outputs.
One can forecast the future As, but there is no way to predict from the As,
the future To, the number everybody wants to know before entering the stock.

To calculate the future To, I do not see another way than to integrate step
by step Jay's Law, using probability calculations.
I think that it is too an example where probability and conditional
Bayesians probability is close to SD.
Regards.
Jean-Jacques Laublé. 
Posted by  Jean-Jacques Laublé <jean-jacques.lauble at wanadoo.fr>
posting date  Fri, 20 Apr 2007 11:46:30 +0200