Conflict Metrics for Traffic Streams: A Two-Layer Model with a Micro–Macro Link

Surrogate safety measures (SSMs), such as time-to-collision (TTC) and deceleration rate to avoid a crash (DRAC), are widely used as safety proxies when crash statistics are insufficient. However, SSMs are applied pairwise and have no formal link between the micro- and macro-levels; moreover, fixed thresholds (e.g., TTC = 3 s) lose discriminative power in dense traffic. This paper proposes a two-layer model of conflict metrics. Layer 1 is environment-specific: it contains the movement models and the micro-level metrics that reflect the physics of a given environment. Layer 2 is universal: it defines a three-level system of metrics - the pairwise index \( \psi(P) \), the meso-level share \( \Psi_{\text{frame}}(P) \), and the macro-level share \( C \) - and is independent of the environment. The basic aggregation inequality \( \max_P \Psi_{\text{frame}}(P) \le C \le \sum_P \Psi_{\text{frame}}(P) \) provides a formal micro-macro link and yields two state parameters: the limiting conflict \( M \) and the boundary gap \( \Delta \), with the integral metric \( r=\sqrt{M^2+\Delta^2} \). The control objective for conflict is formulated as \( (M\to 0,\ \Delta\to 0) \), i.e., \( r\to 0 \). The TTC threshold is calibrated per lane on the longest continuous interval with at least three vehicles per frame, using the 5th percentile of the empirical TTC distribution. The model is applied to a real HDV stream from the UTE dataset: calibrated thresholds range from 0.78 s to 11.57 s across the analysed lanes (lane 0 is excluded), and the most conflicting pairs reach \( \psi=0.915 \).