Modified Bureau of Public Roads Link Function

Abstract

The Bureau of Public Roads (BPR) function is a widely used link cost function in transportation planning because of its simple mathematical form, easily measurable field variables, and consistent performance. However, the BPR function is deterministic and does not capture the stochastic relation between travel time and traffic flow. The present study develops a modified BPR (MBPR) function by incorporating travel time uncertainty (TTU) in the deterministic BPR function. In the MBPR function, the effect of TTU is incorporated using two parameters, [Formula: see text] and [Formula: see text]. A nonlinear optimization problem is formulated, and the generalized reduced gradient method is used to calibrate the BPR and the MBPR function. The applicability of the proposed MBPR function is demonstrated using empirical data collected for an urban arterial in India and simulated data developed for a real-world urban road network. The proposed MBPR function captures the heterogeneity in travel time for different traffic flow values. The function (a) captures the variability in travel time under oversaturated conditions and (b) captures the time-dependent relation between traffic volume and delay. The physical meaning of [Formula: see text] and [Formula: see text] in the context of inter-day heterogeneity, infrastructure potential, and traffic flow heterogeneity are discussed. The practical application of MBPR as an analytical tool for system-wide performance evaluation is demonstrated by investigating the impact of traffic signal control on travel times using a before–after perspective. Compared with the before case, a 13% reduction in travel time is observed for the after case. Therefore, the installation of traffic signal control has reduced congestion.

Application of optimized BPR function in pedestrian evacuation

“…The Bureau of Public Roads (BPR) function is a widely used link cost function in transportation planning because of its simple mathematical form, easily measurable field variables, and consistent performance [6] .The BPR function model is established by fitting a large amount of data from intercity highway transportation in the United States, which may not be suitable for China. Although the Greenhills model and the BPR function model are both models for traffic flow, the pedestrian flow and traffic flow are of great similarity, so they can also be applied to the pedestrian flow as follows: first, the three-element formula of the Greenhills model is substituted into the BPR function model, and then several groups of pedestrian data of Barkhor Street are fed into the model for data fitting to obtain the BPR function model suitable for Barkhor Street in Lhasa.…”

A two-stage stochastic programming for the integrated emergency mobility facility allocation and road network design under uncertainty

“…The travel time of each link r gh (x, s, d) (for each (g, h) ∈ A) within the road network is influenced by three factors: the disaster size s, the timing of the disaster occurrence d, and the road network design strategy x. In transportation engineering literature, the travel time of link (g, h) can be computed as the sum of the free-flow travel time r gh and the impacts from disaster size s and time slot d, modeled using the Bureau of Public Records (BPR) function (Gore et al, 2023). For the disaster size s and time slot d, we introduce variables r gh (s, d), assessed based on the degree of influence exerted by disaster size s on the road link, drawing insights from engineering structural disciplines (Salawu, 1997).…”