Railway timetable stability analysis using max-plus system theory

Goverde, Rob M.P.

doi:10.1016/j.trb.2006.02.003

Cited by 204 publications

(120 citation statements)

References 5 publications

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“…The internal states are start times for the injection or completion times for the outflow. Several problems in transportation planning using max-plus algebra are reported (Heidergott & Veries, 2001;Moh et al, 2005;Goverde, 2007). These problems can be formulated by setting the system variables in the following manner: For instance, in railway networks, the respective inputs and outputs correspond to departure times from stations of origin, and arrival times at terminals.…”

Section: Applicationsmentioning

confidence: 99%

Modeling Methods Based on Discrete Algebraic Systems

Goto¹

2010

Discrete Event Simulations

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Section: Applicationsmentioning

confidence: 99%

Modeling Methods Based on Discrete Algebraic Systems

Goto¹

2010

Discrete Event Simulations

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“…Many of these methods are based on Petri nets and Max-plus algebra (see Goverde, 2005Goverde, , 2006, for recent work) and consider three types of stability evaluation:…”

Section: The Stability Evaluation Modelmentioning

confidence: 99%

Stability evaluation of a railway timetable at station level

Delorme

Gandibleux

Rodríguez³

2009

European Journal of Operational Research

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This research deals with a real-world planning problem in railway infrastructure operations. It is part of the RECIFE project, which seeks to develop a decision support software to help evaluate the capacity of a rail junction or station. To this end, the project is working on a timetable optimization model, as well as timetable evaluation modules. This paper presents a module for evaluating timetable stability, which uses an original method based on delay propagation and using shortest path problem resolution. A didactic example and a complete case study applying this method to the Pierrefitte-Gonesse junction are also presented.

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“…The goal was to place train running paths as much as possible, while taking the timetable into consideration at the same time [11]. Goverde presented the method based on max-plus to analyze the timetable stability and took the Netherlands national railway timetable as a computing case to prove the feasibility of using the method to design the timetable of the railway network [12]. Zong and Li studied the reasonable time supplement of the trains running in the sections [13].…”

Section: Introductionmentioning

confidence: 99%

“…He again hired the max-plus algebra to analyze the timetable stability of the railway network. On this basis, he proposed a new method to generate the paths for the trains on a large-scale railway network [17]. Delorme et al presented a station capacity evaluating model and evaluated the stability on the fundamental parts of the railway network: stations [18].…”

Section: Introductionmentioning

confidence: 99%

“…And we can see that the timetable stability is not only related to time but also the utilization coefficient capacity of the railway network [17,18]. That is to say, the networked timetable stability study requires the combination of the railway network capacity utilization and the time supplement distribution in the sections and on the stations.…”

Section: Introductionmentioning

confidence: 99%

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Train Timetable Stability Evaluation based on Analysis of Interior and Exterior Factors Information Entropy

Meng¹,

Jia²

2014

Appl. Math. Inf. Sci.

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Abstract:To evaluate the quality of the train timetable roundly, train timetable stability is defined based on the analysis of the interior and exterior factors affecting the timetable stability. The exterior factors include the grade of the railway lines, the blocking system type, the station interlocking type, the leading locomotive performance and the average mileage of the sections. The interior factors are the capacity load of the sections, the capacity load of the stations, the total time supplement for running in the sections, the total time supplement for dwelling on the stations, the timetable periodic time and the buffer times between train paths. We define the information entropy of the exterior factors and the interior factors and present the equation to calculate the information entropy. Then train timetable stability is quantized according to the definitions above. The computing case proves the method to evaluate the train timetable stability is feasible and efficient.

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Railway timetable stability analysis using max-plus system theory

Cited by 204 publications

References 5 publications

Modeling Methods Based on Discrete Algebraic Systems

Modeling Methods Based on Discrete Algebraic Systems

Stability evaluation of a railway timetable at station level

Train Timetable Stability Evaluation based on Analysis of Interior and Exterior Factors Information Entropy

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