Comprehensive optimization of urban rail transit timetable by minimizing total travel times under time-dependent passenger demand and congested conditions

The comprehensive optimization of the timetables of urban rail transit systems under more realistic conditions is essential for their practical operation. Currently, most time-dependent timetabling models do not adequately consider train capacity and variable operation parameters. To bridge this gap, this study mainly investigates the timetable design problem of the urban rail transit system so as to adapt to time-dependent passenger demand under congested conditions by considering the variable number of trains, train running time, and train dwell time. Two nonlinear non-convex programming models are formulated to design timetables with the objective of minimizing the total passenger travel time (TTT) under the constraints of train operations, and passenger boarding and alighting processes. The difference between the two models is that one is a train-capacity unconstrained model and the other is a train-capacity constrained model. The proposed models are examined through real-world cases solved by the adaptive large neighborhood search algorithm. The results show that the first model can minimize passenger TTT under dynamic passenger demand, whereas the second can comprehensively optimize passenger TTT and meantime keep the train load factor within a reasonable level. Accordingly, it is concluded that the proposed models are more realistic.     

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.     

考虑路网可靠性和空间公平性的次优拥挤收费模型

根据随机路网环境下出行者规避风险的路径选择行为,提出了一种考虑路网可靠性和空间公平性的次优拥挤收费双层规划模型。其中,上层模型以具有空间公平性约束条件下最大化路网的社会福利为目标,下层模型是实施拥挤收费条件下考虑行程时间可靠性的弹性需求用户平衡模型。鉴于双层规划模型的复杂性,设计了基于遗传算法和FrankWolfe算法的组合式算法来求解提出的模型。算例结果表明:考虑行程时间可靠性的次优拥挤收费会产生不同于传统次优拥挤收费的平衡流量分布模式,表明出行者的路径选择行为对拥挤收费结果会产生直接影响;此外,算例结果还说明遗传算法对参数设置具有很强的鲁棒性。     

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。     

城市公交查询系统的设计与实现

针对含有“公汽、地铁、步行”的复杂公交网络环境,首先对公交问题所提供的数据进行分析,并优化数据的存储结构;其次充分考虑到公交网络客流分配的主要因素一换乘次数、票价、时间,提出了公交网中这三个目标的加权平均最优路径模型及其算法;最后对模型的算法用Matlab软件实现.通过测试,结果显示本系统能快速响应出满足乘客不同需求的公交出行路径。     

Integrating link-based discrete credit charging scheme into discrete network design problem

In this paper, we present an optimization model for integrating link-based discrete credit charging scheme into the discrete network design problem, to improve the transport performance from the perspectives of both transport network planning and travel demand management. The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users. The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem. The network user at the lower level tries to minimize his/her own generalized travel cost (including both the travel time and the value of the credit charged for using the link) by choosing his/her route. While the transport authority at the upper level tries to find the optimal number of lanes and credit charging level with their locations to minimize the total system travel time (or maximize the transportation system performance). A genetic algorithm is used to solve the proposed mixed-integer nonlinear bilevel programming problem. Numerical experiments show the efficiency of the proposed model for traffic congestion mitigation, reveal that interaction effects across the tradable credit scheme and the discrete network design problem which amplify their individual effects. Moreover, the integrated model can achieve better performance than the sequential decision problems.     

Optimization of transit route network,vehicle headways and timetables for large-scale transit networks

This paper presents a metaheuristic method for optimizing transit networks, including route network design, vehicle headway, and timetable assignment. Given information on transit demand, the street network of the transit service area, and total fleet size, the goal is to identify a transit network that minimizes a passenger cost function. Transit network optimization is a complex combinatorial problem due to huge search spaces of route network, vehicle headways, and timetables. The methodology described in this paper includes a representation of transit network variable search spaces (route network, headway, and timetable); a user cost function based on passenger random arrival times, route network, vehicle headways, and timetables; and a metaheuristic search scheme that combines simulated annealing, tabu, and greedy search methods. This methodology has been tested with problems reported in the existing literature, and applied to a large-scale realistic network optimization problem. The results show that the methodology is capable of producing improved solutions to large-scale transit network design problems in reasonable amounts of time and computing resources.     

