Evaluating safety effects of variable speed limit systems via joint modeling

Variable Speed Limits (VSL) systems are key components in Active Traffic Management System (ATMS). They dynamically and coordinately adjust speed limits to harmonize traffic flow thereby enhancing travel safety and reliability. The objective of this study is to evaluate the safety impacts of the VSL deployed on the I-24 Smart Corridor, Nashville, Tennessee, which went online in June of 2023. Safety indicators were measured by various crash outcomes, and they were typically modeled separately in previous studies. The potential correlations between collision type and its consequence represented by severity were often overlooked, leading to the underestimation of treatment effects. Hence, this study attempts to jointly model the rear-end, injury, and Property Damage Only (PDO) under the copula framework. The treatment effect, which is also known as the Crash Modification Factor (CMF) in before-after studies, is estimated by the Difference-in-Differences estimator in the marginal Negative Binomial (NB) model. Gaussian, Frank, and Clayton copulas were compared, and the best-fitting copula was used to estimate the model parameters. The results indicate that the copula models significantly outperform the separate NB models. The CMFs of rear-end and injury crashes resulting from VSL implementation are 0.677 and 0.686 respectively. Their scale-invariant correlation is very high (i.e., 0.91 out of 1), which suggests that the reduction in injury crashes may be attributed to the reduction of rear-end crashes. However, the change in PDO crashes was not statistically significant, possibly due to the shift from injury crashes to PDO crashes after traffic slowing down in adverse traffic conditions. Finally, the study results confirm the positive impact of implementing VSL systems and help justify future investments for candidate corridors.