Stochastic networks and queues

Philippe Robert

416 pages, parution le 02/07/2003

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Résumé

Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks.

In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.

Point processes
GI/GI/1 FIFO Queues and random walks
Limit theorems for GI/GI/1 Queues
Stochastic networks and reversibility
The M/M/1 Queue
The M/M/&#8734 Queue
Queues with poisson arrivals
Recurrence and transience of Markov chains
Rescaled Markov processes and fluid limits
Ergodic theory : basic results
Stationary point processes
The GI/GI/1 FIFO Queue
Martingales
Markovian jump processes
Convergence in distribution
An introduction to Skorohod problems

References
Research papers
Index

L'auteur - Philippe Robert

Robert, P., INRIA, Le Chesnay, France

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Philippe Robert
Parution	02/07/2003
Nb. de pages	416
Format	16 x 24
Couverture	Relié
Poids	740g
Intérieur	Noir et Blanc
EAN13	9783540006572