{"product_id":"large-deviations-for-gaussian-modelling-communication-networks-9780470015230","title":"Large Deviations for Gaussian Modelling","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book describes how modern queuing theory can be applied to problems in telecommunication engineering. It starts with a survey of the essential theory behind Gaussian processes, large deviations, and queuing theory and then introduces the idea of a traffic processes in communication systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The book maybe useful for specialists connected with queuing theory and working in applied probability.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2008)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface and acknowledgments.  \u003cp\u003e1 Introduction.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart A: Gaussian traffic and large deviations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The Gaussian source model.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Modeling network traffic.\u003c\/p\u003e \u003cp\u003e2.2 Notation and preliminaries on Gaussian random variables.\u003c\/p\u003e \u003cp\u003e2.3 Gaussian sources.\u003c\/p\u003e \u003cp\u003e2.4 Generic examples-long-range dependence and smoothness.\u003c\/p\u003e \u003cp\u003e2.5 Other useful Gaussian source models.\u003c\/p\u003e \u003cp\u003e2.6 Applicability of Gaussian source models for network traffic.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Gaussian sources: validation, justification.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Validation.\u003c\/p\u003e \u003cp\u003e3.2 Convergence of on-off traffic to a Gaussian process.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Large deviations for Gaussian processes.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Cram´er's theorem.\u003c\/p\u003e \u003cp\u003e4.2 Schilder's theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart B: Large deviations of Gaussian queues.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Gaussian queues: an introduction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Lindley's recursion, the steady-state buffer content.\u003c\/p\u003e \u003cp\u003e5.2 Gaussian queues.\u003c\/p\u003e \u003cp\u003e5.3 Special cases: Brownian motion and Brownian bridge.\u003c\/p\u003e \u003cp\u003e5.4 A powerful approximation.\u003c\/p\u003e \u003cp\u003e5.5 Asymptotics.\u003c\/p\u003e \u003cp\u003e5.6 Large-buffer asymptotics.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Logarithmic many-sources asymptotics.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Many-sources asymptotics: the loss curve.\u003c\/p\u003e \u003cp\u003e6.2 Duality between loss curve and variance function.\u003c\/p\u003e \u003cp\u003e6.3 The buffer-bandwidth curve is convex.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Exact many-sources asymptotics.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Slotted time: results.\u003c\/p\u003e \u003cp\u003e7.2 Slotted time: proofs.\u003c\/p\u003e \u003cp\u003e7.3 Continuous time: results.\u003c\/p\u003e \u003cp\u003e7.4 Continuous time: proofs.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Simulation.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Determining the simulation horizon.\u003c\/p\u003e \u003cp\u003e8.2 Importance sampling algorithms.\u003c\/p\u003e \u003cp\u003e8.3 Asymptotic efficiency.\u003c\/p\u003e \u003cp\u003e8.4 Efficient estimation of the overflow probability.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Tandem and priority queues.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Tandem: model and preliminaries.\u003c\/p\u003e \u003cp\u003e9.2 Tandem: lower bound on the decay rate.\u003c\/p\u003e \u003cp\u003e9.3 Tandem: tightness of the decay rate.\u003c\/p\u003e \u003cp\u003e9.4 Tandem: properties of the input rate path.\u003c\/p\u003e \u003cp\u003e9.5 Tandem: examples.\u003c\/p\u003e \u003cp\u003e9.6 Priority queues.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Generalized processor sharing.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Preliminaries on GPS.\u003c\/p\u003e \u003cp\u003e10.2 Generic upper and lower bound on the overflow probability.\u003c\/p\u003e \u003cp\u003e10.3 Lower bound on the decay rate: class 2 in underload.\u003c\/p\u003e \u003cp\u003e10.4 Upper bound on the decay rate: class 2 in underload.\u003c\/p\u003e \u003cp\u003e10.5 Analysis of the decay rate: class 2 in overload.\u003c\/p\u003e \u003cp\u003e10.6 Discussion of the results.\u003c\/p\u003e \u003cp\u003e10.7 Delay asymptotics.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Explicit results for short-range dependent inputs.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Asymptotically linear variance; some preliminaries.\u003c\/p\u003e \u003cp\u003e11.2 Tandem queue with srd input.\u003c\/p\u003e \u003cp\u003e11.3 Priority queue with srd input.\u003c\/p\u003e \u003cp\u003e11.4 GPS queue with srd input.\u003c\/p\u003e \u003cp\u003e11.5 Concluding remarks.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Brownian queues.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Single queue: detailed results.\u003c\/p\u003e \u003cp\u003e12.2 Tandem: distribution of the downstream queue.\u003c\/p\u003e \u003cp\u003e12.3 Tandem: joint distribution.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart C: Applications.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Weight setting in GPS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 An optimal partitioning approach to weight setting.\u003c\/p\u003e \u003cp\u003e13.2 Approximation of the overflow probabilities.\u003c\/p\u003e \u003cp\u003e13.3 Fixed weights.\u003c\/p\u003e \u003cp\u003e13.4 Realizable region.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 A link dimensioning formula and empirical support.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Objectives, modeling, and analysis.\u003c\/p\u003e \u003cp\u003e14.2 Numerical study.\u003c\/p\u003e \u003cp\u003e14.3 Empirical study.\u003c\/p\u003e \u003cp\u003e14.4 Implementation aspects.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Link dimensioning: indirect variance estimation.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Theoretical foundations.\u003c\/p\u003e \u003cp\u003e15.2 Implementation issues.\u003c\/p\u003e \u003cp\u003e15.3 Error analysis of the inversion procedure.\u003c\/p\u003e \u003cp\u003e15.4 Validation.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 A framework for bandwidth trading.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Bandwidth trading.\u003c\/p\u003e \u003cp\u003e16.2 Model and preliminaries.\u003c\/p\u003e \u003cp\u003e16.3 Single-link network.\u003c\/p\u003e \u003cp\u003e16.4 Gaussian traffic; utility as a function of loss.\u003c\/p\u003e \u003cp\u003e16.5 Sanov's theorem and its inverse.\u003c\/p\u003e \u003cp\u003e16.6 Estimation of loss probabilities.\u003c\/p\u003e \u003cp\u003e16.7 Numerical example.\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402254229847,"sku":"9780470015230","price":101.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470015230.jpg?v=1730479846","url":"https:\/\/bookcurl.com\/products\/large-deviations-for-gaussian-modelling-communication-networks-9780470015230","provider":"Book Curl","version":"1.0","type":"link"}