Ph.D Thesis
Ph.D Student Mattar Caroline Stochastic and Statistic Prediction of Capacity and Flow Breakdown on Freeways Department of Civil and Environmental Engineering Professor Abishai Polus Mr. Moshe Pollatschek (Deceased)

Abstract

This research focuses on the analysis, understanding, and modeling of heavy-flow breakdowns when no bottlenecks exist. Two models have been developed in order to describe the breakdown phenomenon. The first is termed Hoiker model (Dromedary-Shaped Model), which was developed in the density-time plane. The second is the dynamic oscillation model.

The Hoiker model is a combination of an exponential model, a logistic model, and weighting function; it describes the density-time relationship by using data collected in one-minute time intervals. Three important definitions were obtained from the Hoiker model: (1) the pre-breakdown process; (2) the breakdown process and (3) the beginning of the unstable flow. The Hoiker model and its definitions can help predict the breakdown time. To examine this model, data was collected from Interstate I-66 in Virginia, USA, and QEW near Toronto, Canada. The Hoiker model was fitted to the data.

The dynamic oscillation model describes the breakdown phenomenon on speed-time plane. This model is an exponential model that describes the minimal points of the speed “envelop” as a function of time. It was found that the power of the exponential model was similar for all analyzed days. In addition, it was found that the distance between the torsion and the beginning of the unstable flow was on average 540 seconds (9 minutes). These two findings help predict the beginning of the unstable flow nine minutes prior to its occurrence.

One of the goals of this study was to explore the definition of capacity and investigate its meaning and analyze its stochastic nature. Two capacities were defined, capacity of dense flow and capacity at the beginning of the unstable flow. Shifted Gamma distribution was selected to describe the capacity values in dense flow and at the beginning of the unstable flow.

In sum, the two models, the Hoiker and the dynamic oscillation, describe the breakdown phenomenon and define the flow regimes. The prediction of the unstable flow made by the dynamic oscillation model could help freeway control centers in directing the drivers, and the capacity model (shifted Gamma distribution) could help in prediction of capacities and using its values in transportation planning and analysis.