Empirical Analysis of Traffic Breakdown Probability Distribution with Respect to Speed and Occupancy

From an operation viewpoint, traffic breakdown (from free-flow) was defined as when the average speed of traffic drops below a certain threshold. It is known that traffic breakdown is a stochastic phenomenon which can happen even when the traffic flow is below the capacity. The capacity has many definitions, such as that in HCM or the average of maximum daily flow. This study investigates the probability of breakdown at certain locations of freeway. The motivation is to find a practical capacity for each freeway section for active traffic control/operation purposes, which could be different from previous viewpoints. Capacity is usually expressed in terms of flow rate. Nevertheless, it is well known that a particular value of flow rate could represent two different traffic states: uncongested and congested. Therefore, simply considering flow rates as the main factor is inadequate for operational purpose. In this study, a bivariate Weibull distribution is adopted to model the probability of breakdown as a function of both mean speed and occupancy of the incoming traffic. The methodology of constructing and calibrating the bivariate distribution is introduced. In addition, three case studies are performed to test the methodology proposed herein. The case studies are carried out by using three different datasets: PORTAL, PeMS, and BHL (Berkeley Highway Lab). PORTAL is an archived data source collected from freeways in Oregon, while the other two are collected from freeways in California PATH. The datasets measure and process flow rates, occupancies, and speeds of traffic from the loop stations on the freeways. Empirical results derived and their potential applications are discussed for developing various traffic control strategies including Variable Speed Limit (VSL) and ramp metering.