Volume Delay Functions Based on Stochastic Capacity

Abstract

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.

Link Cost Function and Link Capacity for Mixed Traffic Networks

“…It is a polynomial function, whose coefficients need to be calibrated using empirical data ( 4 ). Generally, 0.15 and 4 are used for α and β, respectively ( 2 ). Simple mathematical form, fewer and easily field-observable inputs, and reasonable performance are some of the reasons for its popular acceptance ( 5 ).…”

“…The empirical travel time is obtained as explained in the previous section. The BPR travel time values are calculated using the BPR function (Equation 1) with the assumed values of α = 0.15, β = 4, and free-flow velocity, uf = 40 km/h, which is the speed limit on the study corridor ( 2 ). Similarly, the intersection delay values are obtained from the HCM delay model (Equation 2).…”

“…Link cost function and link capacity play a vital role in transportation planning applications. To compute the link flows, link-specific cost function and link capacity are among the inputs required in traffic assignment problems ( 2 ). The link cost function is the relationship between the mean travel time and traffic flow on the links of urban networks.…”

Context-specific volume–delay curves by combining crowd-sourced traffic data with automated traffic counters: A case study for London

“…Past studies have identified the need to inform these functions with empirical and context-specific data (Rose et al, 1989;Spiess, 1990), but also recognize the difficulty and cost associated with collecting such empirical data as being prohibitive (Rose et al, 1989). There have been studies that incorporate different forms of field sensor data for such calibration (Mtoi and Moses, 2014;Neuhold and Fellendorf, 2014;Kucharski and Drabicki, 2017). Nevertheless, the data used in these studies have been generated specifically for that application and requires specific hardware and software for use.…”

Full cost accessibility

“…Focusing on auto travelers, the internal and external costs are defined as follows: Travel time can be divided into congested and uncongested components, in which congested time implies the external cost imposed on others from the point-of-view of travelers, as additional vehicles on the roadways result in incremental delay borne by others (e.g., following travelers in the stream of traffic) (Levinson and Gillen 1998). Delay is highly related to traffic flow, which increases significantly as traffic flow reaches and exceeds capacity (Neuhold and Fellendorf 2014). Considering link properties, traffic and capacity, the marginal cost of travel time represents the external time cost.…”