@article{ref1,
title="Understanding Traffic Breakdown: A Stochastic Approach",
journal="Transportation and traffic theory",
year="2007",
author="Kuhne, Reinhart and Mahnke, Reinhard",
volume="17",
number="",
pages="777-789",
abstract="Observations from different freeways indicate that traffic breakdowns do not necessarily occur at maximum flow and can occur at flows lower or higher than those traditionally accepted as capacity value. The notion breakdown means a stochastic transition from an uncongested traffic state to a congested state which is comparable with a phase transition in nature between different states of matter. Suggested by recent studies quoting data from German freeways the paper addresses the probabilistic approach for understanding of traffic breakdown. The phenomenon will be described by a balance equation which models the dynamics of jam formation similar to nucleation by two contributions only, called inflow or adhesion rate mainly depend on the traffic volume of the considered road section and discharge rate depending on the length of the congestion. With this balance equation it is feasible to calculate the dynamics of traffic pattern formation especially the first passage time distribution for a transition from free flow condition to congested traffic including the influence of the parameters affecting the adhesion and discharge rates.<p />",
language="en",
issn="",
doi="",
url="http://dx.doi.org/"
}