Over the past few decades, traffic conflict modelling with proximity-based conflicts has emerged as a key approach for estimating crash risk from traffic conflicts, with extreme value models providing a rigorous framework for extrapolating rare-event probabilities. However, proximity-based definitions of conflicts may lead to biased estimation, as they often include interactions arising from deliberate and controlled driving behaviours that may not correspond to actual crash likelihood. In contrast, failure-induced conflicts that take into account evasive action and response delays can potentially overcome this limitation. Despite these advances, a comprehensive comparison of proximity-based and failure-induced conflicts within crash risk modelling is still lacking. This study addresses this gap by comparing and evaluating the performance of different threshold-exceedance modelling approaches for crash frequency estimation. Three threshold-exceedance models are evaluated in the study, including (i) a Lomax model applied to response delays during failure-induced conflicts, (ii) a Generalized Pareto Distribution model for proximity-based conflicts, and (iii) a Generalized Pareto Distribution model for failure-induced conflicts. Empirical analysis is conducted using high-resolution trajectory data from four signalized intersections in Brisbane, Australia. The results indicate that both the Generalized Pareto Distribution model for failure-induced conflicts and the Lomax model, representing response delays within failure-induced conflicts, provided reasonable estimates of historical rear-end crashes, with predicted crash counts contained within the 95 % confidence interval of the observed crash data. In contrast, the Generalized Pareto Distribution model for the proximity-based conflicts overestimated the crash frequency. Notably, within the failure-induced conflicts, the Generalized Pareto Distribution model demonstrated greater accuracy than the Lomax model, yielding estimates closer to the observed mean and with narrower confidence bounds, thereby indicating higher predictive precision. Overall, the findings underscore the value of incorporating failure-induced conflicts into traffic conflict modelling, revealing that the Generalized Pareto Distribution model with failure-induced conflicts provides more accurate and reliable crash risk estimates.
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