Download or read book On the Distributions of Infinite Server Queues With Batch Arrivals written by Andrew Daw and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Queues that feature multiple entities arriving simultaneously are among the oldest models in queueing theory, and are often referred to as "batch" (or, in some cases, "bulk") arrival queueing systems. In this work we study the affect of batch arrivals on infinite server queues. We assume that the arrival epochs occur according to a Poisson process, with treatment of both stationary and non-stationary arrival rates. We consider both exponentially and generally distributed service durations and we analyze both fixed and random arrival batch sizes. In addition to deriving the transient mean, variance, and moment generating function for time-varying arrival rates, we also find that the steady-state distribution of the queue is equivalent to the sum of scaled Poisson random variables with rates proportional to the service distribution of its order statistics. We do so through viewing the batch arrival system as a collection of correlated sub-queues. Furthermore, we investigate the limiting behavior of the process through a batch scaling of the queue and through fluid and diffusion limits of the arrival rate. In the course of our analysis, we make important connections between our model and the Harmonic numbers, generalized Hermite distributions, and truncated polylogarithms.

Download or read book Infinite Server Queues with Batch Arrivals written by Liming Liu and published by . This book was released on 1990 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Some Results for Infinite Server Poisson Queues written by Sheldon M. Ross and published by . This book was released on 1968 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalization of the M/G/infinity queueing system with batch arrivals to one with time dependent arrival rates, service times, and batch size distributions is considered. It is shown that both W(t), the number of people being served at t, and S(t), the number of people who have completed service by t, are distributed as compound Poisson laws. The distributions of the traffic time average (the integral from 0 to T of the quantity W(t)dt)/T and the occupation time 0(t) (the amount of time past t until the system becomes empty, under the assumption that no new customers are served after t) are also derived. The limiting proportion of busy time and the asymptotic behavior of the traffic time average are also discussed in the time homogeneous case. (Author).

Download or read book Recent Developments in Bulk Queueing Models written by Jyotiprasad Medhi and published by . This book was released on 1984 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Single Server Queue written by J.W. Cohen and published by Elsevier. This book was released on 2012-12-02 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work, now available in paperback, concentrates on the basic models of queueing theory. It has a dual aim: to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.

Download or read book The Infinite Server Queue with Poisson Arrivals and Semi markovian Services written by Marcel F. Neuts and published by . This book was released on 1970 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: The queue with an infinite number of servers with a Poisson arrival process and with semi-Markovian service times is considered. The queue length process and the type of the first customer to join the queue after time t are studied jointly and the transient and asymptotic results are obtained which are of matrix extensions of the corresponding results of the M/G/infinity queue. In particular, it is proven that the limiting distribution of the queue length process is Poisson. (Author).

Download or read book Some Inequalities for Single Server Queues written by Kneale Thomas Marshall and published by . This book was released on 1966 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The expected wait in the Gl/G/1 queue is related to the mean and variance of the idle time. For arrival distributions which are IFR or have man residual life bounded by 1/lambda, simple bounds are obtained which give, for example, the expected number in queue to within at most one customer. By equating input with output, relations between random variables are used to obtain expressions for the moments of the waiting time in terms of moments of the inter-arrival, service, and idle time distributions. By bounding the idle time moments, bounds are obtained on the mean and variance of the waiting time, the mean length of a busy period, and the probability an arrival finds the system empty. Bounds on the mean wait lead to bounds on the expected virtual wait. Similar results are obtained for some generalizations of the G1/G/1 queue, including batch arrivals, batch service and priority queues. Queues where the first customer in each busy period has some added delay are also considered. Some preliminary results for tandem queues are given. (Author).

