A significant growth of the railway transportation demand is forecasted in the next decades which needs an increase of network capacity. Where possible, infrastructure upgrading can provide extra capacity; although in some cases, this is not enough to satisfy the entire transportation demand even if optimised timetabling is performed. We propose a heuristic model to develop a stable timetable which maximises the satisfaction of transportation demand in situations where network capacity is limited. In case the demand cannot be fully satisfied, the model relaxes the given line plan and timetable design parameters. The aim is to keep as many train services as possible and reduce the level of service minimally. We develop a mixed integer linear programming (MILP) model for minimising the cycle time to find an optimised stable timetable for the given line plan. The heuristic iteratively solves the MILP model and applies relaxation measures. We tested the model on the Dutch network. The results showed that the model can generate stable timetables by removing train services from the critical circuit, and also, higher transportation demand can be satisfied by additionally relaxing timetable design parameters.

中文翻译：

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解决铁路时间表问题中的不稳定性

预计未来几十年铁路运输需求将显着增长，这需要网络容量的增加。在可能的情况下，基础架构升级可以提供额外的容量；尽管在某些情况下，即使执行了优化的时间表，这也不足以满足整个运输需求。我们提出一种启发式模型来开发稳定的时间表，以在网络容量有限的情况下最大程度地满足运输需求。如果无法完全满足需求，则模型会放宽给定的线路计划和时间表设计参数。目的是保持尽可能多的火车服务，并最小程度地降低服务水平。我们开发了一种混合整数线性规划（MILP）模型，以最大程度地缩短周期时间，以找到针对给定生产线计划的优化稳定时间表。启发式迭代地解决了MILP模型并应用了松弛措施。我们在荷兰网络上测试了该模型。结果表明，该模型可以通过从关键电路中删除火车服务来生成稳定的时间表，并且，通过额外放松时间表的设计参数可以满足更高的运输需求。