Priority order, highest first: speed (Speed_up / Slow_down) → time headway, only if speed is steady (Catch_up / Fall_behind) → acceleration, only if speed and headway are both steady (Follow_behind, else Hold_speed). Reading the trend of each signal over a phase — Increasing (I), Decreasing (D), or Steady (S) — against this order gives the pattern label directly:

I = increasing, D = decreasing, S = steady, – = not decisive for this pattern (a higher-priority signal has already determined the label).

A real car-following segment from the study, with the four tracked variables plotted against elapsed time and background shading showing the resulting Action pattern for each phase. Pick a different follower vehicle to see how the same rule-based cascade plays out on a different trajectory:

Background color marks each phase's assigned pattern: lavender = Fall_behind, sage green = Catch_up, salmon = Speed_up, pale yellow = Slow_down, tan = Follow_behind, light blue = Hold_speed (not every pattern occurs in every segment). Vertical boundaries are the retained turning points from step 02. Segments are drawn from the 2022‑11‑21 trajectory_examples output.

Once every phase in a day's traffic flow carries an Action pattern label, two complementary quantities characterize the population: how likely a driver is to move from one pattern to another, and how long each pattern tends to last.

Transition probabilities

Within a day's phase sequence (primary and headway-refined sequences are treated separately), let ψ(P_i→P_j) be the observed count of transitions from pattern P_i to pattern P_j. The transition probability is the row-normalized frequency:

so each pattern's six outgoing probabilities sum to one. Because consolidation (step 05) forbids a phase from following another of the same label, the diagonal Pr(P_n+1=P_i | P_n=P_i) is zero by construction, for every pattern P_i.

Duration distributions

Rather than assuming a parametric form, each pattern's duration distribution is estimated non‑parametrically. For pattern P_i, let {t₁, …, t_z} be the durations, in seconds, of every retained phase labeled P_i on that day. A Kernel Density Estimate (KDE) with a Gaussian kernel gives a smooth density f_i(t):

where z is the number of observed durations and h is the kernel bandwidth. Four moments of the fitted density then summarize pattern P_i's duration characteristics — mean μ (typical duration), variance σ² (spread), skewness γ₁ (asymmetry), and kurtosis γ₂ (tail weight):

This mirrors the distribution-based duration knowledge used to characterize Action patterns in Yao et al. 2024.

Day-to-day transition change (L1 distance)

To quantify how much one day's transition structure differs from another's, let A and B be the two days' 6×6 row-normalized transition matrices from Equation 1. The L1 (Manhattan) distance sums the absolute difference over every entry:

summed over all 36 ordered pattern pairs (i, j). L1(A, B) = 0 only when the two days share identical transition probabilities for every pattern pair; since each row of A and B sums to 1, the theoretical maximum is 12 (each of the six rows contributing at most 2 to the sum). A small L1 distance between two days is therefore direct, interpretable evidence that the underlying car-following behaviour was stable across them, while a large one flags a day whose drivers moved between patterns in a measurably different way.

Vehicle trajectories reconstructed from a fixed camera network along a multi-mile section of Interstate 24 near Nashville, TN. Each record gives back-center longitudinal and lateral position (feet) and vehicle length; speed, acceleration, and lane are all derived during preprocessing. Data are released as one file per calendar day, each on the order of 10⁵–10⁶ trajectories and tens of gigabytes.

This study uses ten weekdays: 2022-11-21 through 2022-12-02, split into Week 1 (with the Thanksgiving holiday) and Week 2 (ordinary).

Raw file size and the daily camera-network collection window vary day to day, and matter for interpreting the Results tab: most days cover a 4‑hour window, but Friday 11/25 was collected over 11 hours — nearly three times as long — so its raw scale is not directly comparable to an ordinary day.

"Segments extracted" counts an earlier candidate-segment pipeline stage, logged per day before the retention criteria in step 03 are applied — it is not the same count as the final retained car-following segments used elsewhere in this dashboard. Friday 11/25 collected for almost three times as long as an ordinary day, yet still recorded barely a quarter of the segments seen on the following week's ordinary Friday (12/02) — so the holiday-week effect visible in the Results tab extends into Friday as well, not just Thanksgiving Thursday itself.

Each day's raw JSON is streamed record-by-record rather than loaded into memory. Position is smoothed with a 0.6 s centered moving average, resampled to a fixed 0.1 s grid, and differentiated by central difference for speed and acceleration. Lateral position is matched to lane-center offsets (±5.5 ft tolerance) for lane assignment, and the nearest same-lane vehicle ahead is identified as leader at every instant.

Continuity is enforced during segment extraction: consecutive samples from the same follower–leader–lane combination remain part of one car-following segment only if the gap between them is ≤ 0.25 s; a larger gap, or a change of leader or lane, closes the current segment and starts a new one from the next sample. No interpolation is performed across a gap — small gaps are simply tolerated within a segment, they are not filled in.

A direct comparison against unsmoothed raw positions found a maximum difference of 0.016 m/s in speed and 0.024 m/s² in acceleration — one to two orders of magnitude below the pattern thresholds below — indicating the smoothing step is a small safety margin, not a shaping filter.

Raw (red) vs. pipeline-smoothed (blue) speed and acceleration for one example segment — the curves are visually indistinguishable, matching the maximum differences reported above.

Identical to the Lyft5 study's thresholds, so any differences observed between the two datasets' results reflect differences in the underlying traffic, not a re-tuning of the method.