A stock is drained at a rate proportional to its content



This information is part of the Business Simulation Library (BSL). Please support this work and ► donate.

ExponentialDecay is identical to →ExponentialDecline, e.g., the connected stock is drained at a rate proportional to its content into a sink with infinite capacity outside the border of the system in focus. Instead of using a fractional rate λ to describe the process, we are using the mean residence time τ (aka mean lifetime or the exponential time constant) to parameterize the process:

tau = 1/lambda

The mean residence time can be given either as a constant parameter (residenceTime) or as a continuous time input u.

The effective rate of decay with respect to a connected stock x at any time will be given by

dx/dt = -x/tau


  • The effective rate of decay (e.g the product of the rate and amount in stock) must never be negative, as filling the connected stock is prohibited. Should the rate of outflow from the stock become negative, it will be set to zero.
  • In case of a constant residence time τ there will be 1/e ≈ 37% of the initial amount in the connected stock left after the residence time has elapsed.

  • Often the half-life of an exponential decay process is of interest, whith can be obtained by

    t_1/2 = log(2) tau

See also

ExponentialDecline, DecayExponentialChange

Parameters (2)


Value: false

Type: Boolean

Description: = true, if the constant residence time is used instead of the real input u


Value: 1

Type: Time (s)

Description: Constant time of average residence (optional) (decaying.residenceTime)

Connectors (5)


Type: RealOutput

Description: Rate information


Type: RealOutput

Description: Rate information


Type: RealOutput

Description: Rate information


Type: FlowPort

Description: Inflow to or outflow from connected stock


Type: RealInput

Description: Residence time input

Components (3)


Type: ConstantConverterTime

Description: Constant residence time (optional)


Type: Decay

Description: Draining a stock with a given average residence time


Type: Cloud

Description: System boundary - the stock will be assumed to have infinite capacity