Award Date

12-1-2013

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Hongtao Yang

Second Committee Member

Pushkin Kachroo

Third Committee Member

Zhonghai Ding

Fourth Committee Member

Xin Li

Fifth Committee Member

Sajjad Ahmad

Number of Pages

69

Abstract

In this thesis we study the travel time problem based on the known traffic density model. Using the conservation law, we model the travel time function by a boundary value problem of a non homogeneous linear hyperbolic equation. The equation is transformed into an initial value hyperbolic equation, and the well-posedness of the problem is discussed. The mathematical analysis for both density and travel problems are given. We also derive the analytic solutions for several special cases of traffic density. Numerical schemes are proposed for solving for travel time problem. Several numerical examples are presented and error analysis on the solutions obtained is performed to illustrate the rates of convergence of the numerical schemes.

Keywords

Differential equations, Partial; Exponential functions; Hyperbolic equations; Numerical analysis; Partial differential equations; Traffic density; Travel time (Traffic engineering)

Disciplines

Mathematics | Transportation

Language

English


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