Denied boarding in congested transit systems induces queuing delays and departure-time shifts that can reshape passenger flows. Correctly modeling these responses in transit assignment hinges on the enforcement of two priority rules: continuance priority for onboard passengers and first-come-first-served (FCFS) boarding among waiting passengers. Existing schedule-based models typically enforce these rules through explicit dynamic loading and group-level expected costs, yet discrete vehicle runs can induce nontrivial within-group cost differences that undermine behavioral consistency. We revisit the implicit-priority framework of Nguyen et al. (2001), which, by encoding boarding priority through the notion of available capacity, characterizes route and departure choices based on realized personal (rather than group-averaged) travel experiences. However, the framework lacks an explicit mathematical formulation and exact computational methods for finding equilibria. Here, we derive an equivalent nonlinear complementarity problem (NCP) formulation and establish equilibrium existence under mild conditions. We also show that multiple equilibria may exist, including behaviorally questionable ones. To rule out these artifacts, we propose a refined arc-level NCP formulation that not only corresponds to a tighter, behaviorally consistent equilibrium concept but also is more computationally tractable. We reformulate the NCP as a continuously differentiable mathematical program with equilibrium constraints (MPEC) and propose two solution algorithms. Numerical studies on benchmark instances and a Hong Kong case study demonstrate that the model reproduces continuance priority and FCFS queuing and captures departure-time shifts driven by the competition for boarding priority.

翻译：拥挤公交系统中的拒载会导致排队延误和出发时间偏移，从而重塑客流分布。在公交分配中正确建模这些响应，关键在于强制执行两项优先级规则：车上乘客的持续优先权与候车乘客的先到先得上车原则。现有基于时刻表的模型通常通过显式动态加载和群体级期望成本来实施这些规则，然而离散的车次运行可能导致显著的组内成本差异，从而破坏行为一致性。我们重新审视Nguyen等人（2001）提出的隐式优先级框架——该框架通过可用容量的概念编码上车优先级，基于已实现的个人（而非群体平均）出行体验来刻画路线与出发时间选择。然而，该框架缺乏明确的数学表述及求解均衡的精确计算方法。本文推导出等价的非线性互补问题（NCP）表述，并在温和条件下证明均衡的存在性。同时指出可能存在多个均衡解，包括行为合理性存疑的解。为排除这些伪解，我们提出改进的弧级NCP表述，该表述不仅对应更严格且行为一致的均衡概念，还具有更优的计算可行性。我们将NCP重构为连续可微的带均衡约束数学规划（MPEC），并提出两种求解算法。在基准算例和香港案例的数值研究中，该模型成功再现了持续优先权与先到先得排队机制，并捕捉到由上车优先级竞争驱动的出发时间偏移现象。