## Queueing Networks and Product Forms: A Systems ApproachUses a theoretical and practical approach to evaluate the performance of a system when a product form can be concluded--for instance, to compare the system under diverse workloads or parameter values or to determine by which system protocols a product form expression is violated so that further numerical or approximate computations can be developed. Contains numerous examples drawn from applications. |

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### Contents

Practical motivation | 1 |

An introduction to partial balance principles | 18 |

Some fundamental tools | 29 |

Copyright | |

5 other sections not shown

### Common terms and phrases

applies arbitrary arriving job assume breakdowns channels Chapter circuit switching closed-form expressions cluster balance computer networks consider CSMA delay departures Dijk Engset equivalence Erlang Erlang distributions exponential service exponentiality assumptions exponentially distributed factor Figure finite capacity constraint formal function global balance equations Hordijk idle illustrated individual stations input intuitive Jackson network jobs at station loss probability manufacturing systems Markov chain metropolitan area networks 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 recirculate protocol Reconsider recycling reversibility routing probabilities satisfied saturated scheduling Section service at station service capacity service rate service speed set of admissible simple solution source balance source h station balance equations station balance relations steady-state distribution steady-state probabilities stop protocol structures subnetwork substituting Theorem total number traffic equations transition rates transmission request two-station verified