Assessing Freeway Breakdown and Recovery: A Stochastic Model

AbstractConditions at a freeway bottleneck are predicted with a two-dimensional stochastic differential equation (SDE) model of flow and speed. Stochastic behavior is assumed to be standard Brownian motion. To fully describe conditions observed in the field, it is necessary to couple the SDE model with a stochastic capacity model, thus forming a stochastic capacity-differential equation (SCDE) model. The model contains mechanisms to (1) trigger a breakdown event when the traffic flow reaches or exceeds the freeway capacity, and (2) identify when recovery takes place. Measures of freeway performance are derived from SCDE model predictions. They include breakdown probability, expressed as a function of traffic flow and time-of-day, and recovery time, i.e., the length of time the freeway remains in a congested state before returning to a free-flow state. To achieve dependable model forecasts, it is necessary to impose constraints when fitting the stochastic capacity model. The constraint condition consists o...