Public transportation delays due to systematic failures have a major impact on network users. We propose designing capacity pooling contracts to facilitate horizontal cooperation among operators to mitigate those costs and improve service resilience. When two or more public transport providers agree upon sharing resources, the total transportation costs can be reduced due to added flexibility in the system. These operators may contribute capacity to be used in cost-effective routes owned by other operators. We formulate a two-stage stochastic model to determine the cost savings under different collaboration scenarios. We provide several solution methods: a deterministic equivalent problem, the L-shaped method, and sample average approximation. Coalitional stability under Shapley value, nucleolus, and tau-value are tested. The proposed model is applied to a regional multimodal network in the Randstad area of the Netherlands, for four operators, 80 origin-destination pairs, and over 1400 links where disruption data is available. Using the proposed method, we identify stable cost allocations among four operating agencies that could yield a 44% improvement in overall network performance over not having any risk pooling contract in place.

中文翻译：

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移动运营商资源池合同设计以对冲网络中断

由于系统故障导致的公共交通延误对网络用户有重大影响。我们建议设计容量池合同，以促进运营商之间的横向合作，以降低这些成本并提高服务弹性。当两个或多个公共交通供应商同意共享资源时，由于系统增加了灵活性，可以降低总运输成本。这些运营商可能会贡献容量以用于其他运营商拥有的具有成本效益的路线。我们制定了一个两阶段随机模型来确定不同协作场景下的成本节约。我们提供了几种解决方法：确定性等效问题、L 形方法和样本平均近似。测试了 Shapley 值、核仁和 tau 值下的联合稳定性。所提出的模型应用于荷兰 Randstad 地区的区域多模式网络，适用于四个运营商、80 个起点-目的地对以及 1400 多个可用中断数据的链路。使用建议的方法，我们确定了四个运营机构之间的稳定成本分配，与没有任何风险分担合同的情况相比，可以将整体网络性能提高 44%。