Traffic breakdowns and freeway capacity as extreme value statistics

An analysis of traffic volume time series for dense traffic shows traffic breakdowns, which can be sorted by the frequency of breakdowns dependent on the traffic volume at the beginning of the breakdown. From this empirical breakdown a probability can be extrapolated and breakdowns can be described as extreme events.Three different traffic situations can be distinguished:(a)stable traffic flow where any fluctuations decay over time,(b)metastable traffic flow where fluctuations neither decay nor grow, and(c)unstable traffic flow where a breakdown can be expected with certainty, if a reasonable observation time is provided.The results open new insights in probabilistic description and prognosis of the traffic break-downs. They lead directly to the probabilistic definition of the capacity as a traffic volume leading to an unstable traffic pattern with a given probability within a given observation time. This definition can substitute the existing definitions for the capacity of a freeway and opens the possibility to quantitatively describing the influence of traffic control systems on the traffic flow.