公共自行车租赁时长分布特性的引力场模型

租赁时长分布特性是公共自行车系统中一项重要的基本特性，通过获取乘客刷卡信息数据，得到了宁波、杭州和北京3 座城市多个工作日的公共自行车租赁时长特性 数据.统计分析得出，不同城市、不同工作日的公共自行车租赁时长分布特性差异较小，由此表明租赁时长分布特性的研究具有一般性意义.在此基础上，基于物理学中的引力场理 论，建立了租赁时长分布特性的两个引力场模型，实际数据检验表明，模型1 和模型2 分 别与租赁时长大于11 min 时及小于11 min 时的分布特性能较好地吻合，并得到了引力场模型的具体函数表达式.研究成果将为公共自行车系统租赁需求预测、租赁站点规划和站 点车辆配置等方面的工作提供重要的理论支撑.

Gravitational Field Modeling for Distribution Characteristics of Public Bicycle Rental Duration

The rental duration distribution characteristic is an important basic characteristic of public bicycle system. The rental duration distribution characteristic with several weekdays was obtained based on the passengers’card dada of three cities, Ningbo, Hangzhou and Beijing. The statistical analysis shows that, the difference of rental duration distribution characteristic among the different cities and different weekdays is very small, so the research of rental duration distribution characteristic has the significance of universality. On this basis, two gravitational field models of rental duration distribution characteristic are founded based on the gravitational field theory in physics. The test is carried out using the actual data and the result shows that, the model one is well identical with the distribution characteristic while the rental duration is long than 11min and the model two is well identical while the rental duration is short than 11min. At last, the function expression of gravitational field models is given. The study results provide important theoretical support for the demand forecast of bicycle sharing systems, as well as rental station planning, the allocation, and dispatch of public bicycles.