Award Date


Degree Type


Degree Name

Master of Science in Mathematical Science


Mathematical Sciences

First Committee Member

Monika Neda

Second Committee Member

Pushkin Kachroo

Third Committee Member

Zhonghai Ding

Fourth Committee Member

Amei Amei

Fifth Committee Member

Laxmi Gewali

Number of Pages



Traditionally, one of the ways traffic flow has been studied is by using the kinematic wave model. This model is studied in the Eulerian framework. Recently, the kinematic wave model has been transformed into Lagrangian coordinates. This model of traffic flow together with the concept of observability for linear time invariant discrete time systems is applied to study the observability of four sections of a freeway in both Eulerian and Lagrangian coordinates. A system with densities in four sections of a freeway is designed, and the observability of the system is studied with different situations for sensors. When the system evolves exactly according to the models, the states of the system could be obtained from measurements from certain situations. For both, Eulerian and Lagrangian simulations, as long as the fourth section was measured, the states of the system could be obtained. To compare different situations of measurements, the condition number of the observability matrix is used.


Eulerian graph theory; Kinematics—Models; Lagrangian functions; Traffic flow--Mathematical models


Electrical and Computer Engineering | Mathematics | Transportation