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, $\gamma$ and $\delta$ . 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 $\gamma$ and $\delta$ 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.