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Author: Krzysztof Dębicki
Publisher: Springer
ISBN: 3319206931
Category : Mathematics
Languages : en
Pages : 256
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Book Description
The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
Author: Krzysztof Dębicki
Publisher: Springer
ISBN: 3319206931
Category : Mathematics
Languages : en
Pages : 256
Get Book Here
Book Description
The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
Author: Andreas E. Kyprianou
Publisher: Springer Science & Business Media
ISBN: 3540313435
Category : Mathematics
Languages : en
Pages : 382
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Book Description
This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness.
Author: Jean Bertoin
Publisher: Cambridge University Press
ISBN: 9780521562430
Category : Mathematics
Languages : en
Pages : 275
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Book Description
This is an up-to-date and comprehensive account of the theory of Lévy processes. This branch of modern probability theory has been developed over recent years and has many applications in such areas as queues, mathematical finance and risk estimation. Professor Bertoin has used the powerful interplay between the probabilistic structure (independence and stationarity of the increments) and analytic tools (especially Fourier and Laplace transforms) to give a quick and concise treatment of the core theory, with the minimum of technical requirements. Special properties of subordinators are developed and then appear as key features in the study of the local times of real-valued Lévy processes and in fluctuation theory. Lévy processes with no positive jumps receive special attention, as do stable processes. In sum, this will become the standard reference on the subject for all working probability theorists.
Author: Andreas E. Kyprianou
Publisher:
ISBN: 9783642376337
Category :
Languages : en
Pages : 476
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Book Description
Author: Lajos Takács
Publisher: Praeger
ISBN:
Category : Business & Economics
Languages : en
Pages : 292
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Book Description
This book is an introduction to the probabilistic treatment of mass servicing. It deals with different theoretical models which can be applied to the servicing of telephone traffic, airplane operation, road traffic, storage, operation of dams, and customer service.
Author: Ronald A. Doney
Publisher: École d'Été de Probabilités de Saint-Flour
ISBN:
Category : Mathematics
Languages : en
Pages : 168
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Book Description
Lévy processes, i.e. processes in continuous time with stationary and independent increments, are named after Paul Lévy, who made the connection with infinitely divisible distributions and described their structure. They form a flexible class of models, which have been applied to the study of storage processes, insurance risk, queues, turbulence, laser cooling, ... and of course finance, where the feature that they include examples having "heavy tails" is particularly important. Their sample path behaviour poses a variety of difficult and fascinating problems. Such problems, and also some related distributional problems, are addressed in detail in these notes that reflect the content of the course given by R. Doney in St. Flour in 2005.
Author: Alexandr Borovkov
Publisher: Springer Science & Business Media
ISBN: 1461298660
Category : Mathematics
Languages : en
Pages : 291
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Book Description
The object of queueing theory (or the theory of mass service) is the investigation of stochastic processes of a special form which are called queueing (or service) processes in this book. Two approaches to the definition of these processes are possible depending on the direction of investigation. In accordance with this fact, the exposition of the subject can be broken up into two self-contained parts. The first of these forms the content of this monograph. . The definition of the queueing processes (systems) to be used here is dose to the traditional one and is connected with the introduction of so-called governing random sequences. We will introduce algorithms which describe the governing of a system with the aid of such sequences. Such a definition inevitably becomes rather qualitative since under these conditions a completely formal construction of a stochastic process uniquely describing the evolution of the system would require introduction of a complicated phase space not to mention the difficulties of giving the distribution of such a process on this phase space.
Author: Gordon Frank Newell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 170
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Book Description
Fluid approximations; Simple queueing systems; Stochastic models; Equilibrium distributions; Diffusion approximations; Time-dependent queues; Neglected subjects.
Author: K Gunavathi
Publisher: S. Chand Publishing
ISBN: 8121923565
Category : Mathematics
Languages : en
Pages : 571
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Book Description
Common to CSE and IT for all Anna Universities
Author: Natarajan Gautam
Publisher: CRC Press
ISBN: 1439806586
Category : Business & Economics
Languages : en
Pages : 804
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Book Description
Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples. In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.
