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Performance Analysis of Communications Networks and Systems

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Performance analysis belongs to the domain of applied mathematics. The
major domain of application in this book concerns telecommunications systems
and networks. We will mainly use stochastic analysis and probability
theory to address problems in the performance evaluation of telecommunications
systems and networks. The first chapter will provide a motivation
and a statement of several problems.

This book aims to present methods rigorously, hence mathematically, with
minimal resorting to intuition. It is my belief that intuition is often gained
after the result is known and rarely before the problem is solved, unless the
problem is simple. Techniques and terminologies of axiomatic probability
(such as definitions of probability spaces, filtration, measures, etc.) have
been omitted and a more direct, less abstract approach has been adopted.
In addition, most of the important formulas are interpreted in the sense of
“What does this mathematical expression teach me?” This last step justifies
the word “applied”, since most mathematical treatises do not interpret as
it contains the risk to be imprecise and incomplete.

The field of stochastic processes is much too large to be covered in a single
book and only a selected number of topics has been chosen. Most of the topics
are considered as classical. Perhaps the largest omission is a treatment
of Brownian processes and the many related applications. A weak excuse
for this omission (besides the considerable mathematical complexity) is that
Brownian theory applies more to physics (analogue fields) than to system
theory (discrete components). The list of omissions is rather long and only
the most noteworthy are summarized: recent concepts such as martingales
and the coupling theory of stochastic variables, queueing networks, scheduling
rules, and the theory of long-range dependent random variables that currently
governs in the Internet. The confinement to stochastic analysis also
excludes the recent new framework, called Network Calculus by Le Boudec
and Thiran (2001). Network calculus is based on min-plus algebra and has
been applied to (Inter)network problems in a deterministic setting.
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