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Dealing With Time In System Dynamics Models
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Dealing With Time In System Dynamics Models

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  • 1. Dealing with Time in System Dynamics Models Sourced from Geoff Coyle
  • 2. Importance of Time in Simulation
    • For discrete event: “Time moves forward when something happens”.
    • For system dynamics: “Time is a fundamental issue”. Outputs and inputs are plotted against time.
  • 3. Aspects of Time in Dynamo
    • Delays
    • The time unit used
    • Time-dependent exogenous influences
    • LENGTH (reserved word)
    • TIME (reserved word)
    • DT (reserved word)
    • Output control
  • 4. Delays
    • Physical Delays
      • Delay1 – a distribution delay (similar to erlang)
      • Delay2 – a pipeline delay contains a number of internal levels (seldom happens in actual systems)
    • Information Delays
      • Smooth or DLINF3
    • Delays produced by decision rules
      • Ex. PR.KL=(DESIRED.K-ACTUAL.K)/STAT
      • Where STAT is stock adjustment time (used as a first order delay of STAT in the system)
  • 5. Note about Delays
    • Delays should be measured in the same time units.
    • A model with delays in days and delays in years are confusing.
    • Modeling Production Policy uses delays in days
    • Modeling Capacity planning and acquisition uses delays in years
  • 6. Time Unit
    • Time units must have the same dimensions as delays.
    • Follow the natural choice of the system, when selecting time.
    • If there is a conflict in choosing time, then the purpose of the model is not clear (both the modeler and user)
    • Time magnitude can be 1 week, 1 year, 1 month, etc. The important things is that it resides in the modeler’s mind and understanding of the problem.
  • 7. Time dependent Exogenous Inputs
    • May or may not happen in your model.
    • It includes simulated demand patterns such as STEP and PULSE (there are others).
    • STEP is used to test model’s stability and to detect errors.
    • PULSE should be handled carefully. It differs on the software packages.
  • 8. LENGTH
    • It is a built in feature of dynamo
    • It connotes the duration of the model run.
    • The dimension of LENGTH should be the same as the Time Unit.
  • 9. How long is LENGTH?
    • The LENGTH should be at least 10 times as long as the longest delay in the model.
    • It must be long enough to allow any exogenous input to have sufficient time to show their effects.
    • For STEP and PULSE, LENGTH must be long enough until no further changes are seen in the model’s behavior.
    • It must allow for at least 4 cycles.
    • It must be sufficient to allow policies in the model to reveal their consequences.
  • 10. How long is LENGTH?
    • It must be credible to the client/user.
    • If confusion arises on the length, the longest is not necessarily better.
    • Recall the fundamental aspect of the system (modeling a business for 100 years maybe absurd)
    • A simple test is to run it with LENGTH doubled and LENGTH half and see if there is a difference. (Watch out for absurd realities such as negative values)
    • It should be a sensible round number.
  • 11. A Special command “TIME”
    • A counter which represents the passage of time in the model
    • Automatically creates a level equation of the form: L TIME.K=TIME.J+DT
    • N TIME=1900 (Time can be initialized, but extra care)
    • LENGTH should be adjusted when time is initialized.
    • Initializing time does not mean that you are predicting the future instead of showing policy effects.
  • 12. DT
    • It is the time step in the model that progressively moves time towards its termination at LENGTH.
    • DT for Dynamo and TIMESTEP for other packages
    • DT is an artefact of the modeller’s mind and not the system.
  • 13. DT
    • It should have the same dimension as TIME.
    • It is never placed on the right hand side of a rate or auxiliary.
    • It has nothing to do with the problem.
    • If DT is too large it becomes numerically unstable. If DT is too small it will take a longer run.
  • 14. DT
    • Observe this: DT<= DEL/4N
    • Where DEL is the magnitude or duration of delay in the model and N is the order.
    • In practice, the lower possible value from the limit shown above is chosen (binary fraction).
    • Most common values of DT are 0.5, 0.25, and 0.125
    • If there are multiple delays inside the model, choose DT that is a common multiple of the delays’ magnitude.
  • 15. Output Control
    • Not a key determinant of time.
    • It is good practice to print, on paper, or tables of all variables in a model while the model is being debugged.
    • An equivalent set of calculations can be made using a spreadsheet (such as EXCEL) to be able to see clearly the numerical changes that happens in the model.
    • The same equations from dynamo can be used in printing or constructing the table for the variables.