Object modeling and path computation for multimodal travel systems

This paper describes a multimodal travel system (MTS) designed to address the needs of a variety of demand-responsive transport. An origin–destination (O–D) trip in transportation network can be accomplished by using multiple modes. In urban network passengers may boarding buses or metros to go from one place to another, and modes as autobus or trains are used by passengers to travel between cities. The work focuses on the network object modeling and multimodal shortest path algorithm. A solution to the problem of long-run planning of transit on multimodal network has been implemented and tested. The work presents the general results found, and the proposed algorithm recognizes the set of constraints related to the time schedule and the sequence of used modes in a O–D trip. The aim is to provide a tool for detecting the facilities of using different travel modes through a transportation network. Routings may include distinct combination of rail, and route. Geographic Information Systems (GIS) were invaluable in the cost-effective construction and maintenance of this work and the subsequent validation of mode sequences and paths selections. Attention is devoted to the multimodal path operator as well as to the use of GIS-transit planning.     

多方式弹性需求下公交定价双层规划模型

为描述多方式城市交通网络下公交定价与出行选择行为的相互作用与影响,将出行方式选择与路径选择涵盖于同一网络,建立了上层模型分别以企业利润最大化、乘客出行成本最小化和社会福利最大化为目标函数,下层模型为多方式弹性需求随机用户配流模型的公交定价双层规划模型。运用改进遗传算法对模型整体进行求解,下层模型采用综合对角化算法和MSA算法的组合求解算法。最后,设计了一个算例以说明模型应用。结果表明:运用双层规划模型所确定的公交票价较传统静态票价可使政府、企业及出行者三方都获得更高收益,且上层模型以社会福利最大化为目标函数能代表社会群体中多数人利益,优化效果最为理想。     

网约车新政下平台和乘客的Stackelberg博弈模型及策略研究

近年来,滴滴和优步等网约车平台的出现给城市居民出行带来了新的选择,然而随着新政的实施以及垄断巨头的酝酿诞生,网约车平台是否会降补贴提车价成为消费者最为关心的问题。文章构建网约车平台和乘客之间的Stackelberg博弈模型,分析了网约车平台的补贴和抽成策略对乘客是否选择网约车出行的决策行为以及网约车市场均衡的影响。理论研究和仿真结果表明：网约车平台合理的补贴力度和抽成力度可以有效规避行政监管成本增加和乘客资源流失的风险,提高双方的收益,实现社会的帕累托最优。     

Adjustment boarding and alighting passengers on a bus transit line using qualitative information

Obtaining data to use in an urban public transport operation planning and analysis is problematic, particularly in urban bus transit lines. In an urban environment and for bus services, most ticketing methods can be used to record passengers getting on board but not getting off, and current methods are unable to make a proper adjustment of boardings and alightings based on the available data unless they do alighting counts. This paper presents a method whereby counts are made at fewer stops and qualitative information on alightings and/or vehicle loads between consecutive stops is used to make the boarding and alighting adjustment as a previous step to obtain the real origin and destination (O/D) of passengers allowing the O/D matrix calibration by using the loads between stops. Qualitative information can be obtained by the vehicle’s driver or an on board observer, avoiding the necessity of counting many stops in planning period. The method is applied to a real bus transit line in Malaga (Spain) and to a set of 50 different bus transit lines with number of stops ranging from 10 to 75. The results show that the proposed method reduces the adjustment errors with regard to traditional methods, such as Least Square Method, even in the situation where no qualitative information is used. When qualitative data is used on alightings and loadings, the reduction of the average error is over 50%.     

Exact algorithms for multi-criteria multi-modal shortest path with transfer delaying and arriving time-window in urban transit network

This paper investigates the solution algorithms for the multi-criteria multi-modal shortest path problem (M-SPP), which belongs to the set of problems known as NP-hard, in urban transit network (UTN). The related M-SPP is one of the important and practical problems in several fields such as urban transportation system and freight transportation. The UTN is composed of multiple modes (e.g., automobile, bus, subway, light rail, pedestrian and so on). To get their destination, the passengers can alternate between different modes. As a special demand, the time-window is usually associated with the M-SPP. Because of the service time-limit of modes, the available modes at a stop are varied with the time. So the optimal M-SPP with arriving time-window cannot be simply obtained by finding the optimal M-SPP firstly and then reversely deducing the leaving time-window of the origin according to the arriving time-window of destination. In this paper, the M-SPP with arriving time-window is firstly proposed. To solve the multi-criteria M-SPPs (MM-SPP) with transfer delaying, an improved exact label correcting algorithm (LCA) is designed and, to solve the proposed MM-SPPs with both of transfer delaying and arriving time-window, an exact reverse LCA is designed. Finally, some computing examples are given to test the effectiveness of the designed algorithms.     

