对“乘客等车消耗的时间”问题的探究

1 引言 北京的地铁在各个时段总是不乏等车的乘客,而车次的数量相比于高峰时段汹涌的人流来说总是显得少之又少.那么,乘客等车消耗的时间又是多少呢?地铁车次开来的频率是否能在满足总体运输量的前提下,尽量不让任何一个乘客等车太久呢?这些问题的答案或许能让人们了解地铁车次频率配置得是否合适.对于车次频率配置问题的研究应包括对人流总体运输量需求的分析计算、对乘客等车时间的人性考虑,以及地铁公司经济性的考虑等诸多方面因素.笔者研究了如何用数学工具对地铁六号线乘客等车时间进行统计计算,试图为地铁车次频率的安排提供一个科学的计算工具.     

电梯决策问题的占线算法分析

结合现实生活中电梯的运营状况,从占线算法角度分析并解决了电梯运行中碰到的两个问题:乘客如何选择乘坐电梯的策略以及多少楼层以上应该开放电梯.通过对问题的描述,建立了求解模型并提出一种竞争策略;运用占线算法得到该策略的竞争比,并将此策略作为等待电梯的较优策略;通过对竞争策略的分析,并利用实地考察得到的数据,得出楼层达到4层及以上时才应该开放电梯的结论,并以此为基础对电梯运营者提出相关建议.     

基于实时公交信息的乘客乘车决策研究

实时交通信息的发布使乘客出行更具灵活性.调查乘客对实时公交系统的应用情况及功能需求,并提取乘客乘车决策规则.考虑乘客决策的"有限理性"特征构建决策模型:将乘车舒适性因素转换为时间成本,运用云模型建立定量时间到定性概念的映射;依据出行参考点确定出行方案的因素权重,建立期望效用函数;构建不同的出行场景,运用决策模型进行出行方案排序.结果表明:该模型能够更大限度地克服乘客理性限制对决策的影响,对多线路多因素方案下的乘客乘车行为做出决策,决策结果符合乘客决策规则,有助于为公交资源的规划与管理提供指导依据.     

农夫过河问题新解

以一种新视角讨论了趣味逻辑题"农夫过河问题",通过引入位置状态向量与运送过程向量,建立了一个向量方程,它对应于一个线性方程组,其解是唯一确定的.考虑到运送过程的顺序,这个唯一解对应于两种安全过河运送方案.最后,用线性代数建模方法重新表述趣味问题"嫉妒的丈夫"及其矩阵表示.     

高层电梯系统运行方案的建模与求解

随着社会的发展,运用垂直交通系统的高层建筑和智能化建筑不断出现。而有效的电梯交通配置,是垂直交通系统高效运行的基本保证。本文针对高层商务建筑中的电梯运行管理方案设计问题,分析了影响电梯耗能和用户满意度的主要因素。分别建立了电梯数目已知和电梯数目未知情况下的电梯调度优化模型,并设计相应动态规划算法和遗传算法。结合算例,求解算例中的电梯优化调度方案,以验证模型的合理性。最后根据我们建立的电梯调度模型,借助VC++作出可视化的电梯调度示意界面,将本文的研究结果用于实际的电梯调度中。     

基于APC和GPS数据的青奥会期间南京公共交通的调度与优化

为了得到青奥会期间南京市合理有效的公交调度方案,本文针对青奥会场馆、运动员村、旅游点等附近的南京公共交通线路,建立模型与算法.首先,通过APC数据与GPS数据的匹配,对客流数据进行站点匹配预处理,根据已有客流量数据,训练小波神经网络,从而对客流分布情况进行预测,然后基于客流预测结果,采用有序聚类法,实现客流高低峰时段的合理划分.其次,详细分析调度问题的关键所在,以时段总发车次数和乘客等待时间两个因素作为目标函数,将时段最大、最小发车间隔和满载率等作为约束条件,提出基于APC和GPS的公交车辆辅助调度模型,通过遗传算法对模型进行求解,得出不同时段的发车间隔和配车次数,并对模型的性能进行评估.以南京市D7路公交运营线路的实际客流数据为例,采用MATLAB软件进行仿真实验,得出优化结果.结果表明所建模型是合理的,从而为调度时刻表的生成提供了科学的依据.     

考虑繁忙率的多时段救护车优化布局研究

救护车布局对院前急救服务中需求的响应具有决定性作用。本文重点研究了考虑繁忙率的多时段救护车优化布局问题,在传统双覆盖模型基础上引入救护车繁忙率因素,提出改进后的双覆盖模型。首先计算考虑繁忙率的期望覆盖需求量,进而结合实际,将一天以早晚高峰划分为5个时段,探究不同时段下繁忙率差异带来的不同布局方案。以上海市松江区2014年数据为例,应用改进后的模型进行了系统深入的实证研究,并绘制繁忙率对需求覆盖率的影响曲线。结果表明,本文提出的布局方案比实际方案得到的期望覆盖需求量提高了3.19%,比传统双覆盖模型得到的期望覆盖需求量提高了0.54%,证明了改进后模型的有效性;需求覆盖率曲线随繁忙率增加而下降,与实际意义相符。该方法能够直观简洁地得出救护车布局方案,利于院前急救服务水平的提升,为社会安全提供有力保障。     

