Automatic calibration of fundamental diagram for first‐order macroscopic freeway traffic models

Abstract

Despite its importance in macroscopic traffic flow modeling, comprehensive method for the calibration of fundamental diagram is very limited. Conventional empirical methods adopt a steady state analysis of the aggregate traffic data collected from measurement devices installed on a particular site without considering the traffic dynamics, which renders the simulation may not be adaptive to the variability of data. Nonetheless, determining the fundamental diagram for each detection site is often infeasible. To remedy these, this study presents an automatic calibration method to estimate the parameters of a fundamental diagram through a dynamic approach. Simulated flow from the cell transmission model is compared against the measured flow wherein an optimization merit is conducted to minimize the discrepancy between model-generated data and real data. The empirical results prove that the proposed automatic calibration algorithm can significantly improve the accuracy of traffic state estimation by adapting to the variability of traffic data when compared with several existing methods under both recurrent and abnormal traffic conditions. Results also highlight the robustness of the proposed algorithm. The automatic calibration algorithm provides a powerful tool for model calibration when freeways are equipped with sparse detectors, new traffic surveillance systems lack of comprehensive traffic data, or the case that lots of detectors lose their effectiveness for aging systems. Furthermore, the proposed method is useful for off-line model calibration under abnormal traffic conditions, for example, incident scenarios.The boundary conditions are not in the exact form as those in [10,23], but an equivalent formulation derived to convert the MCTM into a uniform characteristics of the sending and receiving functions as will be shown later. This formulation also makes the MCTM more suitable as a network loading model for the automatic calibration method. AUTOMATIC CALIBRATION OF FUNDAMENTAL DIAGRAM

Empirical Approximation for the Stochastic Fundamental Diagram of Traffic Flow on Signalized Intersection

“…Once the traffic flow on freeway has been modeled by SCTM with FD [9,16], the parameters , can be obtained from the maximum likelihood estimation (MLE) method by giving the independent observation sequence { ( )} =1: and state mode sequence { } =1: [17], which equals the parameter calibration on freeway condition [9,16]. But we want to obtain the distribution of parameters , in (12) on the basis of Definition 1 for the traffic flow on signalized intersection, which can be computationally approximated as the posterior distribution by the variational Bayes (VB) learning method for SLDS [18].…”

Automatic Multiregime Fundamental Diagram Calibration Using Likelihood Estimation

“…Quandt's likelihood estimation technique (1958) was adopted by Northwestern researchers to identify breakpoints between regimes for freeway traffic and performed regression analysis to select the best models (May, 1990 (Zhong et al, 2016) proposed optimization based automatic calibration of FD. (Li, 2014) developed a tool to identify traffic state automatically and calibrate FD using historical data.…”

Bottleneck mitigation through a variable speed limit system using connected vehicles

“…A number of studies exist in the literature where various methods for calibration of the fundamental diagram were proposed, see e.g. Van Aerde and Rakha (1995), Dervisoglu et al (2010), Qu, Wang, and Zhang (2015), Zhong et al (2016), Qu, Zhang, and Wang (2017) and Knoop and Daamen (2017). In the proposed methods, optimization and regression techniques were commonly applied based on empirical observations from stationary detectors and a predefined functional form of the fundamental diagram.…”