#### Date Awarded

1993

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Department

Computer Science

#### Advisor

Stephen K Park

#### Abstract

Frequency Domain Experiments (FDEs) were first used in discrete-event simulation to perform system parameter sensitivity analysis for factor screening in stochastic system simulations. FDEs are based on the intuitive assertion that if one or more system parameters are oscillated at fixed frequencies throughout a simulation run, then oscillations at the same frequencies will be induced in the system's response. Spectral (Fourier) analysis of these induced oscillations is then used to characterize and analyze the system. Since their introduction 12 years ago, significant work has been done to extend the applicability of FDEs to regression analysis, simulation optimization and gradient estimation. Two fundamental theoretical and data analysis FDE problems remain, however. Both problems are addressed in this dissertation.;To perform a FDE Fourier analysis, a sampled data sequence of response observations is used; i.e., the selected system response is sampled using a suitable oscillation (sampling) index. The choice of an appropriate oscillation index is an open problem in the literature known as the FDE indexing problem. This dissertation presents a solution to the FDE indexing problem. Specifically, a FDE Fourier data analysis algorithm is developed which uses the simulation clock as the oscillation index. This algorithm is based on the well-established theory of counting (Poisson) processes. The algorithm is implemented and tested on a variety of systems including several networks of nonstationary M/G/1 queues.;To justify the use of Fourier methods, a basic FDE model assumption is that if a particular system response statistic is sensitive to a system parameter, then sinusoidal variation of that system parameter at a fixed frequency will induce similar sinusoidal variations in the response statistic, at the same frequency. There is, however, a lack of theoretical support for this model assumption. This dissertation provides some of that theoretical support; i.e., the FDE Fourier data analysis algorithm developed in this dissertation is used to analyze the frequency response of a M/M/1 queuing system. An equation is derived which accurately characterizes the extent to which the departure process from a M/M/1 queuing system can be modeled as an amplitude-modulated, phase-shifted version of the oscillated arrival process.

#### DOI

https://dx.doi.org/doi:10.21220/s2-73xy-sz22

#### Rights

© The Author

#### Recommended Citation

Hazra, Mousumi Mitra, "Fourier analysis of frequency domain discrete event simulation experiments" (1993). *Dissertations, Theses, and Masters Projects.* William & Mary. Paper 1539623843.

https://dx.doi.org/doi:10.21220/s2-73xy-sz22