Optimisation of timetable-based, stochastic transit assignment models based on MSA

Public transport assignment models have increased in complexity in order to describe passengers' route choices as detailed and correctly as possible. Important trends in the development are (1) timetable-based assignment, (2) inclusion of feeder modes, (3) use of stochastic components to describe differences in passengers' preferences within and between purposes and classes (random coefficients), as well as to describe non-explained variation within a utility theory framework, and (4) consideration of capacity problems at coach level, system level and terminal level. In the Copenhagen-Ringsted Model (CRM), such a large-scale transit assignment model was developed and estimated. The Stochastic User Equilibrium problem was solved by the Method of Successive Averages (MSA). However, the model suffered from very large calculation times. The paper focuses on how to optimise transit assignment models based on MSA combined with a generalised utility function. Comparable tests are carried out on a large-scale network. The conclusion is that there is potential of optimising MSA-based methods. Examples of different approaches for this is presented, tested and discussed in the paper.     

Determination of the number and locations of time points in transit schedule design — Case of a single run

An analytical model for the determination of the number and locations of time points as well as the amount of slack times in transit schedule design is developed. The model considers a bus route with a special passenger demand pattern in which all boarding passengers coordinate their arrivals at each stop in such a way that they never miss their intended bus, and therefore designing the schedule separately a single run at a time, becomes possible. The model employs the dynamic programming method to deal with the trade-offs among various cost components associated with the schedule quantitatively, and yet is flexible enough to incorporate the existing rules of thumb as well as transit operators' policies. Numerical examples that illustrate the applications of the model are given. The model, although not quite applicable to bus routes with general passenger demand patterns, is useful in the analysis of the contributing factors to the design of an economical, reliable, and operational transit schedule, and is likely to be adaptable for more realistic cases.     

Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues

Recently, it has been pointed out that transport models should reflect all significant traveler choice behavior. In particular, trip generation, trip distribution, modal split as well as route choice should be modeled in a consistent process based on the equilibrium between transport supply and travel demand. In this paper a general fixed-point approach that allows dealing with multi-user stochastic equilibrium assignment with variable demand is presented. The main focus was on investigating the effectiveness of internal and external approaches and of different algorithmic specifications based on the method of successive averages within the internal approach. The vector demand function was assumed non-separable, non-symmetric cost functions were adopted and implementation issues, such updating step and convergence criterion, were investigated. In particular the aim was threefold: (i) compare the internal and the external approaches; (ii) investigate the effectiveness of different algorithmic specifications to solve the variable demand equilibrium assignment problem through the internal approach; (iii) investigate the incidence of the number of the links with non-separable and/or asymmetrical cost functions. The proposed analyses were carried out with respect to two real-scale urban networks regarding medium-size urban contexts in Italy.     

中国城市公共交通行业技术效率实证研究

本文选取1999-2004年间中国城市公共交通行业的面板数据,在Cobb-Douglas函数的基础上运用随机边界法对我国城市公共交通行业的技术效率进行了考察,并从时间、地域、交通工具类型和客运规模方面,分析了该行业的效率差异及其产生原因,旨在为该行业的未来发展和管制改革提供决策依据。研究结果表明,我国城市公共交通行业技术效率情况为:近几年虽有小幅上升,但基数总体不高;东部地区技术效率偏高;客运量大和拥有轨道交通的省市的技术效率较高。     

弹性需求下城市公交网络服务的优化

对具有弹性需求的城市公交网络系统进行了票价结构与发车频率组合的优化。考虑到公交定价和发车频率会影响乘客需求以及乘客对路径的选择行为,将这一问题描述为一个双层规划问题,上层是寻求社会福利最大的优化问题;下层考虑了乘客的出行选择行为,为弹性需求下乘客在城市公交网络上流量分布的随机用户平衡分配模型。鉴于双层规划问题的非凸性,运用模拟退火算法对模型进行求解,并给出一个仿真算例说明提出的模型和算法的合理性。     

