大型自行车共享系统的平均场极限理论与排队模型研究

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。     

A multi-periodic optimization formulation for bike planning and bike utilization

The number of policy initiatives to promote the use of bike, or the combined use of bicycle and public transport for one trip, has grown considerably over the past decade as part of the search for more sustainable transport solutions. This paper presents an optimization formulation to design a bike-sharing system for travel inside small communities, or as a means to extend public transport for access and egress trips. The mathematical model attempts to optimize a bike-sharing system by determining the minimum required bike fleet size that minimizes simultaneously unmet demand, unutilized bikes, and the need to transport empty bikes between rental stations to meet demand. The proposed approach is applied to an example problem and is shown to be successful, ultimately providing a new managerial tool for planning and analyzing bike utilization more effectively.     

共享单车调度优化问题研究

针对共享单车站点经常出现的供需不平衡问题,提出人工调度策略,以提高单车利用率和用户满足率.首先将一天划分为几个用车高峰时段,根据每个站点的单车使用历史数据,计算各站点在每个时段的需求量区间;在区域内单车总投放量不变的前提下,基于每个时段初期各个站点存放的单车数量,确定单车调出站点和单车调入站点,进一步以站点之间的单车调度数量为决策变量,建立共享单车调度问题的整数规划模型,使区域内各个单车站点的供需量基本达到平衡,并且总调度成本最小.利用北京市海淀区共享单车数据进行模拟计算,对比分析了调度优化前后的共享单车利用率和用户满足率.结果显示,调度优化后,单车利用率平均提高7.78%,用户满足率平均提高13.09%;综合考虑企业调度成本和收入情况可以发现,通过调度优化,企业的平均利润增长率为7.53%.本文的研究结果可以帮助共享单车企业提升管理水平,增加利润.     

Some recent results in infinite divisibility

In this paper, a survey is given of some recent developments in infinite divisibility. There are three main topics: (i) the occurrence of infinitely divisible distributions in applied stochastic processes such as queueing processes and birth-death processes, (ii) the construction of infinitely divisible distributions, mainly by mixing, and (iii) conditions for infinite divisibility in terms of distribution functions and densities.     

Single server with linear state-dependent mean rate

A birth-death queueing system with asingle server, first-come first-served discipline, Poisson arrivals and mean service rate which depends linearly on the number of customers in the system, is considered. Explicit expressions are derived for the equilibrium densities of the sojourn and waiting times. Simple approximations to the densities, including the first order correction terms, are obtained in a heavy-traffic situation.     

Testing for increasing convex order in several populations

Increasing convex order is one of important stochastic orderings. It is very often used in queueing theory, reliability, operations research and economics. This paper is devoted to studying the likelihood ratio test for increasing convex order in several populations against an unrestricted alternative. We derive the null asympotic distribution of the likelihood ratio test statistic, which is precisely the chi-bar-squared distribution. The methodology for computing critical values for the test is also discussed. The test is applied to an example involving data for survival time for carcinoma of the oropharynx.     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

Correlated Brownian Motions as an Approximation to Deterministic Mean-Field Dynamics

We analyze the transition from deterministic mean-field dynamics of several large particles and infinitely many small particles to a stochastic motion of the large particles. In this transition the small particles become the random medium for the large particles, and the motion of the large particles becomes stochastic. Under the assumption that the empirical velocity distribution of the small particles is governed by a probability density ψ, the mean-field force can be represented as the negative gradient of a scaled version of ψ. The stochastic motion is described by a system of stochastic ordinary differential equations driven by Gaussian space-time white noise and the mean-field force as a shift-invariant integral kernel. The scaling preserves a small parameter in the transition, the so-called correlation length. In this set-up, the separate motion of each particle is a classical Brownian motion (Wiener process), but the joint motion is correlated through the mean-field force and the noise. Therefore, it is not Gaussian. The motion of two particles is analyzed in detail and a diffusion equation is deduced for the difference in the positions of the two particles. The diffusion coefficient in the latter equation is spatially dependent, which allows us to determine regions of attraction and repulsion of the two particles by computing the probability fluxes. The result is consistent with observations in the applied sciences, namely that Brownian particles get attracted to one another if the distance between them is smaller than a critical small parameter. In our case, this parameter is shown to be proportional to the aforementioned correlation length. __________ Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 6, pp. 757–769, June, 2005.     

成批到达排队系统的随机比较

本文研究成批到达排队系统中队长过程的随机比较问题．利用随机比较方法我们对成批到达指数服务的多服务台排队系统进行分析,得到了该排队系统中队长过程的随机比较以及队长函数关于时间的凹性和凸性．同时我们也给出了成批到达一般服务的单服务台排队系统队长过程、稳态队长的随机比较以及队长函数关于时间的凹性和凸性．     

A stability criterion via fluid limits and its application to a polling system

We introduce a generalized criterion for the stability of Markovian queueing systems in terms of stochastic fluid limits. We consider an example in which this criterion may be applied: a polling system with two stations and two heterogeneous servers. This revised version was published online in June 2006 with corrections to the Cover Date.