A stochastic risk model for incident occurrences and duration in road networks

Based on a modelling approach of continuous-time piecewise-deterministic Markov processes, and inspired by the risk model of Cramer Lundberg applied in insurance, we propose a stochastic risk model for incident occurrences and duration in road networks. We model the occurrence of incidents (accidents, works, vehicle breakdowns, etc.) as well as the evolution of the time required for the free flow recovery. Our model assumes that the time required for free flow recovery between two incident occurrences decreases linearly. We derive stochastic laws of some variables and processes which permit the evaluation of quantities and thresholds of interest interpreted in terms of traffic incidents, including the probability of exceeding a given congestion threshold. We propose four applications with practical implications in helping road operators to better manage their interventions under different traffic conditions and evaluating the maximum incident occurrences frequency and the incident duration severity.