Path-Based Progression Optimization Model for Multimodal Traffic System Signal Coordination

Passive transit signal priority (TSP) strategies are widely recognized as effective tools for mitigating bus delays along urban arterials. However, existing TSP models primarily focus on through movements of transit vehicles, leading to potential delays for buses making turning movements. Moreover, these models do not adequately address signal coordination in multi-modal traffic systems involving both buses and private vehicles, resulting in increased delays and frequent stops for private vehicles. To address these limitations, this study proposes a binary mixed-integer linear programming (BMILP)-based signal progression band optimization model designed for multi-modal, path-level signal coordination. The model creates multiple progression bands for both straight and turning buses to minimize potential transit delays and enhance public transport service levels. By incorporating the mutual interactions between buses and private vehicles, progression bands for private vehicles are simultaneously optimized, enabling coordinated signal control that considers all users. The objective function maximizes passenger-equivalent service demand satisfied by the progression bands, explicitly accounting for mixed traffic flows and passenger loads. Numerical experiments on an urban arterial corridor demonstrate that, compared with the benchmark BUSBAND method, the proposed model achieves a 26% reduction in average bus delays, a 37% reduction in passenger car delays, and a 22% decrease in total stops, while also improving overall travel time reliability.