Sample-path Analysis Of Queueing Systems (international Series In Operations Research & Management Science)
by Shaler Stidham Jr. /
1998 / English / PDF
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Sample-Path Analysis of Queueing Systems
Sample-Path Analysis of Queueing Systems uses a
deterministic (sample-path) approach to analyze stochastic systems,
primarily queueing systems and more general input-output systems.
Among other topics of interest it deals with establishing
fundamental relations between asymptotic frequencies and averages,
pathwise stability, and insensitivity. These results are utilized
to establish useful performance measures. The intuitive
deterministic approach of this book will give researchers,
teachers, practitioners, and students better insights into many
results in queueing theory. The simplicity and intuitive appeal of
the arguments will make these results more accessible, with no
sacrifice of mathematical rigor. Recent topics such as pathwise
stability are also covered in this context.
uses a
deterministic (sample-path) approach to analyze stochastic systems,
primarily queueing systems and more general input-output systems.
Among other topics of interest it deals with establishing
fundamental relations between asymptotic frequencies and averages,
pathwise stability, and insensitivity. These results are utilized
to establish useful performance measures. The intuitive
deterministic approach of this book will give researchers,
teachers, practitioners, and students better insights into many
results in queueing theory. The simplicity and intuitive appeal of
the arguments will make these results more accessible, with no
sacrifice of mathematical rigor. Recent topics such as pathwise
stability are also covered in this context.
The book consistently takes the point of view of focusing on one
sample path of a stochastic process. Hence, it is devoted to
providing pure sample-path arguments. With this approach it is
possible to separate the issue of the validity of a relationship
from issues of existence of limits and/or construction of
stationary framework. Generally, in many cases of interest in
queueing theory, relations hold, assuming limits exist, and the
proofs are elementary and intuitive. In other cases, proofs of the
existence of limits will require the heavy machinery of stochastic
processes. The authors feel that sample-path analysis can be best
used to provide general results that are independent of stochastic
assumptions, complemented by use of probabilistic arguments to
carry out a more detailed analysis. This book focuses on the first
part of the picture. It does however, provide numerous examples
that invoke stochastic assumptions, which typically are presented
at the ends of the chapters.
The book consistently takes the point of view of focusing on one
sample path of a stochastic process. Hence, it is devoted to
providing pure sample-path arguments. With this approach it is
possible to separate the issue of the validity of a relationship
from issues of existence of limits and/or construction of
stationary framework. Generally, in many cases of interest in
queueing theory, relations hold, assuming limits exist, and the
proofs are elementary and intuitive. In other cases, proofs of the
existence of limits will require the heavy machinery of stochastic
processes. The authors feel that sample-path analysis can be best
used to provide general results that are independent of stochastic
assumptions, complemented by use of probabilistic arguments to
carry out a more detailed analysis. This book focuses on the first
part of the picture. It does however, provide numerous examples
that invoke stochastic assumptions, which typically are presented
at the ends of the chapters.