考虑乘客分流的异质车型通勤定制公交网络优化

定制公交作为城市需求响应交通的重要组成部分,其线网规划的优劣直接影响乘客满意度和系统运营成本.针对一类新的考虑乘客分流和异质车型的早晚高峰时期通勤定制公交网络规划向题,以最小化乘客旅行成本和公交系统运营成本为目标,同时优化异质车队路线、车型选择、行车时刻及乘客分配,构建了一个混合整数非线性规划模型.为有效求解该模型,提出了一种融合问题特征的改进自适应大邻域搜索算法,设计了基于问题特征的乘客分流破坏算子,以提升算法寻优能力.最后,大量算例结果验证了模型的正确性和算法的有效性.实验结果表明:求解小规模算例时,改进自适应大邻域搜索算法能在12秒以内获得距离最优解平均差距为0.24%的满意解;求解大规模算例时,与文献中大邻域搜索算法和遗传算法相比,所提出算法能获得更高质量解,平均成本节约分别为1.20%和2.27%;此外,与未考虑乘客分流和同质车型情形相比,考虑乘客分流和异质车型,得到的方案成本降低11.46%,提高了资源利用率.     

基于近邻传播聚类的地铁运营时段划分

地铁在每天不同时段客流量差异较大,运营时段的科学划分,是低峰与高峰列车运行计划合理交替的前提。目前地铁运营时段划分主要依据人工经验,主观性强且难以保证精度。以10min为时间间隔,把全天运营时间6∶00～23∶00分为102个时间点样本,将地铁沿线各车站每个时间点的进站客流量作为样本描述变量。采用近邻传播聚类算法将各时间点归并为不同类别,并引入CH、Hart以及IGP等聚类有效性评估指标对聚类结果加以检验以确定最优类别数,从而得到运营时段的最优划分方案和最佳时段分割点。天津地铁二号线实例研究表明,基于近邻传播聚类算法得到的运营时段划分结果更能体现实际客流需求波动特性,在此基础上优化行车计划后,旅客等待时间明显下降。     

公交车优化调度中的几个问题的研究

本文将 2 0 0 1 CMCM B题公交车调度的最优化问题分成两个相对独立的问题来讨论 ,由所要运送的乘客数来决定公交公司的最小车辆数 ,由乘客到达来决定发车时刻表 .我们求出了最小车辆数和一个可行的最优时刻表 .     

Performance analysis of an elevator system during up-peak

We model and analyze an elevator system during up-peak. We study the round-trip time, whose distribution depends strongly on the number of passengers waiting at the lobby, as well as the number of stops and the highest reversal floor. The distribution functions of the passenger queue length in the lobby, the round-trip time, the waiting time, the ride time and the journey time are derived.     

Two elevators serving up-traffic

A model is described for the motion of two elevators serving traffic only from a single lobby floor to multiple higher floors. Over a certain range of passenger arrival rates, the average round trip time of an elevator can be approximated by a linear function of the number of passengers carried which, in turn, is proportional to the time since the last elevator departure from the lobby (the headway). A pair of deterministic equations for the means of two state variables describes the approximate evolution of the system behavior. These equations lead to a very strange chaotic type of motion in the two-dimensional state space. For moderately light traffic the two elevators tend to travel close together, but for heavy traffic the headways tend to be nearly uniformly distributed over the mean round trip time of a single elevator.     

Dynamic optimization of the operation of single-car elevator systems with destination hall call registration: Part I. Formulation and simulations

The purpose of this two-part study is to investigate the operation problem of single-car elevator systems with destination hall call registration. Destination hall call registration is such a system in which passengers register their destination floors at elevator halls before boarding the car, while in the ordinary systems passengers specify only the directions of their destination floors at elevator halls and register destination floors after boarding the car. In this part of the study, we formulate the operation problem as a dynamic optimization problem and demonstrate by computer simulations that dynamically optimized operation considerably improves the transportation capability compared to conventional selective collective operation. How to solve the dynamic optimization problem is given in the second part of this study.     

乘客到达时间不确定的机场动态拼车策略与算法研究

网约车拼车服务作为共享经济领域重要应用,已成为国内外研究热点。针对机场在线拼车平台运营中乘客等待时间过长和车辆行驶成本较高的突出问题,本文提出前瞻式动态拼车匹配策略。该策略将未来随机到达乘客信息纳入当前已到达乘客的拼车匹配决策中,建立了乘客匹配与车辆路径联合优化两阶段随机规划模型。为了在动态环境中实时产生高质量的匹配与路径规划方案,首先基于贝叶斯估计压缩乘客随机到达情景空间,建立了问题的确定性近似最优模型。为了快速求解模型,提出基于订单目的地和乘客期望到达时间相似度的匹配规则,并以此开发改进的差分进化算法。最后,基于某拼车平台真实订单数据,通过对比测试验证了前瞻式匹配策略和改进差分进化算法的有效性与计算效率。     

