Modeling Car Rental Services Through Transient Analysis, Steady State Analysis, and Monte-Carlo Simulation of Free Processes and M/M/1/k Queueing Processes

Abstract

The goal of this thesis is to explore the properties of Free Processes, Steady State Equations, and the M/M/1/k Queue to model two types of car rental businesses. I use Monte Carlo simulation to produce transient data that I then analyze to receive the mean, variance, standard deviation, and other valuable information that can be beneficial to individuals who operate and work in the car rental industry. A crucial aspect of my paper is to build off of the recently developed M/M/1/k queueing model for bike sharing stations and elaborate on the work of Dr. William A. Massey, Emmanuel Ekwedike, Robert C. Hampshire and Dr. Jamol J. Pender. I credit the inspiration for the perspective of The Entrepreneur to Hashim Moore ’17, the owner of a rental car company based in Austin, TX. Through my conversations with Mr. Moore, I am able to present a realistic application of the mathematical contents of this paper. The collaboration allowed me to design a model that most accurately resembles a modern business, like his, without making gross assumptions. Along with the supervisor of Professor Massey, I utilized the expertise of Professor Pender of Cornell University in my efforts of preparing my simulation code. He aided me in developing a conceptual framework to implement my code, as well as assisting in debugging. Complex analysis is a fundamental theme to this thesis as it at the root of most of the computational results derived herein.