Modeling Aging Chains Using a Series of Reservoirs or Pools

Perhaps the simplest way of modeling aging chains is to create a series of Reservoirs (or Pools; the example here uses Reservoirs). The transition rate from one cohort (say C2) to the next, is set equal to C2/Residence_Time (a first-order rate), where C2 is the quantity in cohort 2, and Residence_Time is the average residence time in cohort 2.

In such a situation, the Reservoir for cohort 2 would look like this:

In this example, the cohort represents people aged 1 to 2 years. Hence, the Residence_Time is equal to 1 year. The rate of addition is the withdrawal rate from the previous cohort (C1), and the rate of withdrawal is C2/Residence_Time. Note that this simple representation does not represent any losses (e.g., due to death). To do so, you would simply need to add an additional withdrawal (which typically would be some fraction of C2).

It is important to understand that due to the nature of a Reservoir, such a representation results in a behavior which is typically inappropriate for modeling specific age groups. To illustrate this, let’s assume 1) that cohort 2 starts with 1000 one-year olds; 2) there is no addition to the cohort (C1 has an initial value of 0), and 3) there is no death rate. Cohort 2 only decreases due to graduations to the next cohort. Under these circumstances, the number of people in cohort 2 would look like this:

As can be seen, rather than staying at 1000 for the first year, and then abruptly changing to 0 (when all of the one-year olds actually become 2 and hence should immediately graduate to the next cohort), the number of one-year olds gradually decays over a period of 5 years. As a result, modeling an aging chain in this manner is most appropriate when the residence time in the cohort represents an average time, with some people leaving earlier and some later. This is the case, for example, if the cohort represents a group of employees (e.g., inexperienced), rather than a specific age group (e.g., between 1 and 2 years old). One of the other two methods of modeling aging chains (using Material Delay or Integrators with discrete pushes) should generally be used when modeling specific age groups.

An example file which illustrate how aging chains can be modeled using a series of Reservoirs (AgingChain.gsm) can be found in the General Examples folder in your GoldSim directory (accessed by selecting File | Open Example... from the main menu).