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 | 16 |
Some fundamental tools | 29 |
16 | 42 |
Copyright | |
8 other sections not shown
Common terms and phrases
applies arbitrary assume breakdowns channels Chapter circuit switching closed-form expressions cluster balance communications computer networks consider CSMA cyclic delay departures Dijk Engset equivalence Erlang Erlang distributions example exponential service exponentially distributed factor Figure finite capacity constraint formal function global balance equations idle illustrated input insensitivity intuitive Jackson network jobs at station loss probability M₁ manufacturing systems Markov chain metropolitan area networks n₁ n₂ node normalizing constant Norton's theorem number of jobs obtain overflow servers parameter parameterization partial balance Poisson Poisson process practical processor product-form expression product-form results queueing networks random recirculate protocol recycling reversibility routing probabilities s₁ satisfied 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 verified