Abstract
Accurate estimation of branch-level traffic flows at urban Y-intersections from limited mainline measurements remains a critical challenge in intelligent transportation systems. Y-intersections, with their symmetric geometric configuration where multiple branches converge, pose unique challenges from flow coupling, signal-induced periodicity, and merging delays. This study develops a hybrid mathematical modeling framework that integrates piecewise linear segments with periodic components for each branch flow. The model enforces physical constraints including flow conservation, non-negativity, and segment continuity, while incorporating operational features such as signal timing and merging delays. Parameter estimation employs a two-stage optimization approach combining least-squares fitting with constrained nonlinear programming, utilizing sparse mainline detector data and minimal historical priors. Experimental validation across five progressive problem formulations demonstrates robust performance, achieving RMSE values of 3.3432 and 5.4467 for complex multi-branch scenarios while accurately capturing 10-min green/8-min red signal cycles and 2-min merging delays. The method successfully reconstructs branch flow profiles at required time points (07:30 and 08:30), reducing observation requirements by 60–80% while maintaining estimation accuracy. The proposed framework provides a practical and interpretable solution for branch flow estimation under sparse sensing conditions, bridging physics-based modeling with data-driven techniques and offering transportation agencies a deployable tool for intersection monitoring without extensive instrumentation.