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Complex Systems

Complex Systems. Terminology and Concepts. System Dynamics. Operations Research Developed during World War II Team of experts in various fields System Dynamics Developed by Dr. Jay Forrester in 1960’s Team approach to complex systems View problems from systems perspective

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Complex Systems

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  1. Complex Systems Terminology and Concepts

  2. System Dynamics • Operations Research • Developed during World War II • Team of experts in various fields • System Dynamics • Developed by Dr. Jay Forrester in 1960’s • Team approach to complex systems • View problems from systems perspective • Growth in use with microcomputer software

  3. System Dynamics Study system behavior over time Discover patterns of behavior Discover structures that cause patterns

  4. Structure Determines Behavior System Structure Pattern of Behavior Events

  5. Systems Building Blocks Stocks Flows Information Links Decision Points Converters Auxiliary Variables

  6. Stock and Flow Diagram Stocks in boxes Flows as straight double arrows Information Links as thin curved arrows Decision Points as closed in X

  7. Stocks “Things” that accumulate in a system Physical or non-physical things Value is a quantity or level Persistent (remain even if all flows stop) Conservation (stock units enter from environment and return to environment)

  8. Naming Stocks • Use nouns • “population” • “sales force” • “CO2” • Qualify the nouns to increase precision • “pre-school population” • “motivation to avenge” • Each Stock must have a unique name

  9. Flows Movement of “things” in and out of stocks Not persistent (can be stopped and started) Value is a rate of change (will always have a time dimension) Flow unit = stock unit / time The unit of measurement for a flow will always be the unit of measurement of a stockdivided byan element of time

  10. Naming Flows • Depict action - the changing of a stock’s level • Use the “type of thing” in an action phrase • Use “ing” • birthing babies • students enrolling • selling units • hiring employees • Each Flow must have a unique name

  11. Examples

  12. Exercise 1 • Scenario 1 • People are born, they live for a while, then they die

  13. Stocks & Flows

  14. Exercise 2 Draw the stocks and flows for the following situations: • Domain – car rental agency • Activities – the renting and returning of cars • Domain – personnel department of company • Activities – hiring and separation of employees • Domain – Workplace • Activities – building and dissipation of morale

  15. Exercise 2 • Scenario 3 • At birth we are susceptible to smallpox. We remain susceptible unless we are immunized either by vaccination or by contracting and surviving the disease.

  16. Stocks & Flows

  17. Decision Points Controls rate of flow Increases or decreases flow rate Think “value” or “faucet”

  18. Converters • Used to calculate flow rate • compounding fraction • time constant

  19. Converters:Compounding Fraction • Multiplied by stock level to calculate rate of flow • interest rate of 4% • graduation rate of 25% • death rate of 12.5 per 1000

  20. Converters: Average Time • Divide into stock level to calculate rate of flow • average time in college of 4 years (graduation rate of 25% ) • 80 years average life span (death rate of 12.5 per 1000 )

  21. Information Links Shows what information is needed to compute the value of a variable or flow Ultimately leads to a flow’s Decision Point Comes from a stock, flow, converter, or auxiliary variable Goes to a flow or variable, never to a stock (except for initial value)

  22. Auxiliary Variables Used to make computations more explicit

  23. Classification of Components • Endogenous components • Value is computed within the system • Flows, Stocks, Auxiliary variables • Exogenous components • Value is set outside of the system • Converters, Initial values of stocks (not normally shown on diagrams)

  24. Drawing Stock and Flow Diagrams Draw all stocks first Draw flows next Add converters and auxiliary variables Draw information arrows last

  25. Lab again! Look at the exercise you did in last week’s lab.

  26. End

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