31247 Chap.11 Stock and Flow Models in System Dynamics
Stock and Flow Models in System Dynamics
From influences to quantities
A stock and flow model turns a causal diagram into something that can be simulated. Stocks are quantities that accumulate or deplete, flows are their rates of change, and the software recomputes the stocks over repeated time steps.
The lab model and the report
The Week 7 lab builds a four-stock epidemic model in AnyLogic.
The group report accepts only stock and flow diagrams as quantitative models and rewards five stocks with their flows correctly represented and explained.
Why it matters for the report
A causal loop diagram can say that a change helps; a stock and flow model can say by how much and how fast.
That is what Task 2.4 of the group report asks for when it wants the impact of the chosen solution predicted and a stock and flow model built for it.
What this chapter covers
- 01
Why build a quantitative model
- 02
Stocks, flows and factors
- 03
Stock and flow notation
- 04
Six stages of a system dynamics study
- 05
The four-stock epidemic lab model
- 06
Seven steps to convert a causal loop diagram
- 07
Hand-simulating a stock
Worked example · free
Compute the epidemic model’s flows mid-outbreak
- 1ExposedRate = Infectious × contact rate × infectivity × Susceptible ÷ population = 2,000 × 1.25 × 0.6 × 6,000 ÷ 10,000 = 900 people a day.
- 1InfectiousRate = Exposed ÷ incubation time = 1,500 ÷ 10 = 150 people a day.
- 1RecoveredRate = Infectious ÷ illness duration = 2,000 ÷ 15 = 133.3 people a day.
- 1Net change in Infectious = inflow − outflow = 150 − 133.3 = +16.7 people a day, so the infectious stock is still rising.
Key terms
- Stock
- A quantity that builds up or runs down over time, counted at a single instant.
- Flow
- The rate at which a stock changes, measured per unit of time.
- Auxiliary Variable
- A factor in a stock and flow model that helps define a flow without being a stock itself.
- Source and Sink
- Clouds marking where a flow comes from or goes to outside the model’s boundary.
- System Dynamics
- A computer simulation method for analysing complex systems that change over time.
Stock and Flow Models in System Dynamics FAQ
How do I tell a stock from a flow?
Use the units test from the lab. A flow is always a quantity per unit of time, such as people per day; a stock is a quantity you could count at an instant, such as people currently infected.
What software does the stock and flow lab use?
The Week 7 tutorial uses AnyLogic 8.8.3 Personal Edition and a step-by-step chapter from the AnyLogic guide. It flags a mistake in the printed steps: at step 15 on page 110, pick Fix Dependency Links, not Fix Variable Links.
How do I turn my causal loop diagram into stocks and flows?
Follow the lecture’s seven steps: give every variable units, create the stocks, create the flows, connect them, connect the remaining variables, write the flow equations, and add any variables the equations need.
How many stocks does the group report need?
The top band of the rubric for the problem models asks for five stocks with their relevant flows, correctly represented and explained in detail; the band for the solution’s quantitative model counts stocks the same way.
What does a cloud mean in a stock and flow diagram?
A cloud at the start of a flow is a source and a cloud at the end is a sink. It means the model does not track where the quantity comes from or goes to, because that lies outside the model’s boundary.
What are the stages of a system dynamics study?
The lecture lists problem definition, model conceptualisation with causal loop diagrams, model formulation as a quantified stock and flow model, validation and simulation, analysis, and interpretation with stakeholders. It calls problem definition arguably the hardest stage.
Assessment move
Convert your causal loop diagram into stocks and flows using the seven steps, starting with units for every variable. Then hand-simulate three time steps of one stock to check the equations make sense before building it in software. Ask Sia to check your units with you, then run the model and compare its first steps with your hand calculation. Save the hand calculation in an appendix as a check on the software.
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