A Semi-Markov Stochastic Process for Primary and Secondary Incidents Modeling

Incidents are notorious for their delays to road users. Secondary incidents – i.e., incidents that occur within a certain temporal and spatial distance from the first/ primary incident – can further complicate clearance and add to delays. While there are numerous studies on the empirical analysis of incident data, to the best of our knowledge, an analytical model that can be used for primary and secondary incident management planning that explicitly considers both the stochastic as well as the dynamic nature of traffic does not exist. In this paper, the authors contribute to the literature by presenting a semi-Markov stochastic process that allows for unprecedented generality in the modeling of stochastics during incidents on freeways. Particularly, the authors relax the oftentimes restrictive Poisson assumption (in the modeling of vehicle arrivals, vehicle travel times, and incidence occurrence and recovery times) and explicitly model secondary incidents. Numerical case studies are provided to illustrate the proposed model.