具有严格车辆容量的基于时刻表的公交网络均衡模型
An Equilibrium Model for Schedule-Based Transit Networks with Hard Vehicle Capacities
AI总结：
该研究构建了带严格车辆容量约束的基于时刻表的公交网络用户均衡模型，通过拟变分不等式刻画均衡并证明存在性，给出单/多商品情形的算法及启发式方法，实测显示所得均衡社会成本效率较高。
摘要：
对公共交通网络中的乘客分配进行建模是城市规划者的一项基础任务，尤其是在考量网络基础设施决策时。一个符合现实的模型的关键方面是要纳入车辆容量有限情况下乘客的自私路径选择行为。我们在基于时刻表的公交网络中构建了一个带侧约束的用户均衡模型，其中乘客被建模为连续的非原子智能体，从各自的出发地前往目的地。智能体的路径可包含沿给定线路的多次乘车，每条线路使用的车辆都具有严格载客容量。我们通过拟变分不等式给出了（带侧约束的）用户均衡的特征描述，并通过推广Bernstein和Smith（《交通科学》，1994）的一个著名结果，证明了固定出发时间下均衡的存在性。我们进一步推导了固定出发时间下单商品实例的多项式时间算法。对于可选择出发时间的多商品情形，我们证明判定均衡是否存在是NP难问题，并设计了一种指数时间算法，该算法在均衡存在时计算出均衡，否则指示不存在。利用我们的拟变分特征描述，我们构建了一种实际中用于计算多商品用户均衡的启发式方法，并在多个真实世界实例上进行了测试。从社会成本角度看，计算得到的用户均衡与系统最优相比效率相当高。
英文摘要：
Modelling passenger assignments in public transport networks is a fundamental task for city planners, especially when deliberating network infrastructure decisions. A key aspect of a realistic model is to integrate passengers' selfish routing behaviour under limited vehicle capacities. We formulate a side-constrained user equilibrium model in a schedule-based transit network, where passengers are modelled via a continuum of non-atomic agents that travel from their origin to their destination. An agent's route may comprise several rides along given lines, each using vehicles with hard loading capacities. We give a characterization of (side-constrained) user equilibria via a quasi-variational inequality and prove their existence for fixed departure times by generalizing a well-known result of Bernstein and Smith (Transp. Sci., 1994). We further derive a polynomial time algorithm for single-commodity instances with fixed departure times. For the multi-commodity case with departure time choice, we show that deciding whether an equilibrium exists is NP-hard, and we devise an exponential-time algorithm that computes an equilibrium if it exists, and signals non-existence otherwise. Using our quasi-variational characterization, we formulate a heuristic for computing multi-commodity user equilibria in practice, which is tested on multiple real-world instances. In terms of social cost, the computed user-equilibria are quite efficient compared to a system optimum.
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