Award Date

December 2023

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical and Computer Engineering

First Committee Member

Pushkin Kachroo

Second Committee Member

Ebrahim Saberinia

Third Committee Member

Ke-Xun Sun

Fourth Committee Member

Mei Yang

Fifth Committee Member

Monika Neda

Number of Pages



Travel time is an important concept in various intelligent transportation system (ITS) applications. The concept is used in a wide array of applications, such as system planning, system performance, and optimization. Reducing the time required to travel between different points on a network is an important goal. Benefits include reducing time wasted in traveling, and keeping travelers satisfied. Thus, studying and reducing travel time in ITS is beneficial in different applications.

The classic density-based Lighthill Whitman Richards (LWR) equation for modeling traffic flow is the starting point in this dissertation. A more recent travel time dynamics function built on top of the classic equations is reviewed. The travel time dynamics are an asymmetric, one-sided coupled system of hyperbolic partial differential equations (PDEs).

One main contribution of this dissertation is the mathematical development of the method for finding the viscosity solution of the given travel time PDE. Additionally, the viscosity solution is directly related to the entropy solution of the density based LWR equations. This relation is used as evidence in using the travel time dynamics for numerical applications.

Another contribution is expanding the widely applied numerical method for simulating the LWR equations to include travel time analysis. The standard method to evolve LWR dynamics is with the Godunov scheme. The numerical technique is expanded to include dynamic travel time. Nodes for network studies are presented and minimizing travel time is used as a control decision for splitting flow in nodes of a network.

Finally, after introducing the travel time dynamics for the Godunov scheme, some examples of applications using travel time analysis are presented. These examples include bidirectional splitting which can be used for pedestrian modeling, network bidirectional splitting, and bottleneck incidents. These examples are then used as building blocks to simulate a more complex network.


Density; Dynamics; Flow; LWR; Network; Travel


Electrical and Computer Engineering | Engineering | Mathematics | Other Mathematics

File Format


File Size

12570 KB

Degree Grantor

University of Nevada, Las Vegas




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