DelayNMaterial delay of nth Order 
This information is part of the Business Simulation Library (BSL).
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
firstorder 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
increasesâ€”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].
inflow
stock port.init
in the Advanced tab allows to select →InitializationOptions:initialValue
to determine the initial value for all n hidden states as initialValue/n
.inflow.rate * delayTime / n
startValue
.init 
Value: modelSettings.init Type: InitializationOptions Description: Provide InitializationOptions (Free, FixedValue, SteadyState) 

hasStockInfoOutput 
Value: false Type: Boolean Description: = true, if a StockInfoOutput should be added to the stock 
n 
Value: 3 Type: Integer Description: Order of the exponential delay 
initialValue 
Value: 0 Type: OutputType Description: Initial stock 
delayTime 
Value: 1 Type: Time (s) Description: Constant time of delay (optional) 
hasConstantDelayTime 
Value: true Type: Boolean Description: = true, if DelayTime is to be set by a constant parameter 
y 
Type: RealOutput Description: Level or rate information 


y1 
Type: RealOutput Description: Level or rate information 

y2 
Type: RealOutput Description: Level or rate information 

inflow 
Type: StockPort Description: Inflow port of the stock 

outflow 
Type: StockPort_Special Description: Special outflow port of the stock (stock sets rate) 

y_stockInfo 
Type: StockInfoOutput Description: Optional StockInfoOutput 

u 
Type: RealInput Description: Delay time input (optional) 
modelSettings 
Type: ModelSettings 


dynamicStockInfo 
Type: DynamicStockInfo Description: Generate information for StockInfoOutput 

parDelayTime 
Type: ConstantConverterTime Description: Constant delay time (optional) 

actualDelayTime 
Type: ClipProcessTime Description: Delay time 
BusinessSimulation.Examples A first example 

BusinessSimulation.Examples Extending the first example to include replacement purchases 

BusinessSimulation.Examples Further extending the first example to explain new product diffusion 

BusinessSimulation.Examples Classical epidemic model by Kermack and McKendrick 

BusinessSimulation.Examples Human resource planning 
BusinessSimulation.CausalLoop Exponential delay of input flow 