ENGLISH

Elements of Queuing Theory: Palm-Martingale Calculus and Stochastic Recurrences (Applications of Mathematics)

By Francois Baccelli , Pierre Bremaud

Book information

Publisher
Springer-Verlag Telos
Year
1994
ISBN
9780387533476, 3540533478, 0387533478
LCC
QA274.8 .B33 1994
Open Library ID
OL1429941M
Language
english
Format
PDF
Filesize
30 MB (30970520 bytes)
Series
Applications of Mathematics
Pages
134\134
Time added
2010-05-31 15:29:46

Description

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.

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