Mathematical and Simulation Tecniques for Modelling Urban Train Networks

Abstract

Railway systems can pose complex problems for the scheduling and operation of trains. A passenger rail service's first priority is to provide a punctual and safe transport service to its customers. But doing so is a major challenge for rail network operators, as disruptions are inevitable, especially in densely-populated networks. Disruptions can be caused not only by infrastructure or rolling stock breakdowns, but also by maintenance activities, new rolling stock, or new train services. Managing these disruptions and predicting the extent of its effects is a crucial part of rail network operation. Mathematical models and simulation can be applied to these problems. This paper will review the literature concerning the modelling of train networks. OPSOMMINGSpoorwegstelsels skep soms komplekse probleme met betrekking tot die skedulering en die bedryf van treine. 'n Passasiers-spoordiens se eerste prioriteit is om stiptelike en veilige vervoer te verskaf aan sy gebruikers. Om 'n stiptelike en betroubare diens te lewer is 'n groot uitdaging vir netwerk operateurs, aangesien trein dienste maklik ontwrig word in digbevolkte netwerke. Ontwrigtinge word nie net deur infrastruktuur en rollende materiaal falings veroorsaak nie, maar ook deur infrastruktuur onderhoud, nuwe rollende materiaal, en nuwe treindienste wat ingestel kan word. Die bestuur van dié ontwrigtinge en die akkurate vooruitskatting van die effek op die res van die netwerk is 'n kritiese komponent van die bedryf van 'n trein netwerk. Wiskundige modelle en simulasie metodes kan toegepas word op dié tipe probleme. Hierdie artikel bespreek die literatuur wat oor die modellering van trein netwerke handel. INTRODUCTIONRailway network companies often need to model and simulate the operation of their trains. This need usually arises with the expansion or maintenance of infrastructure, or the addition of new rolling stock and services. Infrastructure expansion entails adding new links, stations, or additional lines on a specific route. Furthermore, perway, electrical, and signals maintenance all contributes to train operations being disrupted to some extent. And adding train services or new rolling stock requires major operations planning and rescheduling. Forecasting the effect on the operation of the network before the implementation of such changes is a crucial component of planning. Bottlenecks, line capacities, demand satisfaction, and delay propagations are all areas that need to be identified and calculated before large capital amounts are spent. This can be done through the use of mathematical models and simulation. The optimisation of existing operations can also be done using these tools. OBJECTIVEThe objective of this paper is to review the literature on the different modelling techniques that are used to describe the operation of train networks. This will lay the groundwork for developing

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