Download or read book From Markov Jump Processes to Spatial Queues written by L. Breuer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Markov Jump Processes to Spatial Queues aims to develop a unified theory of spatial queues that yields concrete results for the performance analysis of mobile communication networks. A particular objective is to develop the most natural generalization of existing concepts (e.g. the BMAP) toward the needs of mobile communication networks. To these belong the spatial distribution of batch arrivals and users in the system as well as time-inhomogeneous (e.g. periodic) arrival intensities and user movements. One of the major recent challenges for the stochastic modelling of communication systems is the emergence of wireless networks, which are used by more and more subscribers today. The main new feature of those, which is not covered by classical queuing theory, clearly is the importance of the user location within the area that is served by the base stations of the network. In the framework of queuing theory, this opens up the natural extension of classical queuing models towards queues with a structured space in which users are served. The present book is intended to introduce this extension under the name of spatial queues. The main point of view and the general approach will be that of Markov jump processes. We start with a closer look into the theory. Then we present new results for the theory of stochastic processes as well as for classical queuing theory. Finally we introduce the new concepts of spatial Markovian arrival processes and spatial queues. The main text is divided into three parts. The first part provides a new presentation of the theory of Markov jump processes. We derive a number of new results, especially for time-inhomogeneous processes, which have been neglected too much in the current textbooks on stochastic processes. For the first time, the class of Markov-additive jump processes is analysed in detail. This extends and unifies all Markovian arrival processes that have been proposed up to now (including arrivals for fluid queues) and provides a foundation for the subsequent introduction of spatial Markovian arrival processes. The second part contains new results for classical queues with BMAP input. These include the first explicit formulae for the distribution of periodic queues. The class of fluid Markovian arrival processes is introduced, and we give statistical estimates for the parameters of a BMAP. In the third part, the concepts of spatial Markovian arrival processes (abbreviated: SMAPs) and spatial queues are introduced. After that, periodic spatial Markovian queues are analysed as a model for the cells of a wireless communication network. From Markov Jump Processes to Spatial Queues is intended to reach queuing theorists, researchers in the field of communication systems, as well as engineers with some background in probability theory. Furthermore, it is suitable as a textbook for advanced queuing theory on the graduate or post-graduate level.

Download or read book Sample Path Analysis of Queueing Systems written by Muhammad El-Taha and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context. The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.

Download or read book Issues in Logic Probability Combinatorics and Chaos Theory 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1039 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book Stochastic Storage Processes written by Narahari U. Prabhu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course I have taught at Cornell University since 1965. The primary topic of this course was queueing theory, but related topics such as inventories, insurance risk, and dams were also included. As a text I used my earlier book, Queues and Inventories (John Wiley, New York, 1965). Over the years the emphasis in this course shifted from detailed analysis of probability models to the study of stochastic processes that arise from them, and the subtitle of the text, "A Study of Their Basic Stochastic Processes," became a more appropriate description of the course. My own research into the fluctuation theory for U:vy processes provided a new perspective on the topics discussed, and enabled me to reorganize the material. The lecture notes used for the course went through several versions, and the final version became this book. A detailed description of my approach will be found in the Introduction. I have not attempted to give credit to authors of individual results. Readers interested in the historical literature should consult the Selected Bibliography given at the end of the Introduction. The original work in this area is presented here with simpler proofs that make full use of the special features of the underlying stochastic processes. The same approach makes it possible to provide several new results. Thanks are due to Kathy King for her excellent typing of the manuscript.

Download or read book Estimation from an Infinite Server Queueing System with Two Demands written by Michael J. Phelan and published by . This book was released on 1987 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Performance Engineering and Stochastic Modeling written by Paolo Ballarini and published by Springer Nature. This book was released on 2021-11-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th European Workshop on Computer Performance Engineering, EPEW 2021, and the 26th International Conference, on Analytical and Stochastic Modelling Techniques and Applications, ASMTA 2021, held in December 2021. The conference was held virtually due to COVID 19 pandemic. The 29 papers presented in this volume were carefully reviewed and selected from 39 submissions. The papers presented at the workshop reflect the diversity of modern performance evaluation, with topics ranging from modeling and analysis of network/control protocols and high performance/big data information systems, analysis of scheduling, blockchain technology, analytical modeling and simulation of computer and network systems.

Download or read book Computations with Markov Chains written by William J. Stewart and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.

Download or read book A First Course in Stochastic Models written by Henk C. Tijms and published by John Wiley and Sons. This book was released on 2003-07-22 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved. Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications. Incorporates recent developments in computational probability. Includes a wide range of examples that illustrate the models and make the methods of solution clear. Features an abundance of motivating exercises that help the student learn how to apply the theory. Accessible to anyone with a basic knowledge of probability. A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.

Download or read book Performance Modeling and Design of Computer Systems written by Mor Harchol-Balter and published by Cambridge University Press. This book was released on 2013-02-18 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written with computer scientists and engineers in mind, this book brings queueing theory decisively back to computer science.

Download or read book Fluctuations of L vy Processes with Applications written by Andreas E. Kyprianou and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.