What is accumulation?

The SD Society posted a definition of accumulation on Facebook, and it caught my eye.

This is from the SD Glossary, by David Ford.

accumulation (integration) : a gradual, non-instantaneous increase or decrease of a quantity over time. An accumulator is also referred to as a stock or level and represents the state of a system. To accumulate is the act of increasing and decreasing the size of a state variable (a stock) over time.

I wrote,

I’m not a fan of this definition. Accumulation is not necessarily gradual or non-instantaneous. In fact, it’s quite common to accumulate a flow pulse to produce an abrupt step in a stock. The key feature of accumulation is that it’s, well, cumulative. I’m at a loss for a way to express that without mentioning integration, which won’t help most people. Maybe someone can do better?

I think it’s telling that we don’t have ready words to describe accumulation. That might be a symptom, or a cause, of our problematic mental models about bathtub dynamics and bathtub statistics.

Resorting to “integration” isn’t really helpful, except to the mathematically inclined, which is not the audience for this kind of description I think.

The dictionary definition of “cumulative” turns out to be helpful:

increasing by successive additions

With that in mind, I’d propose something like:

  • accumulation : increasing by successive additions, or decreasing by successive subtractions.
  • stock (level) : A variable representing a persistent state in a system, which can be considered the memory of the system. Stocks change by accumulation of flows.
  • flow (rate): A variable that contributes to cumulative change in a stock over time. Flows represent activity or change in a system. A flow may represent the movement of physical quantities between stocks within a system boundary or across the model boundary and thereby into or out of the system (sinks and sources), or the rate of change of a nonphysical or intangible state.

Note that it’s hard to discuss accumulation without also discussing stocks and flows, so I’ve modified all three glossary entries.