Abstract This paper discusses the operational subsidy issue of urban rail transit (URT) operators. We first analyse the passenger service activities and operator profit in train operation. The operating costs and income are fully considered, combining the train operation plan and passenger elastic demand. The break-even subsidy model is formulated, which account for the effects of two fare regimes (flat and distance-based fare regimes), to determine the optimal fare for passenger and train operation headway for operators, as well as an operational subsidy to the sustainable development of urban rail transit system. The properties of the proposed model are discussed, then a solution algorithm is presented to find the results based on the first-order optimality conditions. Finally, a numerical example based on the actual data in Changsha city metro line 2 to show the effects of two fare regimes and train operating headway on calculating operational subsidies. The major results consist of solutions for optimal operating policies, which are dependent upon train operation plan, passenger demand, and fare regimes.

中文翻译：

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盈亏平衡模式下城市轨道交通运营补贴优化：考虑两种票价制度

摘要 本文讨论了城市轨道交通（URT）运营商的运营补贴问题。我们首先分析列车运营中的旅客服务活动和运营商利润。充分考虑运营成本和收益，结合列车运营计划和旅客弹性需求。制定了盈亏平衡补贴模型，该模型考虑了两种票价制度（固定票价制度和基于距离票价制度）的影响，以确定运营商的客运和火车运营间隔的最佳票价，以及对运营商的运营补贴城市轨道交通系统的可持续发展。讨论了所提出模型的性质，然后提出了一种求解算法，以根据一阶最优性条件寻找结果。最后，一个基于长沙市地铁 2 号线实际数据的数值例子，展示了两种票价制度和列车运行间隔对计算运营补贴的影响。主要结果包括优化运营政策的解决方案，这些解决方案取决于列车运营计划、乘客需求和票价制度。