Queueing Networks and Product Forms: A Systems ApproachQueueing networks are increasingly used as a tool to evaluate the performance of stochastic service systems such as those arising in various industries. This book, the first presentation and survey of its kind, aims to provide simple, practical insights by which both researchers and practitioners may benefit in enabling them to recognize when closed form expressions can be expected for steady state probabilities. In particular, it shows how these same insights can be used to develop simple bounds for systems that are non-solvable when practical features are taken into account. The presentation is both intuitive and formal and richly illustrated by numerous examples motivated by the above application areas. Its clear style and instructive presentation make this book suitable not only as a textbook for students and researchers but also as a practical guide for professionals. |
Contents
Practical motivation | 1 |
An introduction to partial balance principles | 18 |
Some fundamental tools | 29 |
Copyright | |
9 other sections not shown
Common terms and phrases
applies arbitrary arrival loss probability arriving job assume B₁ blocking breakdowns channels Chapter circuit switching closed-form expressions cluster balance communications computer networks consider CSMA departures Dijk Erlang Erlang distributions example exponentially distributed Figure finite capacity constraint function global balance equations illustrated independent input insensitivity intuitive Jackson network jobs at station lower and upper M₁ manufacturing systems Markov chain metropolitan area networks modification N₁ n₂ normalizing constant Norton's theorem number of jobs obtain overflow servers parameter partial balance Poisson Poisson process practical processor product-form expression product-form results queueing networks random recirculate protocol recycling regular servers reversibility routing probabilities S₁ saturated Section service at station service capacity service rate service speed simple solution source balance source h state-dependent station balance equations steady-state distribution steady-state probabilities stop protocol structures subnetwork t₂ Theorem total number traffic equations transition rates transmission request two-station upper bound verified