Optimal parking of idle elevators under myopic and state-dependent policies

In this paper we discuss the problem of optimally parking single and multiple idle elevators under light-traffic conditions. The problem is analyzed from the point of view of the elevator owner whose objective is to minimize the expected total cost of parking and dispatching the elevator (which includes the cost incurred for waiting passengers). We first consider the case of a single elevator and analyze a (commonly used but suboptimal) state-independent myopic policy that always positions the idle elevator at the same floor. Building on the results obtained for the myopic policy, we then show that the optimal non-myopic (state-dependent) policy calls for dispatching the idle elevator to the state-dependent median of a weight distribution. Next, we consider the more difficult case of two elevators and develop an expression for the expected dispatching distance function. We show that the objective function for the myopic policy is non-convex. The non-myopic policy is found to be dependent on the state of the two idle elevators. We compute the optimal state-dependent policy for two elevators using the results developed for the myopic policy. Next, we examine the case of multiple elevators and provide a general recursive formula to find the expected dispatching distance functions. Finally, we generalize the previous models by incorporating a fixed cost for parking the idle elevators that results in a two-sided optimal policy with different regions. Every policy that we introduce and analyze is illustrated by an example. The paper concludes with a short summary and suggestions for future research.     

A model for setting services on auxiliary bus lines under congestion

In this paper, a mathematical programming model and a heuristically derived solution is described to assist with the efficient planning of services for a set of auxiliary bus lines (a bus-bridging system) during disruptions of metro and rapid transit lines. The model can be considered static and takes into account the average flows of passengers over a given period of time (i.e., the peak morning traffic hour). Auxiliary bus services must accommodate very high demand levels, and the model presented is able to take into account the operation of a bus-bridging system under congested conditions. A general analysis of the congestion in public transportation lines is presented, and the results are applied to the design of a bus-bridging system. A nonlinear integer mathematical programming model and a suitable approximation of this model are then formulated. This approximated model can be solved by a heuristic procedure that has been shown to be computationally viable. The output of the model is as follows: (a) the number of bus units to assign to each of the candidate lines of the bus-bridging system; (b) the routes to be followed by users passengers of each of the origin–destination pairs; (c) the operational conditions of the components of the bus-bridging system, including the passenger load of each of the line segments, the degree of saturation of the bus stops relative to their bus input flows, the bus service times at bus stops and the passenger waiting times at bus stops. The model is able to take into account bounds with regard to the maximum number of passengers waiting at bus stops and the space available at bus stops for the queueing of bus units. This paper demonstrates the applicability of the model with two realistic test cases: a railway corridor in Madrid and a metro line in Barcelona.     

Passenger flow control strategies for urban rail transit networks

Urban rail traffic congestion is becoming increasingly serious due to the large traffic demands in modern cities. In order to ensure the safety and quality of station services in peak hours, it's necessary to adopt some reasonable and effective passenger flow control strategies. In this study, through considering the time-dependent passenger demands, a passenger flow control model based on the network-level system is explicitly developed. The passenger successive motion process is discretized by the modeling method. Systematically considering the coordinated relationship between traffic demands and strict capacity constraints (including station passing capacity, platform load capacity and train transport capacity), we establish a mixed integer linear programming model to minimize the total passenger waiting time (including passengers outside stations and on the platforms). The optimization software Cplex is adopted to solve the developed model, and a real network of Beijing urban railway is calibrated to verify the effectiveness of the suggested model. As a result, the proposed flow control strategies can provide detailed information about control stations, control durations and control intensities, and can effectively reduce the total waiting time and relieve the number of stranded passengers in the urban rail transit network.     

Virtual queuing at airport security lanes

Airports continuously seek opportunities to reduce the security costs without negatively affecting passenger satisfaction. In this paper, we investigate the possibilities of implementing virtual queuing at airport security lanes, by offering some passengers a time window during which they can arrive to enter a priority queue. This process could result in a smoother distribution of arriving passengers, such that the required security personnel (costs) can be decreased. While this concept has received attention in a number of settings, such as theme parks, virtual queuing at airports bears an additional level of complexity related to the flight schedules, i.e., passengers can only be transferred forward in time to a limited extent, which we denote by the transfer time limit. We conducted a major simulation study in collaboration with a large international airport in Western Europe to determine the potential impact of virtual queuing and find that nearly one million Euro can be saved on security personnel cost without negatively impacting the passenger waiting time.     

Performance analysis of polling systems with retrials and glue periods

We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.     

The shuttle dispatch problem with compound Poisson arrivals: Controls at two terminals

We consider the control of an infinite capacity shuttle which transports passengers between two terminals. The passengers arrive at each terminal according to a compound Poisson process and the travel time from one terminal to the other is a random variable following an arbitrary distribution. The following control limit policy is considered: dispatch the shuttle at terminali, at the instant that the total number of passengers waiting at terminali reaches or exceeds a predetermined control limitm _i . The objective of this paper is to obtain the mean waiting time of an arbitrary passenger at each terminal for given control valuesm ₁ andm ₂. We also discuss a search procedure to obtain the optimal control values which minimize the total expected cost per unit time under a linear cost structure.