Abstract
Traffic fundamental diagram is extremely important to analyse traffic flow and traffic capacity, and the central part of traffic fundamental diagram is to calibrate speed–density relationship. However, because of unbalanced speed–density observations, calibrating results using Least Square Method (LSM) with all speed–density points always lead to inaccurate effect, so this paper proposed a selecting data sample method and then LSM was used to calibrate four well-known single-regime models. Comparisons were made among the results using LSM with all speed–density points and the selecting data sample. Results indicated that the selecting data sample method proposed by this paper can calibrate the singleregime models well, and the method overcomes the inaccurate effect caused by unbalanced speed–density observations. Data from different highways validated the results. The contribution of this paper is that the proposed method can help researchers to determine more precise traffic fundamental diagram.
Highlights
Traffic fundamental diagram is significant to analyse traffic flow and capacity (Zhang et al 2019), and manage traffic operation (Alonso et al 2019)
The relative error (RE) of using Least Square Method (LSM) with all speed–density points is even larger than 1 when the traffic density is more than 60 veh/km, and the REs of methods using LSM with selecting samples are much similar, which indicates that these methods all can calibrate the Greenberg model well
Using 552 speed–density sample points) to REs of Greenberg model, mean squared error (MSE) of LSM with selecting speed–density samples are much lower than that of method using LSM with all points when the traffic density is more than 30 veh/km, and MSE of LSM125 is the lowest one in a whole, MSE of LSM552 comes second, and is the MSE of LSM238 and these indicates that the calibrating with method of LSM125 is the best one in the concern of MSE
Summary
Traffic fundamental diagram is significant to analyse traffic flow and capacity (Zhang et al 2019), and manage traffic operation (Alonso et al 2019). Since most real speed–density observations are located in the uncongested condition (Maghrour Zefreh, Török 2020), the calibrated models using LSM can reflect the uncongested conditions precisely, but not under jam conditions, which can lead to significant errors for congested conditions. To overcome this problem, Qu et al (2015, 2017) introduced WLSM to calibrate single-regime models, the weights were related to the density distance between adjacent data points and speed–density data points at congested conditions with little observations had large weights.
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