Application of Kronecker algebra in railway operation
We present a methodology for dispatching trains which prevents deadlocks and includes possible limitation of the available energy provided by the power supply. Our approach applies Kronecker algebra to manipulate matrices. Generally blocking of trains occurs due to a lack of some resource which can...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek
2017-01-01
|
| Series: | Tehnički Vjesnik |
| Subjects: | |
| Online Access: | https://hrcak.srce.hr/file/257820 |
| _version_ | 1797207934721064960 |
|---|---|
| author | Mark Stefan (Volcic) Johann Blieberger Andreas Schöbel |
| author_facet | Mark Stefan (Volcic) Johann Blieberger Andreas Schöbel |
| author_sort | Mark Stefan (Volcic) |
| collection | DOAJ |
| description | We present a methodology for dispatching trains which prevents deadlocks and includes possible limitation of the available energy provided by the power supply. Our approach applies Kronecker algebra to manipulate matrices. Generally blocking of trains occurs due to a lack of some resource which can be either infrastructure or energy. Our method can also be used to calculate travel times in a rough way. Thereby blocking time is included in the calculated travel time. To model the movements of trains in a railway system we use graphs, which are represented by adjacency matrices. We assume that the edges in a graph are labelled by elements of a semiring. Usually two or more distinct train route graphs refer to the same track section to model synchronization. Our approach can be used to model a complex railway system. For example, if additional trains have to be scheduled, power stations or interconnection lines fail or are not available due to maintenance, our model can be used to calculate the impact on the travel times of the trains in the system. |
| first_indexed | 2024-04-24T09:30:48Z |
| format | Article |
| id | doaj.art-40aaa806919a4c78a109a9d4b3ae8822 |
| institution | Directory Open Access Journal |
| issn | 1330-3651 1848-6339 |
| language | English |
| last_indexed | 2024-04-24T09:30:48Z |
| publishDate | 2017-01-01 |
| publisher | Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek |
| record_format | Article |
| series | Tehnički Vjesnik |
| spelling | doaj.art-40aaa806919a4c78a109a9d4b3ae88222024-04-15T14:01:10ZengFaculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in OsijekTehnički Vjesnik1330-36511848-63392017-01-01241213010.17559/TV-20131107130926Application of Kronecker algebra in railway operationMark Stefan (Volcic)0Johann Blieberger1Andreas Schöbel2Austrian Institute of Technology GmbH, Giefinggasse 2, A-1210 Vienna, AustriaTU Wien, Institute of Computer Aided Automation Treitlstraße 1-3, A-1040 Vienna, AustriaOpenTrack Railway Technology Ltd., Kaasgrabengasse 19/8, A-1190 Vienna, Austria / Karlsplatz 13, 1040 Vienna, AustriaWe present a methodology for dispatching trains which prevents deadlocks and includes possible limitation of the available energy provided by the power supply. Our approach applies Kronecker algebra to manipulate matrices. Generally blocking of trains occurs due to a lack of some resource which can be either infrastructure or energy. Our method can also be used to calculate travel times in a rough way. Thereby blocking time is included in the calculated travel time. To model the movements of trains in a railway system we use graphs, which are represented by adjacency matrices. We assume that the edges in a graph are labelled by elements of a semiring. Usually two or more distinct train route graphs refer to the same track section to model synchronization. Our approach can be used to model a complex railway system. For example, if additional trains have to be scheduled, power stations or interconnection lines fail or are not available due to maintenance, our model can be used to calculate the impact on the travel times of the trains in the system.https://hrcak.srce.hr/file/257820deadlockdispatchingenergy-awareKronecker algebratravel time |
| spellingShingle | Mark Stefan (Volcic) Johann Blieberger Andreas Schöbel Application of Kronecker algebra in railway operation Tehnički Vjesnik deadlock dispatching energy-aware Kronecker algebra travel time |
| title | Application of Kronecker algebra in railway operation |
| title_full | Application of Kronecker algebra in railway operation |
| title_fullStr | Application of Kronecker algebra in railway operation |
| title_full_unstemmed | Application of Kronecker algebra in railway operation |
| title_short | Application of Kronecker algebra in railway operation |
| title_sort | application of kronecker algebra in railway operation |
| topic | deadlock dispatching energy-aware Kronecker algebra travel time |
| url | https://hrcak.srce.hr/file/257820 |
| work_keys_str_mv | AT markstefanvolcic applicationofkroneckeralgebrainrailwayoperation AT johannblieberger applicationofkroneckeralgebrainrailwayoperation AT andreasschobel applicationofkroneckeralgebrainrailwayoperation |