Title:
Effective Estimation of Marginal Quantiles in Steady-State Simulations
Effective Estimation of Marginal Quantiles in Steady-State Simulations
Author(s)
Lolos, Athanasios
Advisor(s)
Alexopoulos, Christos
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Abstract
Simulation is perhaps the most widely used systems-engineering tool in a variety of engineering and scientific domains. Large-scale applications of simulation provide critical support for planning and analysis in the governmental and military sectors as well as in numerous industries, including aerospace, electronics, finance, healthcare, manufacturing, supply chains, and telecommunications.
Steady-state simulation is a critical tool for the design and performance evaluation of complex systems in a extended list of applications ranging from production systems to financial engineering applications.
While the steady-state mean of a simulation response characterizes central tendency, a (marginal) steady-state quantile characterizes the long-run risk associated with the individual realizations. The estimation of a steady-state quantile is typically a substantially harder problem than the estimation of the mean: while both problems are subject to effects from the potential presence of an initial transient, substantial serial correlation in the simulation output process, and departures from normality, quantile estimation is adversely affected by additional issues ranging from the inherent bias of point estimators and the nature of the marginal distribution such as nonexistence of a probability density function (p.d.f.), or a p.d.f. with discontinuities and multimodalities with sharp peaks. These theoretical and computational challenges associated with steady-state quantile estimation have hindered the growth in this area over the last few decades.
This thesis has two main goals: (1) the formulation of the theoretical foundations for procedures based on Standardized Time Series (STS) for estimating steady-state quantiles with confidence intervals having given coverage probability and, potentially precision; and (2) the development and experimental evaluation of three automated methods for effective estimation of marginal quantiles in steady-state simulations: (i) the first fully automated sequential procedure for estimating steady-state quantiles based on STSs computed from nonoverlapping batches; (ii) a new fully automated fixed-sample-size procedure for steady-state quantile estimation based on a single time series; and (iii) the first fully automated fixed-sample-size procedure for steady-state quantile estimation based on sample paths generated by independent replications.
Chapter 1 presents a detailed literature review of the current methods for steady-state quantile estimation and introduces the main topics of this dissertation. Chapter 2 contains the theoretical results that constitute the basis of the proposed methods in Chapters 4-6 and provides results from an 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. Chapter 4 presents and evaluates SQSTS, the first fully automated sequential procedure for estimating steady-state quantiles based on STSs that are computed from nonoverlapping batches of observations. Chapter 5 presents and evaluates FQUEST, a new 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 method for estimating steady-state quantiles based on a user-specified number of independent replications. Finally, Chapter 7 contains overall conclusions, final remarks, and potential future directions.
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Date Issued
2023-04-26
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Dissertation