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• The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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#### Traffic Modelling Using Parabolic Differential Equations

Yung, Tamara January 2013 (has links)
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.
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