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Author: Krzysztof Dębicki Publisher: Springer ISBN: 3319206931 Category : Mathematics Languages : en Pages : 256
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
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
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
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: Publisher: ISBN: Category : Languages : en Pages : 127
Book Description
"The main objective of this thesis is to develop numerical techniques to calculate the probability distribution of the running maximum of Lévy processes, and consider a number of specific financial applications. The other objective is to propose a numerical method to optimize the energy consumption of servers handling traffic in a communication network. The traffic itself is modeled by a random process, usually an on-off process with random on- and off-times. In this thesis, a numerical technique based on the Wiener-Hopf factorization is developed to evaluate the probability distribution of the running maximum (or minimum) of a general Lévy process. This method can be employed for pricing many options which depend on the maximum and/or minimum attained by the underlying Lévy process, for instance lookback option. The second technique which is presented in this book is importance sampling. This technique is essentially used to reduce the variance of the simulation-based estimator. Straightforward simulation for estimating rare event probabilities being inefficient and inaccurate, the idea of importance sampling is to generate simulation paths under an alternative measure such that the event is not rare anymore. Energy-aware processors are intended to operate efficiently by adapting the speed of the server CPU to the processing load and the service level requirement. In this thesis, we consider a performance objective which is a linear combination of energy usage, queuing cost (reflected by delay) and speed switching cost for a multi-core processor. We discuss several schemes that lead to energy consumption reduction."--Samenvatting auteur.
Author: Soeren Asmussen Publisher: Springer Science & Business Media ISBN: 0387215255 Category : Mathematics Languages : en Pages : 451
Book Description
"This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory....The second edition at hand is a thoroughly updated and considerably expended version of the first edition.... This book and the way the various topics are balanced are a welcome addition to the literature. It is an indispensable source of information for both advanced graduate students and researchers." --MATHEMATICAL REVIEWS
Author: Andreas E. Kyprianou Publisher: Springer Science & Business Media ISBN: 3642376320 Category : Mathematics Languages : en Pages : 461
Book Description
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. 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 tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.
Author: Alexandr Borovkov Publisher: Springer Science & Business Media ISBN: 1461298660 Category : Mathematics Languages : en Pages : 291
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: Lajos Takács Publisher: Praeger ISBN: Category : Business & Economics Languages : en Pages : 292
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: Natarajan Gautam Publisher: CRC Press ISBN: 1439806586 Category : Business & Economics Languages : en Pages : 804
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.
Author: Krzysztof Dębicki
Author: Krzysztof Dębicki
Author: Andreas E. Kyprianou
Author: Jean Bertoin
Author: 
Author: Soeren Asmussen
Author: Andreas E. Kyprianou
Author: Alexandr Borovkov
Author: Lajos Takács
Author: Robert B. Cooper
Author: Natarajan Gautam