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Capacity of Railways in Station Areas using Petri Nets
IFOR Events
Seminar:
'Optimization & Applications'
(see information & program)
Feb 20 - May 28, 2012
IFOR Mitteilungen
This booklet informs about ongoing projects and future events at the IFOR and appears once at the end of the year.
| Author | Dan Burkolter |
| Abstract |
This thesis studies the assessment of available track capacity within a station region. The question is of particular interest as railway operators expect that capacity bottlenecks of the overall railway network will mainly arise in the vicinity of stations which lie at the intersection of the main train lines. However, estimating capacity of a station region is much more taxing than assessing capacity on stretches in between. This is due to the fact that within stations many switches exist, which are in place to ensure that trains can reach any destination. As a consequence, a train may have hundreds of possible routes.Usually, sections with more than two parallel tracks exist such that simply assigning one track to each direction will not suffice. Therefore, train routing has a major impact on capacity utilisation. The developed method states available capacity by constructing a dense schedule where capacity is defined as the time needed to provide a given train service intention on the track topology considered. Additionally, a measure for the stability of a timetable is introduced. Thus, timetables are made comparable according to their capacity utilisation and stability. A two level model is introduced in order to separate choosing train routings from determining the train sequence. On the top level, an aggregated topology is used in which it is assumed that switch regions have unlimited capacity. The task on the aggregated level is to fix the train sequence on stretches between switch regions such that the resulting cycle time of the timetable is minimised. On the lower modelling level, exact topologies of the switch regions are used in order to determine feasibility of the previously derived tentative timetable. Petri Nets are applied for the modelling of the aggregated level. First, a train service intention is depicted as a general Petri Net in which restrictions resulting from the number of available tracks and desired train connections are included. In the next step, the train sequence is chosen on stretches of parallel tracks, which corresponds to transforming the Petri Net into an event graph---a decision free Petri Net. Finally, the cycle time of the resulting tentative timetable is minimised applying Simulated Annealing. The question of feasibility of the tentative timetable in the switch regions is modelled as an independent set problem. All possible routes of a train are depicted as nodes in a graph and nodes are connected if they correspond to routes that are mutually exclusive due to insufficient safety distance. A fixed point iteration heuristics is applied to find independent sets. Should a timetable prove to be infeasible, an additional restriction to include in the Petri Net of the aggregated level is calculated in order to remove the conflict in a renewed calculation of the tentative timetable. The methodology was implemented and tested for the station region of Bern. Results showed that dense timetables could be constructed within an hour. The sections of the region that mainly limit the overall capacity utilisation could be detected by modifying the aggregated topology used in the top level. |
| Download | PDF, PS.gz |
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