Appraisal of the Continuous Second Order Traffic Systems Employing Sensitivity Analysis and Numerical Simulation

This study presents a like-for-like evaluation of Second-Order Traffic Systems (SOTS), calibrated at scale and assessed for accuracy and sensitivity across distinct traffic scenarios. SOTS can be divided into two classes, the Density Gradient Traffic Systems (DGTS) and Speed Gradient Traffic Systems (SGTS), also known as anisotropic traffic systems. While the mathematical properties of SOTS have been extensively studied, their practical performance, calibration behaviour, and sensitivity under varying traffic conditions are less well understood. In this perspective, the paper provides a comprehensive assessment of how a representative set of SOTS reproduces ground-truth traffic generated by a microscopic simulator (Simulation of Urban MObility, SUMO). Two traffic conditions are considered, and for each model and scenario, large simulation is carried out, treating key SOTS parameters as random variables within admissible ranges and calibrating them using a common performance index. Model behaviour is then analysed through spatio-temporal flow patterns, linear correlation analysis, and global sensitivity indices. Results confirm the ability of all considered SOTS to reproduce, with comparable performance, the spatio-temporal pattern formation and evolution of the ground truth in both scenarios, including the dynamics of shock waves. The sensitivity analysis reveals a clear hierarchy of parameters, the free-flow speed is consistently the dominant calibration variable, a small group of spacing and anticipation parameters plays a secondary but non-negligible role, and several other parameters have very limited influence under the chosen settings and data. Overall, the findings provide practical guidance on how to prioritize parameters during calibration and how to use SOTS in a reliable and informed way for different traffic conditions.