Estimating the spatiotemporal impact of traffic incidents: An integer programming approach consistent with the propagation of shockwaves

A fundamental issue in estimating the spatiotemporal impact of an incident is to ensure that the shape of the affected region in the speed map is consistent with the propagation of shockwaves. In this research, we develop an integer programming model with a set of novel constraints to guarantee such consistency, which is new to the literature. The input to our model includes the historical speed on a given road as well as the location and starting time of a known incident. The model then outputs the spatiotemporal region impacted by this incident. We prove that our model produces results that are consistent with the propagation of shockwaves. We then show that our model is computationally more efficient than the current state-of-the-art model because ours requires substantially fewer constraints. Numerical experiments using both simulation and real data demonstrate that the reduction in computational time can be as large as 95-98% on average.