{"product_id":"large-deviations-for-gaussian-queues-modelling-communication-networks-hardback-9780470015230","title":"Large Deviations for Gaussian Queues; Modelling Communication Networks (Hardback) 9780470015230","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLarge Deviations for Gaussian Queues\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eModelling Communication Networks\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMichel Mandjes (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470015230, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 20 April 2007\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e336 pages\u003cbr\u003e23.5 x 15.8 x 2.6 cm, 0.599 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"The book maybe useful for specialists connected with queuing theory and working in applied probability.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2008)\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eIn recent years the significance of Gaussian processes to communication networks has grown considerably. The inherent flexibility of the Gaussian traffic model enables the analysis, in a single mathematical framework, of systems with both long-range and short-range dependent input streams.  \u003cp\u003e\u003ci\u003eLarge Deviations for Gaussian Queues\u003c\/i\u003e demonstrates how the Gaussian traffic model arises naturally, and how the analysis of the corresponding queuing model can be performed. The text provides a general introduction to Gaussian queues, and surveys recent research into the modelling of communications networks. Coverage includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eDiscussion of the theoretical concepts and practical aspects related to Gaussian traffic models.\u003c\/li\u003e \u003cli\u003eAnalysis of recent research asymptotic results for Gaussian queues, both in the large-buffer and many-sources regime.\u003c\/li\u003e \u003cli\u003eAn emphasis on rare-event analysis, relying on a variety of asymptotic techniques.\u003c\/li\u003e \u003cli\u003eExamination of single-node FIFO queuing systems, as well as queues operating under more complex scheduling disciplines, and queuing networks.\u003c\/li\u003e \u003cli\u003eA set of illustrative examples that directly relate to important practical problems in communication networking.\u003c\/li\u003e \u003cli\u003eA large collection of instructive exercises and accompanying solutions.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eLarge Deviations for Gaussian Queues\u003c\/i\u003e assumes minimal prior knowledge. It is ideally suited for postgraduate students in applied probability, operations research, computer science and electrical engineering. The book’s self-contained style makes it perfect for practitioners in the communications networking industry and for researchers in related areas.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\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\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52255784337688,"sku":"9780470015230","price":84.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470015230.jpg?v=1781274132","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/large-deviations-for-gaussian-queues-modelling-communication-networks-hardback-9780470015230","provider":"Freshly Printed Books","version":"1.0","type":"link"}