Term of Award

Summer 2010

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Department

Department of Mathematical Sciences

Committee Chair

Goran Lesaja

Committee Member 1

Scott Kersey

Committee Member 2

Yan Wu

Abstract

In this thesis, we examine the implementation of volume delay functions to the Metropolitan Atlanta Rapid Transportation Authority (MARTA) system. Volume delay functions are n differentiable functions used to estimate the long-term distribution of user traffic on transportation systems. We will demonstrate the graphical behavior of these functions as well as explain the constraints for these functions. These tasks will be completed by developing a simplistic yet unrealistic model, demonstrate how the integral is used to estimate the total sum of this model, and then introduce the two functions which will be used in the analysis. The final task of this paper will be to develop and implement functions which have properties which allow them to directly relate to the unique behavior of public transportation systems. The final analysis will be the interaction of the functions developed in this paper with the preexisting, well-behaved BPR and Davidson functions.

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