LMP-GNN: Probabilistic Reconstruction of Missing Lane Counts for Signed Max-Pressure Traffic Signal Control
Adaptive traffic-signal control relies on timely lane-level observations, yet detector faults, visual obstruction, and communication failures can make part of the traffic state unavailable and distort signal decisions. Prior work has separately advanced traffic-data imputation, state restoration, and estimated-state control. A gap remains at their interface. It is still unclear how to reconstruct only missing lane counts probabilistically using information available at the current decision, preserve all observed measurements, and trace the consequences through an unchanged Signed Max-Pressure controller. To address this gap, we propose LMP-GNN, a compact lane-movement graph neural network that predicts a mean and marginal uncertainty for each lane. Three transparent input rules convert these outputs into missing-lane controller inputs, while observed counts, legal phases, pressure calculation, and phase selection remain unchanged. This design isolates reconstruction effects from policy redesign and evaluates whether they survive lane recovery, pressure and phase fidelity, and closed-loop traffic. A comprehensive study on five CityFlow networks includes additional checks of demand variation, learned comparators, architecture, efficiency, and SUMO transfer. LMP-GNN reconstructs missing lane states accurately and generally preserves controller decisions better than a deterministic Road Mean baseline. Fixed Lane Discount reduces accrued average travel time by up to 13.74% under correlated missingness, while severe random loss reverses the benefit. Compared with two decision-time learned adaptations, the retained model uses 89.4-96.6% fewer parameters and achieves 81.1-95.0% lower median model-path latency. Overall, LMP-GNN provides a lightweight and auditable reconstruction-to-control interface with verified traffic benefits and explicit operating boundaries.