Analysis of a Stochastic Switched Model of Freeway Traffic Incidents

This article introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents on a multi-cell freeway are modeled by reduction in capacity at the affected freeway sections, which occur and clear according to a Markov chain. We develop conditions under which the traffic queue induced by stochastic incidents is bounded. A necessary condition is that the demand must not exceed the time-average capacity adjusted for spillback. A sufficient condition, in the form of a set of bilinear inequalities, is also established by constructing a Lyapunov function and applying the classical Foster-Lyapunov drift condition. Both conditions can be easily verified for realistic instances of the stochastic incident model. Our analysis relies on the construction of a globally attracting invariant set, and exploits the properties of the traffic flow dynamics. We use our results to analyze the impact of stochastic capacity fluctuation (frequency, intensity, and spatial correlation) on the throughput of a freeway segment.