Abstract: In order to capture the competing operational behaviors ( pricing) of operators of multiple parking facilities as well as users’responses to the pricing decision，a three-class parking ( i． e． ，curb parking lot，off-street parking lot，and parkand-ride facility) pricing model is established based on user equilibrium conditions． The upper-level is an optimization model which simulates the parking operators’pricing decisions with objective of maximizing their profits; the lower-level is a user equilibrium model that describes users’travel behaviors，e． g． ，mode choice，path choice，and parking facility choice，under the principle of personal travel cost minimization． The proposed model is a non-linear programming problem，which is resolved by a sensitivity analysis based algorithm． A numerical example is presented to testify the validity of the proposed model and algorithm，and the results show that the competition of multiple parking facilities has significant influences on the optimal solution of parking pricing，and may lead to generally lower pricing level and better effectiveness of TDM ( e． g． ，reduced congestion costs per person trip and improved park-and-ride mode share) ．

Key words: parking pricing, bi-level programming, multiple parking facilities, user equilibrium, competing operation

摘要： 为了模拟多类停车设施运营( 收费定价) 竞争以及出行者的反馈行为，建立了基于用户均衡条件的路外、路内停车场和停车换乘设施等 3 类停车设施的收费定价模型。上层优化模型模拟停车运营者以利润最大为目标的停车费定价决策，下层用户均衡条件描述出行者以个人出行成本最小为原则的旅行选择行为，包括方式、路径和停车设施的选择。采用基于灵敏度分析的算法来求解该非线性规划问题。设计算例对模型和算法的有效性进行验证，结果表明: 考虑多类停车设施运营竞争对停车收费定价最优解有显著影响，并且可能导致较低的停车收费水平和较好的交通需求管理效果，如人均出行的交通拥挤成本降低，停车换乘方式分担率提高等。

关键词: 停车收费, 双层规划, 多类停车设施, 用户均衡, 运营竞争