Peilin Zhao 赵沛霖

Peilin Zhao 赵沛霖

Research Fellow @ NTU CEE

Safety hysteresis in traffic flow: Evidence from vehicle trajectory data

Published in Transportation Research Part C: Emerging Technologies, 2026

Abstract

Safety hysteresis, a dynamic pattern reflecting how traffic safety deteriorates and recovers during disturbances, remains largely unexplored. Using real-world trajectory datasets, this study demonstrates that safety hysteresis exists at both the vehicle-pair and platoon levels, manifested as counterclockwise loops on spacing-TTC−1 diagrams and clockwise loops on density-TTC−1 diagrams. To quantify these patterns, we propose the Safety Hysteresis Intensity (HI), defined as the normalized area enclosed by the safety hysteresis loop. Empirical analyses show that naturalistic traffic exhibits substantially higher safety HI than controlled experiments, while ACC and autonomous vehicles reduce safety HI and promote safer conditions. Correlation analyses reveal that low-speed regimes, large inter-vehicle speed differences, and abrupt acceleration or deceleration amplify pair-level safety HI, whereas variability in flow, density, and average speed governs platoon-level safety HI. Complementary simulations further clarify these causal mechanisms, showing that higher braking intensity and greater macroscopic fluctuations lead to stronger safety hysteresis. The results highlight safety HI as a system-level diagnostic indicator of safety. By incorporating hysteresis dynamics into safety evaluation, this study offers new theoretical perspectives and practical insights for improving traffic safety.

Highlights

  • Reveals the hysteresis phenomenon in traffic safety using real-world trajectory data.

  • Identifies pair-level and platoon-level hysteresis loops in traffic safety.

  • Proposes Safety Hysteresis Intensity (HI) as the quantification metric.

  • Empirical results show clear differences between naturalistic and controlled environments.

  • Finds speed differences, harsh braking, and flow fluctuations amplify safety HI.

Existence of Safety Hysteresis

  • Safety hysteresis loop (d) on the spacing-TTC−1 diagram at the vehicle-pair level:

    1

  • Safety hysteresis loop (d) on the density-\(\overline{TTC^{-1}}\) diagram at the platoon level:

    2

Quantification of Safety Hysteresis

  • Pair-level safety Hysteresis Intensity (HI):
\[I_s = \frac{|A|}{\Delta s_A}\]

where:

  • |A| — area of the hysteresis loop A on the spacing-TTC−1 diagram for vehicle pairs

  • ΔsA — corresponding spacing span

  • Platoon-level safety HI:
\[\mathbb{I}_s = \frac{|\mathbb{A}|}{\Delta k_\mathbb{A}}\]

where:

  • |𝔸| — area of the hysteresis loop 𝔸
  • Δk𝔸 — corresponding density span

Empirical Analysis

Safety HI is evaluated on the NGSIM, OpenACC, and Waymo datasets at both levels, covering its distribution across driving modes and ACC penetration, and its correlation with key traffic variables.

  • Distribution of safety HI at the vehicle-pair level across NGSIM, OpenACC, and Waymo datasets

    3

  • Distribution of safety HI at the vehicle-pair level across different driving modes

    4

  • Correlation coefficients between selected vehicle-pair traffic variables and safety HI

    5

  • Distribution of safety HI at the platoon level across NGSIM and OpenACC datasets

    6

  • Distribution of safety HI at the platoon level across different ACC penetration rates

    7

  • Correlation coefficients between selected platoon-level traffic variables and safety HI

    8

Takeaway: real-world traffic shows higher and more variable safety HI than controlled experiments; automation lowers it, and HI correlates most strongly with speed differences and the variability of flow, density, and speed.

Simulation Experiments

Controlled IDM simulations isolate the effect of each factor, complementing the empirical correlations.

  • Vehicle-pair level. Stronger braking and lower post-deceleration speeds raise safety HI, while acceleration rate and initial speed have little independent effect.

    9

  • Platoon level. Greater variability (standard deviation and range) in density, flow, and average speed consistently amplifies safety HI.

    10

Takeaway: smoothing deceleration and stabilizing macroscopic flow are the two most effective levers for reducing safety hysteresis.

Relation to Traditional Traffic Hysteresis

Does safety hysteresis simply inherit the direction of traditional traffic hysteresis? It does not — the safety loop keeps a fixed orientation regardless of the traditional loop's direction.

  • Vehicle-pair level. Both timid (CW) and aggressive (CCW) traditional loops yield a counterclockwise safety loop: a physical necessity, since a loop can only begin when the follower is faster than the leader, and that same condition forces the counterclockwise direction.

    11

  • Platoon level. Likewise, both clockwise and counterclockwise traditional loops predominantly map to positive (clockwise) safety HI, though aggressive driving raises the chance of the opposite sign.

    12

Conclusion

  • This study provides the first comprehensive examination of safety hysteresis using large-scale trajectory data, showing it exists at both the vehicle-pair and platoon levels, and proposes Safety Hysteresis Intensity (HI), the loop area normalized by its span.

  • Naturalistic datasets (NGSIM, Waymo) exhibit higher HI than controlled ACC experiments; both ACC activation and autonomous driving significantly reduce safety HI.

  • Low-speed regimes, large leader–follower speed differences, and abrupt acceleration or deceleration are key contributors to pair-level HI, while larger fluctuations in flow, density, and speed govern platoon-level HI; ACC penetration mitigates these effects.

  • IDM simulations clarify these mechanisms, indicating that safety hysteresis can be reduced by smoothing deceleration profiles, damping traffic oscillations, and leveraging ACC/AV technologies.

Milestone

  • Jul 2024: Detected safety hysteresis at the vehicle-pair level in the simulation.

  • Sep 2024: Detected safety hysteresis at the platoon level in the simulation.

  • Dec 2024: Presented the findings of simulation experiments at the 28th International Conference of Hong Kong Society for Transportation Studies (HKSTS2024) (Poster).

  • Jan 2025: Preprocessed empirical datasets.

  • Mar 2025: Developed algorithms for safety hysteresis event detection.

  • May 2025: Analysed the distribution of safety HI under different conditions.

  • Jul 2025: Investigated the correlation between safety HI and key traffic characteristics.

  • Nov 2025: Explored control strategies for safety HI via simulation experiments.

  • Jun 2026: Published the article in Transportation Research Part C: Emerging Technologies.

DOI: 10.1016/j.trc.2026.105806

License: © 2026. This manuscript version is made available under the CC BY-NC-ND 4.0 license.

Recommended citation: Zhao, P., Wong, Y. D., & Zhu, F. (2026). Safety hysteresis in traffic flow: Evidence from vehicle trajectory data. Transportation Research Part C: Emerging Technologies, 190, 105806.
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