Traffic Modelling Using Parabolic Differential Equations
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
The need of a working infrastructure in a city also requires an understanding of how the traffic flows. It is known that increasing number of drivers prolong the travel time and has an environmental effect in larger cities. It also makes it more difficult for commuters and delivery firms to estimate their travel time. To estimate the traffic flow the traffic department can arrange cameras along popular roads and redirect the traffic, but this is a costly method and difficult to implement. Another approach is to apply theories from physics wave theory and mathematics to model the traffic flow; in this way it is less costly and possible to predict the traffic flow as well. This report studies the application of wave theory and expresses the traffic flow as a modified linear differential equation. First is an analytical solution derived to find a feasible solution. Then a numerical approach is done with Taylor expansions and Crank-Nicolson’s method. All is performed in Matlab and compared against measured values of speed and flow retrieved from Swedish traffic department over a 24 hours traffic day. The analysis is performed on a highway stretch outside Stockholm with no entries, exits or curves. By dividing the interval of the highway into shorter equal distances the modified linear traffic model is expressed in a system of equations. The comparison between actual values and calculated values of the traffic density is done with a nominal average difference. The results reveal that the numbers of intervals don’t improve the average difference. As for the small constant that is applied to make the linear model stable is higher than initially considered.
Place, publisher, year, edition, pages
2013. , 40 p.
Traffic model, linear differential equation, wave theory, Matematik
IdentifiersURN: urn:nbn:se:liu:diva-102745ISRN: LiU-ITN-TEK-G--13/065--SEOAI: oai:DiVA.org:liu-102745DiVA: diva2:681695
Subject / course