Transit passenger origin-destination estimation in congested transit networks with elastic line frequencies

This paper deals with the transit passenger origin-destination (O-D) estimation problem by using updated passenger counts in congested transit networks and outdated prior O-D matrix. A bilevel programming approach is extended for the transit passenger O-D updating problem where the upper-level problem seeks to minimize the sum of error measurements in passenger counts and O-D matrices, while the lower level is the stochastic user equilibrium assignment problem for congested transit networks. The transit assignment framework is based on a frequency-adaptive transit network model in this paper, which can help determine transit line frequencies and the network flow pattern simultaneously in congested transit networks. A heuristic solution algorithm is adapted for solving the transit passenger O-D estimation problem. Finally, a numerical example is used to illustrate the applications of the proposed model and solution algorithm. The work described in this paper was mainly supported by two research grants from the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU 5143/03E and PolyU 5040/02E).     

Estimation of Transit Origin–Destination Matrices from Passenger Counts Using a Frequency-Based Approach

This paper investigates the transit passenger origin–destination (O–D) estimation problem in congested transit networks where updated passenger counts and outdated O–D matrices are available. The bi-level programming approach is used for the transit passenger O–D estimation problem. The upper level minimizes the sum of error measurements in passenger counts and O–D matrices, and the lower level is a new frequency-based stochastic user equilibrium (SUE) assignment model that can determine simultaneously the passenger overload delays and passenger route choices in congested transit network together with the resultant transit line frequencies. The lower-level problem can be formulated as either a logit-type or probit-type SUE transit assignment problem. A heuristic solution algorithm is developed for solving the proposed bi-level programming model which is applicable to congested transit networks. Finally, a case study on a simplified transit network connecting Kowloon urban area and the Hong Kong International Airport is provided to illustrate the applications of the proposed bi-level programming model and solution algorithm. This revised version was published online in July 2006 with corrections to the Cover Date.     

A simulation-based assessment of route guidance benefits under variable network congestion conditions

The purpose of this study is to establish a quantitative relationship between network congestion and travel-time reduction benefits of a real-time route guidance user service. The approach of the study is to employ the INTEGRATION traffic simulation model and a 2,000 link network based on the Detroit, Michigan roadway system in a series of experiments. While holding the capacity of the roadway fixed, the value of route guidance is evaluated over a range of increasing demand levels. Network demand patterns and trip characteristics are comparable to current national averages. Measures of congestion such as average system commute speed either match or exceed current national averages. Congestion metrics measured for the lightest demand scenario match most current empirical national average data, while the heaviest demand scenario appears roughly comparable with 1994 Tokyo conditions.Results from this study indicate that route-guided vehicles benefit regardless of level of congestion, however, the amount of trip time savings achieved is highly dependent on network congestion conditions. Average benefits for route guided vehicles over unguided vehicles in the A.M. peak period range between 8–26% depending on overall traffic volume.The results indicate a two-part linear relationship between route guidance benefit and network congestion. As congestion increases in the network, benefits of route guidance increase until average network speed drops below 20mph. Beyond that point, benefits decline (but remain positive). This 20mph threshold in our network is the point where the dynamically growing and shifting mass of queued vehicles around bottlenecks begins to impede access to alternative routes for guided vehicles network-wide.In a related experiment, route guided vehicles that receive reliable data on network conditions (including incidents or demand variation) gain 3–9% travel time savings over unguided vehicles that follow optimal routes based on average time-variant network congestion conditions. Route guided vehicles may exploit information about unexpected delays in the network related to incidents as well as variability in daily traffic patterns. This experiment was conducted to isolate the value of route guidance with respect to experienced commuter traffic, rather than an aggregated model of driver behavior including both familiar and unfamiliar drivers.The preliminary results of this study have implications for ITS benefit assessment. First, the benefits of route guidance are directly related to the level of recurrent congestion in a network. Thus, a near-term poor market for route guidance may evolve over time into a good market for these services. Likewise, a good market for a route guidance user service may deteriorate if overall network congestion reaches very high levels. Second, a route guidance user service provides benefits compared to both a model of aggregated unguided traveler behavior and a model of experienced commuter behavior, regardless of congestion levels. Third, route guided vehicles are demonstrated to gain benefit by avoiding the worst congestion in the network. This minimization in day-to-day variability in commute time may be the most significant benefit of the route guidance system for the familiar driver.     

