N-attribute dynamic priority method for railway traffic management using triggered rolling horizon with bidirectional feedback

Train rescheduling involves multiple dimensions such as crew, rolling stock, and passenger demand, making it a multi-objective rescheduling problem, with stakeholders prioritizing different objectives under different scenarios. Meanwhile, the measurable attributes within these dimensions dynamically evolve with train operations, continually altering the severity of conflicts. Train priority is particularly well-suited to capture these dynamics and reflect rescheduling preferences, serving as a key factor in conflict resolution and resource allocation. However, most existing studies adopt static or dynamic train priorities determined only by train-intrinsic attributes, which limits their adaptability to multi-attribute coordination and evolving system states. This paper proposes a generalized dynamic priority calculation method that integrates N-attribute with differentiated importance, and incorporates it into a mixed-integer linear programming (MILP) model for integrated multi-objective rescheduling. A triggered rolling horizon algorithm is further developed, incorporating trigger mechanisms for delay risk warning driven by bidirectional feedback between train-specific trigger thresholds and rescheduling results. This enables timely detection of potential delay risks and adaptive decision-making. We apply the proposed model and algorithm to integrated train rescheduling problems considering attributes related to train type, rolling stock connection time and crew duty time in mixed passenger and freight traffic. Real-world case studies based on a China railway line demonstrate the flexibility and adaptability of the proposed method. Compared with seven representative benchmarks, the proposed method balances optimality on train delays and operational feasibility while maintaining computational efficiency.