Analysis of a Stochastic Switched Model of Freeway Traffic Incidents

This article models the interaction between freeway traffic dynamics and capacity-reducing incidents as a stochastic switched system, and analyzes its long-time properties. Incident events on a multi-cell freeway are modeled by a Poisson-like stochastic process. Randomness in the occurrence and clearance of incidents results in traffic dynamics that switch between a set of incident modes (discrete states). The rates of occurrence and clearance depend on the traffic densities (continuous state). The continuous state evolves in each incident mode according to mode-dependent macroscopic flow dynamics. At steady state, the system state resides in its accessible set, which supports an invariant probability measure. Behavior of the accessible set is studied in terms of inputs (on-ramp inflows) and incident parameters (incident intensity). An over-approximation of accessible set and some useful bounds on the performance metrics (throughput and travel time) are also derived using the limiting states of individual incident modes. These results provide following insights about the steady-state system behavior: (i) Expected loss of throughput increases with the incident intensity for fixed incident rate, but this loss is less sensitive to changes in the occurrence rate for fixed intensity; (ii) Operating an incident-prone freeway close to its capacity significantly increases the expected travel time; (iii) The impact of incidents reduces when certain inputs upstream of incident-prone sections are metered.