Verkehrsplanung und Verkehrstechnik | Institut für Verkehrswissenschaften

Technische Universität Wien

What is Stock-Flow-Modelling?

Introduction

A basic principle of System Dynamics models is that the structure of a system determines its behaviour. Causal-Loop-Diagrams can be used for a qualitative description of the structure of a system. Quantitative System Dynamics models are used to simulate the behaviour of complex, dynamic systems with feedback loops. The basis for these models are the concepts of stocks and flows. Quantitative System Dynamics models take into account important time delays in the adaptation processes and nonlinearities in the various feedback loops. Quantitative System Dynamics models consist of a system of differential or difference equations and use an iterative dynamic computation procedure. Understanding the concepts stock and flow is essential for successful System Dynamics modeling.

Stock

Stocks have a certain value at any time and can change their value over time. Examples of typical stocks are: bank account, population, car fleet, road network, commodity stock, etc. Stocks can be measured in any units, e.g. Euro, number of persons, number of cars, number or kilometres of roads, tonnes, etc. The following rule of thumb can be used to assess whether an element of a system is a stock or not. If time is stopped and the element retains a value, it is a stock variable. Normally the change of stocks is caused by the balance of in- and out-flows, e.g. balance of revenues and expenses, births and deaths, car purchases and scrapping, etc

Flow

Flows are the changes of a stock per time step (equation 1). Examples of typical flows are payments to/withdrawal from an account, births/deaths, car sales/car scrapping, opened roads per year, prospected iron ore per year, etc. The unit of flows is no longer freely selectable. It is rather defined as the unit of the stock per time unit, e.g. number of persons/year, number of cars/quarter, kilometres of road/year, tons/year, etc. If time is stopped, no value can be assigned to a flow.

Equation 1: Relation between stock and flow
Relation between stock and flow

Other elements

Besides stocks and flows System Dynamics models require two additional elements: auxiliary variables and the external world. Typical auxiliary variables are e.g. interest rate, birth rate, average life expectancy, consumption per person, regeneration rates of natural resources, etc. The external world serves as a source or sink.

Symbols

Figure 2 shows the common symbols used to represent the four elements of System Dynamics models. Stocks can be interpreted as containers or boxes. Their value represents the capacity or volume in the box at a given time. Flows can be interpreted as valves. They determine the change of the stock per unit of time. Each flow describes an in-flow or out-flow. Auxiliaries can represent constant values or intermediate steps in calculations. The external world is symbolized by a cloud. The relationships between the various elements are depicted as arrows. The arrows represent all possible types of flows between the elements. This can be both information flows and physical material flows.

Equation 2: Symbols for the elements of System Dynamics models
Symbols for the elements of System Dynamics models

Examples simple model structures

Some simple examples of common model structures: linear growthexponential growth, stock adaptation towards a target

www.fvv.tuwien.ac.at