A Stochastic Model for Traffic Incidents and Free Flow Recovery in Road Networks

Fahem Mouhous (), Djamil Aissani and Nadir Farhi ()
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Fahem Mouhous: Department of Mathematics, Faculty of Sciences, University of Tizi Ouzou, Tizi Ouzou 15000, Algeria
Djamil Aissani: LaMOS Research Unit, University of Bejaia, Bejaia 06000, Algeria
Nadir Farhi: COSYS-GRETTIA, Gustave Eiffel University, 77454 Marne-la-Vallée, France

Mathematics, 2025, vol. 13, issue 3, 1-31

Abstract: This study addresses the disruptive impact of incidents on road networks, which often lead to traffic congestion. If not promptly managed, congestion can propagate and intensify over time, significantly delaying the recovery of free-flow conditions. We propose an enhanced model based on an exponential decay of the time required for free flow recovery between incident occurrences. Our approach integrates a shot noise process, assuming that incidents follow a non-homogeneous Poisson process. The increases in recovery time following incidents are modeled using exponential and gamma distributions. We derive key performance metrics, providing insights into congestion risk and the unlocking phenomenon, including the probability of the first passage time for our process to exceed a predefined congestion threshold. This probability is analyzed using two methods: (1) an exact simulation approach and (2) an analytical approximation technique. Utilizing the analytical approximation, we estimate critical extreme quantities, such as the minimum incident clearance rate, the minimum intensity of recovery time increases, and the maximum intensity of incident occurrences required to avoid exceeding a specified congestion threshold with a given probability. These findings offer valuable tools for managing and mitigating congestion risks in road networks.

Keywords: shot noise process; performance characteristics; congestion risk; incident occurrences; incident clearance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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