Max-plus algebra in njena uporaba pri sestavljanju železniških voznih redov
magistrsko delo
Abstract
Max-plus algebra spada med tista področja matematike, katerih razvoj se je začel relativno pozno, zato postaja vse bolj zanimiva za raziskovalce, novejše raziskave na tem področju pa kažejo tudi na njeno večstransko uporabnost. Ker ima zaradi lastnosti svojih operacij prednost pri reševanju nekaterih problemov, so jo uporabili tudi pri sestavi voznih redov. V magistrskem delu si podrobno ogledamo koncept max-plus algebre in njenih lastnosti. Poleg tega vidimo tudi, s katerimi algoritmi in pod katerimi predpostavkami je mogoče izračunati lastne vrednosti in njim pripadajoče lastne vektorje matrik. Preučimo tudi, kako so na Nizozemskem z njeno pomočjo sestavili železniške vozne rede, in si ogledamo algoritme, uporabljene v ta namen. Potem s tem načinom pripravimo tudi analogno analizo za poenostavljeno slovensko železniško omrežje.
Keywords
matematika;max-plus algebra;grafi;vozni red;optimizacija;lastne vrednosti;lastni vektorji;Petrijeve mreže;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2020 |
| Typology: | 2.09 - Master's Thesis |
| Organization: | UL FS - Faculty of Mechanical Engineering |
| Publisher: | [U. Krampelj] |
| UDC: | 519.8 |
| COBISS: |
32558595
|
| Views: | 1164 |
| Downloads: | 182 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Max-Plus algebra and its use in compiling train timetables |
| Secondary abstract: | Max-plus algebra is one of the areas of mathematics that started developing relatively late. So it is becoming increasingly interesting for researchers. Recent research in this area also indicates its multifaceted applicability. Because it has, due to the nature of its operations, an advantage in solving some problems, it has also been used in compiling timetables. In the master's thesis we look closely at the concept of max-plus algebra and its properties. In addition, we also examine with which algorithms and under which assumptions is it possible to calculate eigenvalues and their associated eigenvectors of matrices. We also look at how railway timetables were put together in the Netherlands with the help of max-plus algebra and which algorithms were used for this purpose. With this method we then prepare an analogous analysis for the simplified Slovenian railway network. |
| Secondary keywords: | mathematics;max-plus algebra;graphs;timetable;optimization;eigenvalues;eigenvalue vectors;Petri nets; |
| Type (COBISS): | Master's thesis/paper |
| Study programme: | 0 |
| Embargo end date (OpenAIRE): | 1970-01-01 |
| Thesis comment: | Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja |
| Pages: | IX, 56 str. |
| ID: | 12046408 |
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