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.
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.