Delay and Smoothing Functions

Delay durations are clamped to at least 0. An omitted initial value initializes from the input value observed when the state is created.

DELAY(input, delay_duration [, initial])

A fixed transport lag. It returns the input from delay_duration time units earlier, using initial before enough history exists. Fractional durations are linearly interpolated between stored simulation samples.

Example: DELAY(Orders, 1.5, 0)

With DT = 1, input TIME * 10, duration 1.5, and initial 99, the sampled result begins 99, 99, 5, 15, 25.

DELAY1(input, delay_duration [, initial])

A first-order exponential delay. Its single state advances once per simulation step.

Example: DELAY1(Orders, 3, Initial_Orders)

DELAY3(input, delay_duration [, initial])

A third-order exponential delay implemented as three cascaded stages. Every stage advances from the previous timestep's stage values, so stages update simultaneously rather than feeding newly updated values through the whole chain in one step.

Example: DELAY3(Orders, 3, 0)

DELAYN(input, delay_duration, order [, initial])

An order-stage exponential delay. order is rounded to the nearest integer and clamped to at least 1. Stages use simultaneous previous-step updates.

Example: DELAYN(Orders, 6, 4, 0)

SMTH1(input, averaging_time [, initial])

A first-order exponential smooth using the same one-stage state mechanism as DELAY1.

Example: SMTH1(Measured_Demand, 4, Initial_Demand)

SMTH3(input, averaging_time [, initial])

A third-order exponential smooth. Its three stages update simultaneously from the previous timestep's state.

Example: SMTH3(Measured_Demand, 3, 0)

SMTHN(input, averaging_time, order [, initial])

An order-stage exponential smooth. order is rounded and clamped to at least 1; stages update simultaneously.

Example: SMTHN(Measured_Demand, 6, 4, 0)

All functions in this article are non-instantaneous dependencies and can break an otherwise algebraic feedback cycle.