A Stochastic Model for Reliability Analysis in Freeway Networks

AbstractThe capacity of a freeway is traditionally considered as a constant value in traffic engineering. In reality, capacities vary according to external conditions such as dry or wet road surfaces, daylight or darkness, and to the prevailing travel purpose of drivers on the freeway. Even under constant external conditions different capacities can be observed on freeways because of variations in driver behaviors. A capacity in this sense is no longer a constant value. Empirical analyses of traffic flow patterns show that this type of capacity can be treated as Weibull distributed. Using the distribution function of capacities, the probability of traffic breakdowns and thus the reliability of the freeway can be estimated. Up to now stochastic capacities have been mainly analyzed at specific points which are considered as bottlenecks. The stochastic relationship between the adjacent bottlenecks has not been taken into account. Furthermore, if a long segment of a freeway without clearly defined bottlenecks is analyzed, no methods are available for estimating the distributed capacities of several combined bottlenecks along a freeway. This paper introduces a concept dealing with the stochastic interpretation of capacity and breakdown probability within a larger freeway network. The stochastic methodology presented delivers a theoretical average capacity and the probability of breakdowns for freeway segments with different lengths. The methodology can also be used to identify the effects of consecutive freeway segments and bottlenecks such as on-ramps, off-ramps, and weaving areas with different characteristics. Using the proposed method, it is possible to determine the probability distribution function of breaking down from free flow into congested flow for a freeway segment as a function of the average volume or density. Using the methodology presented in this paper, the risk of disturbance of traffic flow along a freeway segment or within a freeway network can be analyzed