Volume delay functions based on stochastic capacity

The standard highway assignment problem is solved by using a volume delay function (VDF). The primary link impedance is travel time, which increases with an increasing degree of saturation. VDFs contain link-specific input parameters, such as capacity and free-flow speed, as well as coefficients depending on VDF type. The coefficients either are taken from guidelines or are estimated from site-specific data. Because free-flow speed can be measured directly, mean values usually are used for particular links or link types. Capacity is not easy to determine because of its stochastic nature and large variations. VDFs for traffic assignment are presented that assume stochastically distributed capacity. These VDFs are suitable for two- and three-lane freeways in urban and non-urban areas. The stochastic capacity depends on the probability of traffic breakdowns and is determined with the use of the product-limit method and the Weibull distribution. The Bureau of Public Roads (BPR) function was chosen as a typical representative of a VDF for highway assignment models. Two models were applied. First, one coefficient was fixed, and then both BPR coefficients were estimated by regression analyses with the least squares method. The regression analyses provide suitable results at all measurement points for the model with one fixed coefficient; results differ when both BPR coefficients are estimated. The calibration of widely applied VDFs in travel demand models benefits from stochastic capacity analysis as applied in the field of traffic engineering. These results are unique to measurement points in Austria, but the method can be transferred to other countries where long-term data from freeway detectors are available.