机场新增卫星厅对登机口影响的评估方法

为了解决航站楼客流量饱和的问题,采用一种增加卫星厅的方法,实现了旅客分流.基于单目标整数线性规划和多目标优化的方法,分别构建了登机口优化分配网络模型和多目标优化模型.利用登机口优化分配网络算法筛选出所使用的共同登机口,建立了目标函数并列出约束条件,采用目标约束法对建立的模型进行求解.在此基础上,根据目标建模的思想,建立了可供中转旅客总体流程时间最短且使用登机口数量最小的航班-登机口分配模型.利用MATLAB计算可知,利用42个登机口即可实现303架航班的正常运转.     

双模式网络停车限制交通需求管理模型与方法研究

在轨道网和公路网并存的双模式交通网络, 合理设计出行终点的停车容量可优化汽车出行需求, 改善路网交通环境。本文通过分析私家车与城市轨道两种交通模式的出行需求, 并考虑私家车模式的终点停车收费服务, 建立了一种带路段环境容量和终点停车需求容量共同约束的交通需求管理模型。模型中路网使用者的出行模式采用二元Logit模型来计算, 而私家车的路线选择行为服从Logit随机用户均衡, 因此该模型是一个带不动点约束的数学规划问题。针对模型求解困难, 文中采用灵敏度分析来获取各路段流量和需求量关于终点容量波动的梯度信息, 进而设计了一种新的灵敏度分析求解算法.最后通过数值仿真实验, 验证了算法的有效性, 同时分析了不同停车收费参数对模型各指标变化趋势的影响。     

Traffic assignment model with fuzzy level of travel demand: An efficient algorithm based on quasi-Logit formulas

The place of fuzzy concepts in traffic assignment (TA) models has been studied in recent literature. Keeping fuzzy level of travel demand in mind, we propose a new TA model in which the travel costs of links are depended on their congestion. From the results of such fuzzy TA model, network planners are able to estimate the number of travelers on network links. By using zero–one variables, the proposed model is transformed into a crisp mixed-integer problem with respect to path-flow variables. In order to produce the Logit flows from this problem, Damberg et al. algorithm is modified. Then, the level of certainty is maximized and perceived travel delays are minimized. For a fixed certainty degree, the obtained solution, which is named the fuzzy equilibrium flow, satisfies a quasi-Logit formula similar to ordinary expression of the Logit route choice model. Eventually, we examine the quality of different path enumeration techniques in the proposed model.     

Integration of timetable planning and rolling stock in rapid transit networks

The aim of this paper is to propose an integrated planning model to adequate the offered capacity and system frequencies to attend the increased passenger demand and traffic congestion around urban and suburban areas. The railway capacity is studied in line planning, however, these planned frequencies were obtained without accounting for rolling stock flows through the rapid transit network. In order to provide the problem more freedom to decide rolling stock flows and therefore better adjusting these flows to passenger demand, a new integrated model is proposed, where frequencies are readjusted. Then, the railway timetable and rolling stock assignment are also calculated, where shunting operations are taken into account. These operations may sometimes malfunction, causing localized incidents that could propagate throughout the entire network due to cascading effects. This type of operations will be penalized with the goal of selectively avoiding them and ameliorating their high malfunction probabilities. Swapping operations will also be ensured using homogeneous rolling stock material and ensuring parkings in strategic stations. We illustrate our model using computational experiments drawn from RENFE (the main Spanish operator of suburban passenger trains) in Madrid, Spain. The results show that through this integrated approach a greater robustness degree can be obtained.     

