basic building blocks of sd levels (stocks), rates (flows), auxiliary variables and arrows essential...
Post on 17-Jan-2016
219 Views
Preview:
TRANSCRIPT
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.
top related