Reliability of Freeway Traffic Flow: a Stochastic Concept of Capacity

The paper introduces a new understanding of freeway capacity. Here capacity is understood as the traffic volume below which traffic still flows and above which the flow breaks down into stop-and-go or even standing traffic. It is easy to understand that a capacity in this sense is by no means a constant value. Empirical analysis of traffic flow patterns, counted at 5minute intervals over several months and at many sites, clearly shows that this type of capacity is Weibull-distributed with a nearly constant shape parameter, which represents the variance. This was identified using the so-called Product Limit Method, which is based on the statistics of lifetime data analysis. It is demonstrated that this method is applicable to all types of freeways. The stochastic methodology allows for a derivation of a theoretical transformation between capacities identified for different interval durations. The technique can also be used to identify effects of different external conditions like speed limits or weather on the capacity of a freeway. The statistical distribution of capacity directly indicates the reliability of the freeway section under investigation. This distribution for one section is then transformed into statistical measures of reliability for larger parts of a network composed of sections of different capacity. Thus, the stochastic concept is also expanded into reliabilities of freeway networks. It is found that a freeway operates at the highest expected efficiency if it is only loaded to 90 % of the conventionally estimated (constant-value) capacity. On the one hand, the paper quotes some real world results from German freeways. On the other hand, the reliability-based analysis leads to a new sophisticated concept for highway traffic engineering.