Markovian traffic equilibrium

We analyze an equilibrium model for traffic networks based on stochastic dynamic programming. In this model passengers move towards their destinations by a sequential process of arc selection based on a discrete choice model at every intermediate node in their trip. Route selection is the outcome of this sequential process while network flows correspond to the invariant measures of the underlying Markov chains. The approach may handle different discrete choice models at every node, including the possibility of mixing deterministic and stochastic distribution rules. It can also be used over a multi-modal network in order to model the simultaneous selection of mode and route, as well as to treat the case of elastic demands. We establish the existence of a unique equilibrium, which is characterized as the solution of an unconstrained strictly convex minimization problem of low dimension. We report some numerical experiences comparing the performance of the method of successive averages (MSA) and Newton’s method on one small and one large network, providing a formal convergence proof for MSA. Dedicated to Clovis Gonzaga on the occassion of his 60th birthday.     

寻路行为策略的进化博弈分析

针对我国交通枢纽站中乘客的寻路行为,建立了初访者群体之间以及初访者与熟悉者群体间的博弈模型及其复制动力学方程,并对复制动态做了分析和讨论,得出模型中博弈双方的进化稳定策略。研究结果表明枢纽站内初访者、初访者与熟悉者在有限理性基础上得到的进化稳定策略与标识布设的合理性有关,提出了改进标识布设以推进积极寻路行为发生的合理对策和建议。     

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.     

Stochastic optimization of an urban rail timetable under time‐dependent and uncertain demand

Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two‐stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.     

Transformation of urban public transport financing and its effect on operators’ efficiency: evidence from the Czech Republic

The purpose of this study is to analyze changes in the efficiency of urban public transport in the Czech Republic. Network data envelopment analysis and cluster analysis were applied to data from 19 urban public transport systems during 2004–2016. The series structure of the network was considered, including production and consumption stages with three external inputs (employees, rolling stock, and energy), one final output (passengers), and two intermediate products (vehicle-kilometres and seat-kilometres). The relationship between changes in efficiency and the method of financing for the operation of transport services was explored through standard statistical methods. One of the main findings was that the efficiency of smaller transport systems with complicated access to sources of funding were systematically less efficient, particularly in the consumption stage. These trends were even more significant after the reorganization of urban public transport funding in 2010.     

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.     

Simultaneous estimation of the origin–destination matrices and the parameters of a nested logit model in a combined network equilibrium model

This paper deals with the inverse problem of a type of traffic equilibrium models with combined modes. This problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model. The inputs for the model are an origin–destination (O–D) trip matrix for the various alternatives that have been considered, and a set of parameters for a nested logit model used as a demand model.     

A heuristic approach based on shortest path problems for integrated flight,aircraft, and passenger rescheduling under disruptions

In this paper, we present a heuristic method to solve an airline disruption management problem arising from the ROADEF 2009 challenge. Disruptions perturb an initial flight plan such that some passengers cannot start or conclude their planned trip. The developed algorithm considers passengers and aircraft with the same priority by reassigning passengers and by creating a limited number of flights. The aim is to minimize the cost induced for the airline by the recovery from the disruptions. The algorithm is tested on real-life-based data, as well as on large-scale instances and ranks among the best methods proposed to the challenge in terms of quality, while being efficient in terms of computation time.     

Spectral analysis for performance evaluation in a bus network

This paper deals with the performance evaluation of a public transportation system in terms of waiting times at various connection points. The behaviour of a bus network is studied in the framework of Discrete Event Systems (DES). Two possible operating modes of buses can be observed at each connection stop: periodic and non-periodic mode. Two complementary tools, Petri nets and (max, +) algebra, are used to describe the network by a non-stationary linear state model. This one can be solved after solving the structural conflicts associated to the graphical representation. From the characteristic matrix of the mathematical model, we determine eigenvalues and eigenvectors that we use to evaluate the connection times of passengers. This work is finally illustrated with a numerical example.     

校车站点及线路的优化设计

以高校新校区教师校车站点及线路安排为对象,首先针对乘车站点建立了双目标非线性规划模型,其中目标函数包括乘客到达站点的距离偏差最小与所有乘客到达站点的总的距离最小两个方面;站点确定后针对车辆数最少、车辆行驶的总距离最短、各辆车的运行距离均衡及各辆车的负荷均衡这4个目标建立针对线路优化的多目标非线性规划模型,并给出了解决这类问题的启发式优化算法.与目前国内外研究相比较,该模型与算法更实际,更具体的给出了问题的解答.