Basic building blocks of SD Levels (Stocks), Rates (Flows), Auxiliary variables and Arrows Essential...

Basic building blocks of SD

Levels (Stocks), Rates (Flows), Auxiliary variables and ArrowsEssential building blocksRepresent the way dynamic systems really work

The LEVEL

Levels represent accumulations (physical and non-physical).Levels represent the ‘traces’ left by activities.The material in a stock exists at a point in time.Stock - level persist when activities cease.Examples: water, predators, CO2, frustration, knowledge, vegetation,….

The RATE

Rates represent activities or actions.Rates occur over time.Rates:

Fill and drain stocksTransport staff (physical and non-physical)Can change ‘instantaneously’

Examples: eating, learning, runoff, communicating,….

The RATE

‘infinite’ source spigot

‘infinite’sink

conduit

flow regulator

directionof flow

Example

Arrows

Radiate signals that serve as inputs to decisions or actions.Arrows serve as inputs, rather than inflows, and outputs, rather than outflows.They link stocks and flows (and flows to flows), in order to generate actions.

Auxiliary variables

They modify the activities (within the system)They transform inputs into outputsThey represent information or material quantitiesThey break out the detail of the logicThey do not accumulate (their value is re-calculated in each time step)They can be used for external inputs

Example

Causal loop of natural resources and usage

Level – natural resourcesRate - usage

Example

System Principle 2

•Levels and rates are the primary components of the structure.•System Principle #1 states that feedback loops are the building blocks of systems. In the same way, levels and rates are the building blocks offeedback loops.

Exercises

Everything around us can be represented by either a level (stock) or a rate (flow).

System Principle 3

Do not be fooled by unitsUnits do not determine whether a variable is a level or a rate.

Exercises

What are some of the flows that might be associated with the various stocks below? What are their units?

Exercises

Exercises

buying rate selling rateunits # of computers/day #of computers # of computers/day

Exercises

Exercises

growth rate cutting rate

units

# of trees per year #of trees # of trees per year

Graphical integration

Bathtub example

A. Open faucet permanently, 2 L/min Constant Positive rate

after 2 min, 2 min * 2 L/min = 4 Lafter 6 min, 6 min * 2 L/min = 12 L

Graphical integration

Graphical integration

B. Step function

Graphical integration

Graphical integration

C. Linearly increasing flow

Graphical integration

Graphical integration

Key Ideas:When the net flow is positive, stocks are filled; when the net flow is negative, stocks are emptied.The area under the flow graph over the period of time is equal to the change in the value of the stock over that same time period.

Final value of stock = Initial value of stock + Area under flow graph

Linearly increasing flows cause the stock to exhibit parabolic growth.Linearly decreasing flows cause the stock to exhibit decreasing parabolic behavior.Complex graphs can be broken down into several smaller, simpler ones.

SD Modeling Process

Define the issue/problem

Develop & Represent Hypotheses

Test Hypotheses

Design and Test Policies

Challenge the Boundaries

Make Learning Available

SD Modeling Process

1. Define the Issue / Problema. Explicitly state the purposeb. Develop a reference behavior patternc. Develop a system diagram

2. Develop& Represent Hypothesesa. Seek a dynamic organizing principleb. Map the hypothesesc. Make the map simulatable

SD Modeling Process

3. Test Hypothesesa. Mechanical mistake testsb. Robustness testsc. Reference behavior tests

4. Design & Test Policiesa. Policy testsb. Sensitivity testsc. Scenario tests

SD Modeling Process

5. Challenge the Boundariesa. Extensive boundaryb. Intensive boundary

6. Make Learning Availablea. Develop a dramab. Design a learning processc. Implement the progressiond. Create in-character feedback and

coaching sequences

Simulation structure and behavior

Move from casual loops to flow diagrams is done to provide additional insight into the behavior of a proposed model over time.The strategy in forming a model:1. start with a causal loop diagram2. formulate a flow diagram3. write equations4. use the equations to simulate the model on the

computer

Once a model is developed we can use it to explore the consequences of alternative model assumptions and proposed policy interventions.

Example

World population growthAssumption - constant growth (percent per year) of GF 2% / year.

Example

Causal loop

Net Births = Number of newborns – Number of dead [people/year]

Example

Stock and flow diagram

Example

EquationsRate function for Net Births

NB = POP(T) * GFLevel equation for Population

POP(T) = POP(T-1) + DT * NBwhere DT is time interval = 1 year

Complete Model consists of two equations:NB = POP(T) * GFPOP(T) = POP(T-1) + DT * NB

NB depends on the size of the population POP. POP varies over time. So NB should have a time subscript too. What should be used?

Example

Try out hand simulation.DT = 1 year, start with in T = 1975 POP(T) = 4 billionNB = POP(T) * GF = POP(1975) * GF = 4 * 0.02NB = 0.08 billion per year in 1976POP(1976) = POP(1975) + DT * NB = 4 + 1 * 0.08 = 4.08 billion

So, NB for 1975 to 1976 is calculated using 1975

NB(T, T+1) = POP(T) * GF

Final model for world population:NB(T,T+1) = POP(T) * GFPOP(T) = POP(T-1) + DT * NB(T-1,T)

Example

System Principle 4

Levels accumulate the results of rates (actions) in the system.