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The DelayN is a →MaterialStock with inherent dynamic behavior that will result in a delay—which may have a constant (delayTime) or a variable delay time (u). Internally a material delay of order n is made up of a sequence of n first-order delays (→Decay ) each having a delay time of delayTime/n.

To better grasp the behavior of a DelayN, it helps to be aware of the fact, that given a single pulse input (e.g., a Dirac delta function) as inflow to a DelayN with constant delay time, its outflow will correspond to an Exponential distribution for n = 1 and more generally to an Erlang distribution of order k = n for n ≥ 1. In other words, the time of residence within the stock is distributed according to an Erlang distribution with the mean residence time corresponding to the delay time and a diminishing variance as n increases—in the limit, as n approaches infinity, the DelayN will be equivalent to the →PureDelay (aka pipeline delay). For more detail, see Sterman [3, Chapter 11].

Notes

• The DelayN can only be filled (not drained) via its inflow stock port.

• The parameter init in the Advanced tab allows to select →InitializationOptions:
  
  
  • FixedValue (default) will use the parameter initialValue to determine the initial value for all n hidden states as initialValue/n.
  
  
  • SteadyState will use Little's Law to determine the equilibrium start value for all n hidden states as inflow.rate * delayTime / n
  
  
  • Free there will be no initial equation and thus the solver is free in solving the initial value problem using the FixedValue solutions as startValue.

• There is an optional →StockInfoOutput connector.

See also

MaterialStock, PureDelay, Converters.DiscreteDelay