System Dynamics: Stock and flow modelling

A system is a set of interrelating, interconnected parts or elements that, together, generate some distinct outcome or behavior over time. In dynamical systems modeling, the behavior that the system exhibits over time is called its dynamic.

The causal loop diagrams showed that to go beyond simply analyzing and visualizing the feedback structure of a system, a more powerful technique is needed that included quantitative modelling :

  • a technique that visually distinguishes between the parts of the system and what causes them to change
  • a technique that allows for precise – quantitative – specification of all the system’s parts and their interrelation
  • a technique that can provide a basis for simulating the behavior of the system over time
  • technique that enables us to create a business prototype of the system that will allow us to explore its behavior and to test the effect of changes to the system’s structure and the policies governing its behavior. Stock and flow diagrams, along with the mathematical expressions that specify each construct, provide such a technique.

 To perform a more detailed quantitative analysis, a causal loop diagram is transformed to a stock and flow diagram. A Stock and flow model helps in studying and analyzing the system in a quantitative way.

SFD01

To perform a more detailed quantitative analysis, a causal loop diagram is transformed to a stock and flow diagram. A Stock and flow model helps in studying and analyzing the system in a quantitative way.

SFD001

Stock and flow diagrams provide a richer visual language than causal loop diagrams, we distinguish between six main kinds of elements: stocksflowsconverters, connectors, sources and sinks. These elements are explained below and visualized in the following diagram:

STOCK: A stock represent a part of a system whose value at any given instant in time depends on the systems past behaviour. The value of the stocks at a particular instant in time cannot simply be determined by measuring the value of the other parts of the system at that instant in time – the only way you can calculate it is by measuring how it changes at every instant and adding up all these changes.

  • A stock is a generic symbol for anything that accumulates or drains
  • Stocks are variables that accumulate the effects of other variables.
  • “Nouns” that indicate conditions or states of being at a point in time.
  • They act as shock absorbers, or buffers, from the changes in the flows
  • They can physical or non-physical: non-physical stocks “states of being” like anger, self-esteem, trust, etc.  Importantly, non-physical stocks need not obey the Law of Conservation- they are not zero-su

 

FLOWS: Flows represent the rate at which the stock is changing at any given instant, they either flow into a stock (causing it to increase) or flow out of a stock (causing it to decrease).

  • A flow is the rate of change of a stock / Variable.
  • Flows represent the rate at which the stock is changing at any given instant, they either flow into a stock (causing it to increase) or flow out of a stock (causing it to decrease
  • Verbs” that represent activities or processes

CONVERTERS. Converters either represent parts at the boundary of the system (i.e. parts whose value is not determined by the behaviour of the system itself) or they represent parts of a system whose value can be derived from other parts of the system at any time through some computational procedure.

  • A converter is used to take input data and manipulate or convert that input into some output signal.

SFD002

  • Converters either represent parts at the boundary of the system (i.e. parts whose value is not determined by the behaviour of the system itself : current date or remaining time) or they represent parts of a system whose value can be derived from other parts of the system

CONNECTORS. Much like in causal loop diagrams the connectors of a system show how the parts of a system influence each other.  Stocks can only be influenced by flows (i.e. there can be no connector that connects into a stock), flows can be influenced by stocks, other flows, and by converters. Converters either are not influenced at all (i.e. they are at the systems boundary) or are influenced by stocks, flows and other converters.

SOURCE/SINK. Sources and sinks are stocks that lie outside of the models boundary – they are used to show that a stock is flowing from a source or into a sink that lies outside of the models boundary. On diagrams, sources and sinks are represented by small clouds.

UNDERSTANDING STOCK FLOW DIAGRAM

SFD002

SFD003

 

Advertisements