What is auxiliary variable?

An auxiliary variable is a value that the model recalculates from the current state of the system at every step. It has no memory of its own, unlike a stock, which accumulates. It matters because clear auxiliaries make rates readable, and they turn raw stocks into meaningful measures like price, utilization, or time to completion.

How it works

Think of a model as having three kinds of element. Stocks hold quantities and change only through flows (see stock and flow). Constants are fixed inputs. Auxiliaries sit between them: they take stocks and constants as input, apply a formula, and feed the result into a rate or into another auxiliary. When the stocks change, every auxiliary updates in the same step.

A useful test is to ask whether the value would still be known if the clock stopped. A cash balance would not be reconstructable without its history, so it is a stock. A ratio of cash to monthly spending can be computed on the spot, so it is an auxiliary. Splitting a long formula into several named auxiliaries makes a model easier to validate and to explain, and it makes the links in a causal loop diagram easier to trace to the equations.

Example

Say a shop has 400 items in stock and sells 50 items per week. Weeks of cover is 400 divided by 50, which is 8 weeks. It is not a stock: if sales rise to 100 per week, weeks of cover becomes 4 immediately. A price rule such as lowering price by 1 dollar for every week of cover above 6 is another auxiliary, built on the first. This is an illustration with round numbers.

How to model it in Machinations

Use a Register with a formula for each auxiliary. The Register reads Pools and other Registers through state connections and recalculates each step. Then use it as the rate on a resource connection or as the condition on a Gate. Add a chart of the Register next to the Pool it depends on, and use a Lever to change a constant.