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Given a timetable, we use an incidence graph, the so-called train contraction minor, for representing the consecutive train operations and show that a longest path for spanning the compressed timetable is any path in a graph induced by some topological subsequence of trains that connects the predefined vertices in the train contraction minor. By vector-valued vertex labeling of this minor, we acquire an efficient algorithm that computes the consumed capacity of the timetable. Our algorithm runs in <i>O</i>(<i>mn</i>) time, where <i>m</i> and <i>n</i> are the number of trains and stations, respectively, and is free from the limitation and outperforms the near-linear time policy iteration implementation in the max-plus system of train operations. A toy example and a real-world case study demonstrate the effectiveness and computational performance of the proposed method. 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引用次数: 0
摘要
当两列其他列车的间隔时间不超过一列列车时,就会使用基于三角形间隙问题的方法,在线性时间内计算消耗的运力。这是限制其适用性的一个重要条件,而现实世界中的运营往往以各种速度的混合交通为特征,从而产生超出三角形间隙特征的更复杂结构。在本文中,我们试图研究多列车间隙的情况,并为铁路时刻表结构和运力分析问题提供一个通用解决方案。给定一个时刻表,我们使用一个入射图,即所谓的列车收缩小图,来表示连续的列车运行,并证明跨越压缩时刻表的最长路径是由列车的某个拓扑子序列所诱导的图中的任意路径,该路径连接列车收缩小图中预定义的顶点。通过对该次要顶点进行向量值标注,我们获得了一种计算时刻表消耗容量的高效算法。我们的算法运行时间为 O(mn),其中 m 和 n 分别为列车数和车站数,并且不受时间限制,优于列车运行最大加法系统中的近线性时间策略迭代实现。一个玩具实例和一个实际案例研究证明了所提方法的有效性和计算性能。所提出的基于列车收缩次要性的方法促进了铁路线能力在线性时间内的高效计算,为铁路运营界做出了贡献。
Linear Time Train Contraction Minor Labeling for Railway Line Capacity Analysis
When no more than one train is feasibly contained in the separation headway times of two other trains, a triangular gap problem-based method is used to compute the consumed capacity in linear time. This is a strong condition limiting its applicability, while real-world operations often feature mixed traffic of various speeds, creating more complex structures beyond the characterization of a triangular gap. In this paper, we attempt to investigate the multi-train gap scenario and provide a general solution to the railway timetable structure and capacity analysis problem. Given a timetable, we use an incidence graph, the so-called train contraction minor, for representing the consecutive train operations and show that a longest path for spanning the compressed timetable is any path in a graph induced by some topological subsequence of trains that connects the predefined vertices in the train contraction minor. By vector-valued vertex labeling of this minor, we acquire an efficient algorithm that computes the consumed capacity of the timetable. Our algorithm runs in O(mn) time, where m and n are the number of trains and stations, respectively, and is free from the limitation and outperforms the near-linear time policy iteration implementation in the max-plus system of train operations. A toy example and a real-world case study demonstrate the effectiveness and computational performance of the proposed method. The proposed method based on train contraction minor contributes to the railway operations community by promoting the efficient computation of railway line capacity into linear time.
期刊介绍:
Urban Rail Transit is a peer-reviewed, international, interdisciplinary and open-access journal published under the SpringerOpen brand that provides a platform for scientists, researchers and engineers of urban rail transit to publish their original, significant articles on topics in urban rail transportation operation and management, design and planning, civil engineering, equipment and systems and other related topics to urban rail transit. It is to promote the academic discussions and technical exchanges among peers in the field. The journal also reports important news on the development and operating experience of urban rail transit and related government policies, laws, guidelines, and regulations. It could serve as an important reference for decision¬makers and technologists in urban rail research and construction field.
Specific topics cover:
Column I: Urban Rail Transportation Operation and Management
• urban rail transit flow theory, operation, planning, control and management
• traffic and transport safety
• traffic polices and economics
• urban rail management
• traffic information management
• urban rail scheduling
• train scheduling and management
• strategies of ticket price
• traffic information engineering & control
• intelligent transportation system (ITS) and information technology
• economics, finance, business & industry
• train operation, control
• transport Industries
• transportation engineering
Column II: Urban Rail Transportation Design and Planning
• urban rail planning
• pedestrian studies
• sustainable transport engineering
• rail electrification
• rail signaling and communication
• Intelligent & Automated Transport System Technology ?
• rolling stock design theory and structural reliability
• urban rail transit electrification and automation technologies
• transport Industries
• transportation engineering
Column III: Civil Engineering
• civil engineering technologies
• maintenance of rail infrastructure
• transportation infrastructure systems
• roads, bridges, tunnels, and underground engineering ?
• subgrade and pavement maintenance and performance
Column IV: Equipments and Systems
• mechanical-electronic technologies
• manufacturing engineering
• inspection for trains and rail
• vehicle-track coupling system dynamics, simulation and control
• superconductivity and levitation technology
• magnetic suspension and evacuated tube transport
• railway technology & engineering
• Railway Transport Industries
• transport & vehicle engineering
Column V: other topics of interest
• modern tram
• interdisciplinary transportation research
• environmental impacts such as vibration, noise and pollution
Article types:
• Papers. Reports of original research work.
• Design notes. Brief contributions on current design, development and application work; not normally more than 2500 words (3 journal pages), including descriptions of apparatus or techniques developed for a specific purpose, important experimental or theoretical points and novel technical solutions to commonly encountered problems.
• Rapid communications. Brief, urgent announcements of significant advances or preliminary accounts of new work, not more than 3500 words (4 journal pages). The most important criteria for acceptance of a rapid communication are novel and significant. For these articles authors must state briefly, in a covering letter, exactly why their works merit rapid publication.
• Review articles. These are intended to summarize accepted practice and report on recent progress in selected areas. Such articles are generally commissioned from experts in various field s by the Editorial Board, but others wishing to write a review article may submit an outline for preliminary consideration.