When planning for road building and infrastructure, simulations of tra-c ow are useful tools for
further investigation. Two models are analyzed in this report, both supported by the assumption
that tra-c ow behaves as a continous uid on a macroscopic scale. This means that the vehicle
density will be considered instead of observing the vehicles as discrete objects.
Conservational laws along with piecewise constant initial data are called Riemann problems.
Tra-c ow in one dimension at a tra-c light can be modeled as such a problem with the continuity
equation and a scaled Heaviside function as initial data.
Two special cases of the general problem are solved, in the rst model the velocity of the cars
is a linear function of the density while in the second model the velocty is a function of the denisty
and its derivative. The rst case is solved analytically with a similarity solution. The second case,
where diusion is included, is solved numerically and the method utilized is proved to be stable.
Simulations are presented in order to see how the density of vehicles develop in front of and
after the tra-c light. The results are used to determine a time for the tra-c light to be green,
given a xed time for red, that optimzes the ow of vehicles.
2016. , 34 p.