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

The real output y is the real input u delayed by a fixed delay time which can be constant (delayTime) or variable (u_delayTime) during the simulation.

y[t] = u[t - delayTime]

The input signal is thus effectively shifted forward in time.

During an initial period (at most as long as the initial delayTime or the maximumDelayTime when the delay time can vary over time), we need to provide information about the historical input u (e.g., the input before the start time of the simulation). The historical input can either be given by a constant value (either the initialValue or the initial input u) or by a function of time (usually a TableFunction), that will take the output connector y_timeHistory  as input and then provide the relevant historical input via the input connector u_history.

Given, that the delay time may be variable, we must distinguish two kinds of changes:

• Delay time increases:
  In this case, the delayed information shortly after the increase would be older than what we knew at the instant, the delay time increased. Instead of using older information, we will hold the previous information until more recent information becomes available.


• Delay time decreases:
  In this case, we would disregard historical or older information and jump towards the new level of information.

Implementation

Internally a TimeInput component is used to provide a clock starting at modelSettings.modelStartTime. Whenever the clipped delay time increases, the delayed information and the time it was sampled (t_sampled) will be stored. As long as max(t_sampled, clock.y - clippedDelayTime.y) is less than modelSetting.modelStartTime, the historical information (either the constant initialValue or the input u_hist) is reported as output y.

Once the current delayed output becomes more recent (either because time has proceeded beyond the initial delay time or the current delay time has significantly decreased), it will be used. From then on, the last stored information (e.g., information that is on hold due to an increase in delay time) will be compared with the currently delayed information output and whatever is more recent will be returned.

As checking for increases in the delay time can introduce a lot of events, the checks will only be done a regular time events given by the parameter samplingPeriod in the Advanced tab. 

Notes

• The behavior for DelayInformation and DelayFixed are quite similiar, but there is a subtle difference:
  
  A DelayInformation models the delay in perceiving information where the recipient is aware of the delay time and thus will disregard older informatiion than the one he already has.
  
  In the case of a DelayFixed we will strictly delay any information given the actual delay time at any point in time and thus may receive information that is actually older than previous information when the delay time increases.


• Since information is stored within the component, a rectangle is used for the component to be reminiscent of a stock.


• A DelayInformation is an information delay, that is used to model delays in updating beliefs and perceptions; unlike a material delay matter is not conserved [20]. 


• The parameter init in the Advanced tab allows to select →InitializationOptions (but hasExogenousHistory = true will allways have priority):
  
  • 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

DelayFixed, Smooth, SmoothN, Conveyor

delayTime	Value: 1 Type: Time (s) Description: Constant delay time (optional)
maximumDelayTime	Value: 50 Type: Time (s) Description: Maximal value allowed for delay time (needed for variable delay time)
initialValue	Value: 0 Type: OutputType Description: Initial constant output, if no exogenous history is given
hasConstantDelayTime	Value: true Type: Boolean Description: = true, if the delay time is given by the parameter 'delayTime'
hasExogenousHistory	Value: false Type: Boolean Description: = true, if the input 'u_history' gives the output for an initial period, otherwise the initial output will remain constant until delayTime is reached
init	Value: modelSettings.init Type: InitializationOptions Description: Provide InitializationOptions (Free, FixedValue, SteadyState)
samplingPeriod	Value: modelSettings.samplingPeriod Type: Time (s) Description: Interval at which to check for increases in delay time