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The book is composed of two main parts: mathematical background and
queueing systems with applications. The mathematical background is
a self containing introduction to the stochastic processes of the
later studies queueing systems. It starts with a quick introduction
to probability theory and stochastic processes and continues with
chapters on Markov chains and regenerative processes. More recent
advances of queueing systems are based on phase type distributions,
Markov arrival processes and quasy birth death processes, which are
introduced in the last chapter of the first part. The second part
is devoted to queueing models and their applications. After the
introduction of the basic Markovian (from M/M/1 to M/M/1//N) and
non-Markovian (M/G/1, G/M/1) queueing systems, a chapter presents
the analysis of queues with phase type distributions, Markov
arrival processes (from PH/M/1 to MAP/PH/1/K). The next chapter
presents the classical queueing network results and the rest of
this part is devoted to the application examples. There are
queueing models for bandwidth charing with different traffic
classes, slotted multiplexers, ATM switches, media access protocols
like Aloha and IEEE 802.11b, priority systems and retrial systems.
An appendix supplements the technical content with Laplace and z
transformation rules, Bessel functions and a list of notations. The
book contains examples and exercises throughout and could be used
for graduate students in engineering, mathematics and sciences.
"Et moi, ..., si j'avait su comment en revenir, je One service
mathematics bas rendered the human race. It bas put common sense
back n'y serais point all .' where it belongs, on the topmost shelf
next to lu1esVeme the dusty canister labelled 'discarded nonsense'
Eric T. Bell 1be series is divergent; therefore we may be able to
do something with it O. Heaviside Mathematics is a tool for
thought. A highly necessary tool in a world where both feedback and
nonlineari ties abound. Similarly, all kinds of parts of
mathematics serve as tools for other parts and for other sci ences.
Applying a simple rewriting rule to the quote on the right above
one finds such statements as: 'One ser vice topology has rendered
mathematical physics ... '; 'One service logic has rendered
computer science .. .'; 'One service category theory has rendered
mathematics .. .'. All arguably true. And all statements obtainable
this way form part of the raison d 'etre of this series."
"Et moi, ..., si j'avait su comment en revenir, je One service
mathematics bas rendered the human race. It bas put common sense
back n'y serais point all~.' where it belongs, on the topmost shelf
next to lu1esVeme the dusty canister labelled 'discarded nonsense'~
Eric T. Bell 1be series is divergent; therefore we may be able to
do something with it O. Heaviside Mathematics is a tool for
thought. A highly necessary tool in a world where both feedback and
nonlineari- ties abound. Similarly, all kinds of parts of
mathematics serve as tools for other parts and for other sci-
ences. Applying a simple rewriting rule to the quote on the right
above one finds such statements as: 'One ser- vice topology has
rendered mathematical physics ...'; 'One service logic has rendered
computer science ...'; 'One service category theory has rendered
mathematics ...'. All arguably true. And all statements obtainable
this way form part of the raison d 'etre of this series.
The book is the extended and revised version of the 1st edition and
is composed of two main parts: mathematical background and queueing
systems with applications. The mathematical background is a
self-containing introduction to the stochastic processes of the
later studied queueing systems. It starts with a quick introduction
to probability theory and stochastic processes and continues with
chapters on Markov chains and regenerative processes. More recent
advances of queueing systems are based on phase type distributions,
Markov arrival processes and quasy birth death processes, which are
introduced in the last chapter of the first part. The second part
is devoted to queueing models and their applications. After the
introduction of the basic Markovian (from M/M/1 to M/M/1//N) and
non-Markovian (M/G/1, G/M/1) queueing systems, a chapter presents
the analysis of queues with phase type distributions, Markov
arrival processes (from PH/M/1 to MAP/PH/1/K). The next chapter
presents the classical queueing network results and the rest of
this part is devoted to the application examples. There are
queueing models for bandwidth charing with different traffic
classes, slotted multiplexers, media access protocols like Aloha
and IEEE 802.11b, priority systems and retrial systems. An appendix
supplements the technical content with Laplace and z transformation
rules, Bessel functions and a list of notations. The book contains
examples and exercises throughout and could be used for graduate
students in engineering, mathematics and sciences. Reviews of first
edition: "The organization of the book is such that queueing models
are viewed as special cases of more general stochastic processes,
such as birth-death or semi-Markov processes. ... this book is a
valuable addition to the queuing literature and provides
instructors with a viable alternative for a textbook to be used in
a one- or two-semester course on queueing models, at the upper
undergraduate or beginning graduate levels." Charles Knessl, SIAM
Review, Vol. 56 (1), March, 2014
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