Large deviations for Gaussian queues: Modelling communication networks.

*(English)*Zbl 1125.60103
Chichester: John Wiley & Sons (ISBN 978-0-470-01523-0/hbk; 978-0-470-51509-9/ebook). x, 326 p. (2007).

The significance of Gaussian processes has grown considerably, since the flexibility of the Gaussian traffic model gives the possibility for the analysis of systems with both long-range and short-range dependent input streams. The book provides a general introduction to Gaussian queues and surveys recent results in the modelling of communication networks.

The first part has introductory nature, it defines the basic concepts by focusing on two topics. It introduces the notion of Gaussian traffic and explains why, under rather general circumstances, the Gaussian model offers an accurate description of network traffic. The second topic is large deviations, it is the main tool to probabistically analyze rare events.

In the second part of the book, large deviations results (in particular CramĂ©r’s and Schilder’s theorems) are used to examine overflow behavior of queues with Gaussian input. The emphasis is on many-sources scaling. One chapter deals with the single queues, the larger part is devoted to the ones with more complicated structure: tandem queues, priority queues and operating queues under generalized processor sharing. For these systems, relying mainly on Schilder’s theorem, the many-sources asymptotics are explicitly identified, for the special cases of Gaussian inputs with a weak-dependence structure and with even independent increments closed-form expressions are derived.

The remaining chapters illustrate how Gaussian queues can be applied in a number of networking examples. One chapter studies the weight-setting problem arising in generalized processor sharing. Two chapters are about link dimensioning and the last one focuses on bandwidth trading.

The book may be useful for specialists connected with queueing theory and working in applied probability, operations research, computer science and electrical engineering.

The first part has introductory nature, it defines the basic concepts by focusing on two topics. It introduces the notion of Gaussian traffic and explains why, under rather general circumstances, the Gaussian model offers an accurate description of network traffic. The second topic is large deviations, it is the main tool to probabistically analyze rare events.

In the second part of the book, large deviations results (in particular CramĂ©r’s and Schilder’s theorems) are used to examine overflow behavior of queues with Gaussian input. The emphasis is on many-sources scaling. One chapter deals with the single queues, the larger part is devoted to the ones with more complicated structure: tandem queues, priority queues and operating queues under generalized processor sharing. For these systems, relying mainly on Schilder’s theorem, the many-sources asymptotics are explicitly identified, for the special cases of Gaussian inputs with a weak-dependence structure and with even independent increments closed-form expressions are derived.

The remaining chapters illustrate how Gaussian queues can be applied in a number of networking examples. One chapter studies the weight-setting problem arising in generalized processor sharing. Two chapters are about link dimensioning and the last one focuses on bandwidth trading.

The book may be useful for specialists connected with queueing theory and working in applied probability, operations research, computer science and electrical engineering.

Reviewer: Laszlo Lakatos (Budapest)

##### MSC:

60K25 | Queueing theory (aspects of probability theory) |

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

90B18 | Communication networks in operations research |

90B22 | Queues and service in operations research |

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

60F10 | Large deviations |