Smooth

First-order exponential smooth

Diagram

Information

This information is part of the Business Simulation Library (BSL).

A smooth is a first-order exponential information delay. It is typically used to model time lags in forming an expectation or in perceiving some information.

Inside the converter there actually is a stock x that stores the perceived or expected value of the information input u. The output y is derived immediately from x as can be seen from these equations where τ denotes the delayTime:

y=x

Notes

  • The delayTime given (either as constant parameter or continuous signal) will be clipped to a minimum value of modelSettings.dt, which denotes the smallest possible process time anywhere in the model. The time of delay for the process of information perception or expectation formation can thus never be zero or negative.
  • In the System Dynamics community a smooth is an information delay (as opposed to a material delay) [1, Appendices E and H]. Information delays model the process of updating information to the actual value. Since the technical procedure is called exponential smoothing, the name smooth has prevailed.

  • The parameter init in the Advanced tab allows to select →InitializationOptions:
    • FixedValue (default) will use the parameter initialValue to determine the initial output y.

    • SteadyState will set the initial output y equal to the initial input u.

    • Free there will be no initial equation and thus the solver is free to find an initial output using initialValue as an initial guess.

See also

SmoothNAsymmetricSmoothDecay

Parameters (4)

delayTime

Value: 1

Type: Time (s)

Description: Constant delay time (optional)

initialValue

Value: 0

Type: OutputType

Description: Output at startTime

init

Value: modelSettings.init

Type: InitializationOptions

Description: Provide InitializationOptions (Free, FixedValue, SteadyState)

hasConstantDelayTime

Value: true

Type: Boolean

Description: = true, if delayTime is given by the parameter instead of the input

Connectors (3)

u

Type: RealInput

Description: Input

y

Type: RealOutput

u_delayTime

Type: RealInput

Description: Delay time

Components (7)

modelSettings

Type: ModelSettings

changingPerception

Type: ExogenousChange

gap

Type: Gap

Description: Difference between acutal information and perceived information

rateOfChange

Type: Division_Guarded

Description: Rate of change in perceived information

perceivedInformation

Type: InformationLevel

Description: Smoothed information

positiveDelayTime

Type: ClipProcessTime

Description: Delay time shall never be less than dt

parDelayTime

Type: ConstantConverterTime

Description: Constant delay time (optional)

Used in Examples (1)

ManagingEmployment

BusinessSimulation.Examples

Human resource planning

Used in Components (2)

SmoothN

BusinessSimulation.Converters.DiscreteDelay

N-th order exponential smooth with constant averaging time

Trend

BusinessSimulation.MoleculesOfStructure.InformationProcessing

Calculating a fractional rate of change to be used in forecasting