大型自行车共享系统的平均场极限理论与排队模型研究

Research on Mean Field Limit Theory and Queuing Model for Large-Scale Bike-Sharing Systems

人口的快速增长与空间的高度城市化带来了汽车尾气污染等环境污染问题,这已成为影响社会可持续发展的主要制约因素。基于此,近十年来自行车共享系统在世界多个国家的许多重要城市获得了高度重视并取得了迅速发展。然而,相比于自行车共享系统的快速发展,其相关研究却并未取得较大进展,主要原因在于它是一个大型的复杂系统,涉及密集的城市交通、异构的运营环境、多重的顾客偏好选择以及多渠道的收益管理等多种关联因素。在这种背景下,本文建立了一个通用的大型自行车共享系统,并提出了一种基于平均场极限理论与非时齐排队模型相结合的有效随机模型分析方法,包括利用平均场理论建立了非时齐排队系统、构建了经验测度过程(Empirical measure process)的非线性生灭过程、给出了分段结构下生灭过程的固定点的"几何之和"算法以及提供了问题站点稳态概率的数值计算等等。本文为研究大型自行车共享系统的随机模型提供了一个重要的发展途径,并有望能够用于分析更加一般的大型自行车共享系统。

With rapid growth of population and high urbanization of living space, an environmental pollution has been a main factor affecting the sustainable development of human society, in which the automobile exhaust pol- lution is a large problem. Based on this, bike-sharing systems have received a higher attention and gained rapid development in many major cities of many countries in the world over the past decade. However, few researches on the large bike-sharing systems have been done, and there is one main reason why such a bike-sharing system is always a very complex system including a complicated heavy traffic in each city, heterogeneous operation envi- ronments, different customer preference, revenue management of bike enterprises and so on. In this paper, we study a universal large-scale bike-sharing system, and propose an effective analytic method of stochastic model through combining the mean field limit theory and the queuing models. To this end, we develop some new sto- chastic analytic techniques, which are organized as follows： Establishing a time-inhomogeneous queuing system by means of the mean field theory, analyzing an empirical measure process through a nonlinear birth-death process, computing the fixed point in terms of a segment-structured birth-death process, and discussing the steady-state probability of the problem stations. Therefore, we provide a promising research direction in the study of stochastic models with respect to the large bike-sharing systems, and also hope this method can be applied to analyzing more general large bike-sharing systems.