Temporal Boundaries of Newell's Car-Following Model: Insights from Lane-Free Traffic

Abstract

Newell's simplified car-following model offers behavioral interpretability with minimal parameters, yet the temporal limits within which it holds during actual car-following interactions, particularly in lane-free traffic, remain poorly understood. This has direct consequences for Newell parameter estimation. This study evaluates the model using high-resolution UAV trajectories from a lane-free highway corridor in Chennai, applying two independent estimation approaches: linear regression of the speed-spacing relationship (aggregate and pair specific), and a shifting optimization method that recovers parameters by minimizing spacing variance. A boundary-corrected variant of the shifting method is then introduced to isolate transitional regimes at interaction endpoints while preserving the original Newell formulation. Pair-specific regression substantially outperforms the aggregate specification ($R^2$ = 0.84 vs. 0.54), underscoring pronounced driver heterogeneity. Parameters recovered via trajectory shifting are statistically equivalent to regression estimates, providing independent support for the trajectory translation principle underlying Newell's model. Boundary correction markedly improves model fit, increasing the mean $\bar{R^2}$ from 0.66 to 0.95, and is preferred for 81% of pairs according to the Bayesian Information Criterion (BIC). The results indicate that interaction boundary effects, rather than failures of the core behavioral assumptions, are the principal source of estimation error in this setting. Correcting for these effects improves parameter recovery without compromising model parsimony. Boundary correction is therefore a necessary step in trajectory-based calibration of Newell-type models, with implications for traffic state estimation and microscopic traffic simulation.