Accurate and computationally efficient traffic prediction remained a fundamental challenge for transportation systems, as microscopic simulators are often too expensive for large-scale applications. This study addressed this limitation by proposing a physics-consistent surrogate modeling framework, the graph sequential physics-informed neural network (GSPINN). The approach integrated graph-based spatial representation with sequence-aware path aggregation to model trip travel time. It introduces a physics-informed learning formulation that encouraged monotonic relationships between travel time and key traffic variables through input‒output gradient constraints. To assess robustness across varying traffic conditions, the framework was applied to four heterogeneous road networks, each characterized by distinct topology, demand patterns, and control regimes. The results showed consistent predictive performance and stable behavioral properties across all settings. Complementary SHapley Additive exPlanations (SHAP)-based interpretability further indicated that the model captured network-specific feature dependencies in each case, providing evidence that it adapted to local traffic dynamics rather than overfitting to a single environment. In addition to accuracy and reliability, the proposed surrogate provided substantial computational advantages at inference time, achieving speed-ups of 3–55 times. This work therefore shows that embedding physically meaningful structures into learning objectives is an effective strategy for traffic surrogate modeling, yielding models that maintain competitive predictive accuracy while substantially improving directional behavioral consistency.