Conference article

Modeling and Simulation of Train Networks using Max-Plus Algebra

Hazem Al-Bermanei
Faculty of Business ICT and Life Sciences, Turku University of Applied Sciences, Turku, Finland

Jari M. Böling
Department of Chemical Engineering, Åbo Akademi University, Turku, Finland

Göran Högnäs
Department of Mathematics and Statistics, Åbo Akademi University, Turku, Finland

Download articlehttp://dx.doi.org/10.3384/ecp17142612

Published in: Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016

Linköping Electronic Conference Proceedings 142:89, p. 612-618

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Published: 2018-12-19

ISBN: 978-91-7685-399-3

ISSN: 1650-3686 (print), 1650-3740 (online)

Abstract

Max-plus algebra provides mathematical methods for solving nonlinear problems that can be given the form of linear problems. Problems of this type, sometimes of an administrative nature, arise in areas such as manufacturing, transportation, allocation of resources, and information processing technology. Train networks can be modelled as a directed graph, in which nodes correspond to arrivals and departures at stations, and arcs to travelling times. A particular difficulty is represented by meeting conditions in a single-track railway system. Compared to earlier work which typically include numerical optimization, max-plus formalism is used throughout this paper. The stability and sensitivity of the timetable is analyzed, and different types of delays and delay behavior are discussed and simulated. Interpretation of the recovery matrix is also done. A simple train network with real world background is used for illustration.

Keywords

train schedules, meeting conditions, max-plus algebra, discrete-event systems, delay sensitivity, recovery matrix

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