Thesis Title: Effective Estimation of Marginal Quantiles in Steady-State Simulations
Thesis Committee:
Dr. Christos Alexopoulos (Advisor, ISyE, Georgia Tech)
Dr. David Goldsman (ISyE, Georgia Tech)
Dr. Seong-Hee Kim (ISyE, Georgia Tech)
Dr. Enlu Zhou (ISyE, Georgia Tech)
Dr. Kemal Dinçer Dingeç (Department of Industrial Engineering, Gebze Technical University, Kocaeli, Turkey)
Dr. James R. Wilson (Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh)
Date and Time: Thursday, April 20th, 09:30 am (ET)
Meeting Link: https://gatech.zoom.us/j/4594801503?pwd=d3I5ZWZzWGU5bFJRcjBUbDV4L3R6UT09
Meeting ID: 459 480 1503
Passcode: ddala23
Abstract:
This thesis has two main goals: (1) The formulation of the theoretical foundations for procedures for computing confidence intervals (CIs) for marginal steady-state quantiles with given reliability and, potentially, precision. The underlying methodology is based on the techniques of Standardized time series (STS), batching, and sectioning. (2) The development and experimental evaluation of three automated procedures for steady-state quantile estimation: (i) the first automated sequential procedure based on STS; (ii) the first automated fixed-sample-size procedure based on a single run; and (iii) the first automated fixed-sample-size procedure based on independent replications.
We summarize the main contents in each chapter as follows:
Chapter 1 presents a detailed literature review of the current methods for steady-state quantile estimation and introduces the main problems undertaken by this dissertation.
Chapter 2 contains the theoretical results that constitute the basis of the proposed methods in Chapters 4-6 and provides results from the empirical evaluation of a variety of estimators for the variance parameter of the empirical-quantile process.
Chapter 3 contains exact (or nearly exact) calculations for the expected values of the variance-parameter estimators in Chapter 2 for the special case of independent and identically distributed data. These results provide insight on the rate of convergence of the bias of the aforementioned variance-parameter estimators to zero as the sample size tends to infinity.
Chapter 4 presents and evaluates SQSTS, the first sequential procedure for estimating steady-state quantiles based on STSs that are computed from nonoverlapping batches of observations.
Chapter 5 presents and evaluates FQUEST, the first fully automated, fixed-sample-size method for estimating steady-state quantiles based on a single run.
Chapter 6 presents and evaluates FIRQUEST, the first fully automated, fixed-sample-size procedure for estimating steady-state quantiles based on a given fixed number of independent replications.
Chapter 7 contains overall conclusions, final remarks, and potential future directions.