Award Date
5-15-2026
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Physics and Astronomy
First Committee Member
Bernard Zygelman
Second Committee Member
Michael Pravica
Third Committee Member
Luqing Wang
Fourth Committee Member
Laxmi Gewali
Number of Pages
237
Abstract
This dissertation develops the theory of travel time from fundamental principles of physics in the context of traffic, which can be one dimensional on a single road, or can also be two dimensional in the case of pedestrians moving on a surface.
The theory is built in three different levels of modeling. In the microscopic case, the travel time equation is derived for a single vehicle traveling in different scenarios. Then it is extended for multiple vehicles using various models of traffic some of which have been enhanced in this work.
The macroscopic setting allows us to study travel time as a scalar field, and its dynamics are developed that yield the structure of Hamilton Jacobi Partial Differential Equation (PDE). As that is a hyperbolic PDE, we obtain discontinuities (shocks) as well as rarefaction which are resolved mathematically by considering viscosity weak solutions. The macroscopic model is extended to higher order models, in one and two dimensions, and also for heterogeneous traffic.
In the mesoscopic case, we study the statistical physics of the traffic, where probabilistic distribution is the framework that is utilized. Within the framework of mesoscopic traffic model, the travel time equations and dynamics are developed. There are two different ways this is accomplished. In one, the evolution of the mesoscopic kinetic transport equation is followed by an aggregation of the distribution function to obtain macroscopic traffic density and speeds, which are then utilized to obtain average travel time evolution. In the other methods we obtain an acceleration term by equating Boltzmann equation with the kinetic transport equation of traffic, and then this term is utlized in producing the evolution of the travel time distribution.
Keywords
Macroscopic; Mesoscopic; Microscopic; Traffic; Travel Time
Disciplines
Mathematics | Physics | Transportation
File Format
File Size
2800 KB
Degree Grantor
University of Nevada, Las Vegas
Language
English
Repository Citation
Kachroo, Pushkin, "Theory of Travel Time in Microscopic, Mesoscopic, and Macroscopic Scales" (2026). UNLV Theses, Dissertations, Professional Papers, and Capstones. 5558.
https://oasis.library.unlv.edu/thesesdissertations/5558
Rights
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