基于鲁棒优化的随机时变网络最优路径研究

交通事故、恶劣天气以及偶发的交通拥堵等都会导致道路交通网络中行程时间的不确定性,极大地影响了道路交通系统的可靠性,同时给日常生活中出行计划的制定以及出行路径的选择带来了不便。因此,本次研究将综合考虑道路交通网络中由于交通流量的全天变化所导致的路径行程时间的时变特征,以及由于事故、天气等不确定因素所导致的路径行程时间的随机特征,并以此作为路网环境的假设条件,对出行路径选择问题进行研究。具体地,首先建立行程时间的动态随机变量,并在此基础上模拟构建了随机时变网络。随后,定义了该网络环境下路径选择过程中所考虑的成本费用,并通过鲁棒优化的方法,将成本费用鲁棒性最强的路径视为最优路径。随后,在随机一致性条件下,通过数学推导证明了该模型可以简化为解决一个确定性时变网络中的最短路径问题。最终,具有多项式时间计算复杂度的改进Dijkstra算法被应用到模型的求解中,并通过小型算例验证模型及算法的有效性。结果表明,本研究中所提出的方法可以被高效率算法所求解,并且不依赖于先验行程时间概率分布的获取,因此对后续的大规模实际城市道路网络应用提供了良好的理论基础。此外,由于具有行程时间随机时变特征的交通网络更接近实际道路情况,因此本次研究的研究成果具有较高的实际意义和应用价值。     

考虑运营稳定性的内支线班轮航线网络规划模型

货主选择承运航线的影响因素,既包括挂靠港口的计划到港时间与单箱运价,还包括反映班轮运营稳定性的甩箱率与准班率。对此,文章将挂靠港口的航行与在港时间不确定引入研究,并对挂靠港口间的不确定性建立联系,基于航次仿真来计算各挂靠港的到港时间分布、船舶的航次最大载箱量分布。以班轮航线的甩箱率与准班率限制、内支线最大船型与最长往返时间为约束,在优化内支线航线网络结构的同时,计算航线适配船型、班期密度及挂靠港计划到港时间。针对所构建的带不确定参数的NP难问题,文章设计了基于模拟仿真的智能优化算法,通过方案仿真技术来处理输入模型的众分布函数,借助智能优化原理从大范围解空间内寻找满意方案。文末对船舶航次仿真与网络规划模型的有效性进行了验证,算例分析表明:内支线班轮航线网络的货主选择比例达64%,且不论货主更偏好运输时间或价格,航线方案皆能贴近货主偏好。     

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.     

基于遗传算法的公交智能调度与优化——以南岳衡山景区为例

南岳衡山(以下简称南岳)以“外秀于林,内秀于文”驰名中外,作为风景名胜区近几年游客人数不断攀升。本文利用遗传算法对景区内公交线路的调度模型进行求解。首先,根据景区现有的公共交通资源和旅客的出行规律,构建了以旅游公交营运成本、游客等待成本和游客流失成本三方面优化目标的模型;然后,使用线性加权方法实现对旅客与营运公司双方利益兼顾,进一步完善模型;最后,利用Matlab对实地调研数据的车辆调度方案求解。表明该模型改善了南岳景区旅游交通,满足游客的合理需求,提升了旅游公司经营策略,真正成为“寿岳独秀”的知名品牌。     

基于双层规划的高速公路收费费率优化模型

在全国联网收费的背景下,从动态收费的角度考虑,建立了双层规划模型,上层规划中将路网管理者作为领导者,以高速公路收费效益最大化为目标函数,同时考虑道路运营管理方的合理收益和养护成本支出情况,下层规划则以用户出行效用最大化为目标,充分考虑了道路使用者的道路选择差异性及道路拥堵对交通分布的影响,建立随机用户均衡模型.最后结合某地区AB地高速公路实际情况进行分析,采用了遗传模拟退火算法验证了模型的实用性,并与其他的算法对比,验证了算法的有效性。研究表明:优化模型可以有效提高高速公路的收费效益和用户的出行效用,可以分散高峰时的交通压力,提升高速公路的通行效率.     

A model for the periodic optimization of bus dispatching times

We model the problem of dispatching time control in rolling horizons following a periodic optimization approach reactionary to travel time and passenger demand disturbances. This model provides more flexibility to transport planners allowing them to adjust the bus schedules during the daily operations. We prove that our periodic optimization model is a convex quadratic program, guaranteeing the global optimality of its solution. To reduce the computational burden, we introduce an iterative algorithm that uses gradient approximations to obtain an approximate dispatching solution. The proposed solution method is found to be significantly faster than exact optimization approaches for quadratic programming and maintains an (almost) negligible optimality gap in realistic bus operation scenarios. Finally, we show that our periodic optimization method outperforms myopic methods that adjust the dispatching time of each bus trip in isolation using operational data from bus line 302 in Singapore.