Matematički model prometnog toka

master's thesis

• Author: Lucija Jusup
• Mentor: Igor Pažanin (mentor)
• Committee member: Igor Pažanin (predsjednik povjerenstva)
• Committee member: Nikola Sandrić (član povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu prezentirali smo matematički model prometnog toka na cesti. Promatrali smo gibanje objekata (automobila) duž jednodimenzionalne osi (ceste), te smo pretpostavili da je to gibanje neprekidno. Zatim smo istom gibanju pridružili prostorne i vremenske varijable te pomoću njih definirali gustoću i protok prometa. Izvodimo i prvi matematički model koji se svodi na rješavanje jednostavne parcijalne diferencijalne jednadžbe. Nakon toga uvodimo i pojam brzine pa model postaje kompleksniji. Posebno smo promatrali slučaj konstantne i slučaj nekonstantne brzine te za oba razvili matematički model i kroz primjere pokušali bolje objasniti svaki od njih. Na kraju rad zaključujemo skupljanjem svih rezultata i završnim komentarom.

Abstract (english)

In this work we have developed a mathematical model describing traffic flow. We have investigated the movement of the objects (cars) along a one-dimensional path (highway), assuming that the motion is continuous. Then we have assigned the spatial and temporal variables to the motion and defined density and traffic flux. We have derived a mathematical model for it given by a simple partial differential equation. After that we have introduced a notion of the velocity so our model became more complex. We have developed mathematical models separately for the case of constant and nonconstant velocity and through some examples tried to explain them a bit further. At the end, we have concluded the work by collecting all the results and writing a final comment.

• Keywords: matematički model; prometni tok; parcijalne diferencijalne jednadžbe
• Keywords (english): mathematical model; traffic flow; partial differential equations
• Language: croatian
• URN:NBN: urn:nbn:hr:217:756599
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-05-15 12:38:52