Elements of Queueing Theory: Palm-Martingale Calculus and Stochastic Recurrences: v.26 (Applications of Mathematics) - Hardcover

Baccelli, F; Bremaud, P.

Hardcover

ISBN 10: 3540533478 ISBN 13: 9783540533474

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1994

Synopsis

This book contains an introduction to general probabilistic methods applicable to queueing systems with ergodic inputs. The main aspects treated are stability (construction of stationary states and convergence theory), time and customer averages (system equations), comparison of service disciplines and priority rules. These include, among other topics, Loynes' theory and its extensions, the basic fomulas (L=*LAMBDA*W, L=*LAMBDA*G, Kleinrock's invariance relations), PASTA, insensitivity, and optimality of SPRT. The originality of the presentation lies in the systematic use of recurrence equations to describe the dynamics of the systems, and of the Palm probability framework to describe the stationary behaviour of such systems. Also, the point of view adopted is purely probabilistic, emphasizing the use of coupling and sample path arguments (ergodic and sub-additive ergodic theory, trajectory realization of stochastic orders). The book contains an introduction on the theory of palm probability on the real line, and shows the various connections with the theory of stochastic intensity.

About this title

Review

From the reviews:

No doubt this textbook will further convince the queueing modeller of the essential importance of point processes and martingale technology.

Paul Embrechts. Short Book Reviews, December 2003

"This book is intended for graduate students and researchers in queuing theory and applied probability. ... Overall this is a well-written text that provides an interesting alternative to more classical approaches. ... The results on stability and other qualitative properties of queues provided by this framework are very general and show the power of this modern approach." (Charles Knessl, SIAM Reviews, Vol. 47 (4), 2005)

"The mathematical treatment in the book is careful and thorough enough that it can be understood by anyone with a reasonable preparation in measure-theoretic probability. ... A particularly useful feature ... is the addition of exercises and problems ... . The strength of this book is the careful and rigorous treatment of the framework and of the mathematical tools that unify and derive classical results and formulae for a number of queuing networks. It can definitely be used as a text at an advanced level." (S. Ramakrishnan, Sankhya, Vol. 66 (2), 2004)

"No doubt this textbook will further convince the queuing modeller of the essential importance of point process and martingale technology. Besides providing an elegant and broad theoretical foundation, the general results obtained allow for straightforward explicit calculations ... . The theory presented is non-trivial ... those who master it will be in the possession of a powerful tool with considerable potential for applied work. ... I take pleasure in recommending this text very highly." (P.A.L. Embrechts, Short Book Reviews, Vol. 23 (3), 2003)

"I am convinced that this second edition will be welcomed in the same way by those who need a source for (comparable) easy access to point process methodology. It is well written, a clear presentation of the topics ... . I find its first edition useful as a reference and a source for new material. And in my view the second edition is clearly an enhanced revision of it. ... the book will be welcomed by everyone interested in the field." (Hans Daduna, Statistical Papers, Vol. 44 (3), 2003)

From the Back Cover

The Palm theory and the Loynes theory of stationary systems are the two pillars of the modern approach to queuing. This book, presenting the mathematical foundations of the theory of stationary queuing systems, contains a thorough treatment of both of these.

This approach helps to clarify the picture, in that it separates the task of obtaining the key system formulas from that of proving convergence to a stationary state and computing its law.

The theory is constantly illustrated by classical results and models: Pollaczek-Khintchin and Tacacs formulas, Jackson and Gordon-Newell networks, multiserver queues, blocking queues, loss systems etc., but it also contains recent and significant examples, where the tools developed turn out to be indispensable.

Several other mathematical tools which are useful within this approach are also presented, such as the martingale calculus for point processes, or stochastic ordering for stationary recurrences.

This thoroughly revised second edition contains substantial additions - in particular, exercises and their solutions - rendering this now classic reference suitable for use as a textbook.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1994
• ISBN 10: 3540533478
• ISBN 13: 9783540533474
• Binding: Hardcover
• Language: English
• Number of pages: 258