How does noise change car-following?
Three ring roads run side-by-side with identical IDM parameters and initial
conditions. The only difference is the driver-noise model on the acceleration
residual η(t):
white noise (B-IDM),
AR(p) (DR-IDM),
Gaussian process (MA-IDM).
The autocorrelation of η(t), the fundamental diagram, and summary
metrics reveal the qualitative differences — persistent waves and FD hysteresis
under correlated noise, fine jitter under white noise.
Acceleration noise η(t) — one tagged car
White noise looks like hash; AR is jagged but persistent; GP is smooth.
Autocorrelation ACF(τ) of η(t)
White noise: spike at τ=0, then within the ±2/√N band (grey dashed, 95% CI under i.i.d. noise). AR / GP: slow decay — the temporal correlation that distinguishes them from white noise.
Fundamental diagram — flow vs density
Correlated noise widens the scatter and tends to produce hysteresis around the critical density.
Summary metrics
| Metric | White (B-IDM) | AR(p) (DR-IDM) | GP (MA-IDM) |
|---|---|---|---|
| Empirical std of η(t) (m/s²) | – | – | – |
| Lag-1 autocorrelation of η | – | – | – |
| Effective correlation time (s) | – | – | – |
| Std. of avg ring speed (m/s) | – | – | – |
| % time with min speed < 3 m/s | – | – | – |
Metrics accumulate from reset; let the sim run ~60 s for stable estimates.