Abstract: The capacity of urban publie transport system, its corresponding robustness and resilience, are the hot researching issues recently. According to the characteristics of urban public transport system, a bi-level programming model (BLP) was proposed to determine the reserved transportation capacity of the urban transit network, whose goal was to maximize the interests of both the operation department and travelers. In the bilevel programming model, the upper model was a minimum cost maximum flow model, and the lower model was a stochastic user equilibrium (SUE) allocation model. For the proposed model, a solution algorithm based on OD quantity expansion was designed, and a simple network was given to illustrate the effectiveness of the proposed model and the solution algorithm. The results show that the proposed model and solution algorithm can effectively find the balance of interests between operators and travelers.

Key words: traffic engineering; bi-level programming; public transport network; the reserved transportation capacity; minimum cost maximum flow

摘要： 城市公共交通系统运输能力及其鲁棒性、坚韧性等问题是近年研究的热点。根据城市公共交通系统的特性，以运营部门和出行者双方的利益最大为目标，提出了一个双层规划模型来确定公交网络的潜在运能。在双层规划模型中，上层模型为一个最小费用最大流模型，下层模型是一个随机用户均衡配流模型。针对所提出的模型，设计了基于OD量增广的求解算法，并给出了一个简单的网络来说明模型和求解算法的有效性。结果表明：该模型和求解算法可以有效找到运营者和出行者之间的利益平衡点。

关键词: 交通工程；双层规划；公交网络；潜在运能；最小费用最大流