Extension and Calibration of BPR Function for Traffic Efficiency Based on MFD

Abstract

Considering temporal and spatial characteristics of traffic conditions, traffic efficiency is defined to indicate capacity of urban network. First the BPR volume delay function is expanded as a travelling speed function of traffic density instead of travelling time function of traffic volume, and then the capacity for a network is defined. The parameters are calibrated connecting with traffic parameters such as free speed, optimal speed and capacity. The macroscopic fundamental diagram (MFD) can deal with the relations among the traffic speed and densities of the road network in some scales. While it doesn’t relate the density spread situation to traffic efficiency well and a generalized macroscopic fundamental diagram (GMFD) relating to density spread is proposed. It is found that average speed is a nonlinear function of average density and density spread at urban network level. Considering the density spread, traveled speed function is constructed to indicate traffic efficiency of network for travelers, based on the extended BPR (Bureau of Public Road) function from a road segment to the whole urban network. An improved Levenberg-Marquardt (LM) algorithm is used to calibrate parameters of the function and an improved Levenberg-Marquardt (LM) algorithm is used to calibrate parameters of the function. From case of Taidong business district, it proves that traveled speed function of network considering density spread is more in line with the physical variation of actual traffic and the calibration method is reliable.