N-th order exponential smooth with constant averaging time



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

A smooth is an exponential information delay. It is typically used to model time lags in forming an expectation or in perceiving some information. A smooth of order n is modeled as a cascade of n first-order exponential smooth components, where the output of a preceding component is the input for its successor. The delay time for each smooth in the cascade will be delayTime/n.


  • The delayTime given (either as constant parameter or continuous signal) will effectively be clipped to a minimum value of n × modelSettings.dt. The delay time for any first-order smooth in the cascade can thus never become smalle than dt, which denotes the minimum process time anywhere in the model.

  • 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.

  • Mathematically a cascade of first-order exponential delays can be modeled as a convolution of exponential delays giving an Erlang distribution; see Sterman [3, pp. 462-476] for more details.

  • 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

Smooth, AsymmetricSmoothN

Parameters (5)


Value: 3

Type: Integer

Description: Order of the smooth


Value: 1

Type: Time (s)

Description: Constant delay time (optional)


Value: 0

Type: OutputType

Description: Initial Output


Value: true

Type: Boolean

Description: if true, the constant parameter value is used


Value: modelSettings.init

Type: InitializationOptions

Description: Provide InitializationOptions (Free, FixedValue, SteadyState)

Connectors (3)


Type: RealInput

Description: Input


Type: RealOutput


Type: RealInput

Description: Delay time input

Components (4)


Type: ModelSettings


Type: Division

Description: Delay time for each smooth in the chain of smooths


Type: Smooth[n]

Description: Chain of n first-order exponential information delays


Type: ConstantConverter

Description: Order of the delay

Used in Components (1)



Modeling the influence of excessive workloads on productivity or quality