267. Smoothing

Operators that compute smoothed (averaged) versions of input signals. Implemented as exponential delays but used to model perception rather than physical transit.

267.1. First-order smoothing (exponential smoothing)

tracks with smoothing time — equivalent to single-exponential smoothing.

In discrete time: with .

In Vensim: SMOOTH(input, tau).

267.2. Higher-order smoothing

first-order smooths in series — each one smoother. SMOOTH3 is third-order (very common default in SD models). Removes more noise but adds more phase lag.

267.3. TREND function

Computes a smoothed fractional rate of change:

where is smoothed with time . Gives “perceived growth rate” — used to model planners’ expectations.

In Vensim: TREND(input, perception_time, trend_time).

267.4. FORECAST function

Extrapolates the input forward using TREND:

Forecast time units ahead based on current trend.

Used to model planning under expectations — what someone thinks future demand will be.

267.5. Why smoothing models decision-making

People (and organizations) don’t react to raw data; they react to smoothed versions:

Smoothing operators in SD capture this adaptive expectation behavior. Combined with delays and stocks, they generate the “policy resistance” and stability problems that define Sterman’s beer-game style dynamics.

267.6. Phase lag

Smoothing introduces a delay in perception:

Phase lag = part of why supply-chain bullwhip happens: each echelon’s reaction is delayed relative to actual demand.

267.7. See also