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Diffusion Approximation For Tandem Queues In Heavy Traffic
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Book Synopsis Diffusion Approximation for Tandem Queues in Heavy Traffic by : Stanford University. Department of Operations Research
Download or read book Diffusion Approximation for Tandem Queues in Heavy Traffic written by Stanford University. Department of Operations Research and published by . This book was released on 1977 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a pair of single server queues arranged in series. A limit theorem was proved to justify a heavy traffic approximation for the (two-dimensional) equilibrium waiting time distribution. Specifically the waiting time distribution was shown to be approximated by the limit distribution F of a certain vector stochastic process Z. The process Z was defined as an explicit, but relatively complicated, transformation of vector Brownian Motion, and the general problem of determining F was left unsolved. It is shown that Z is a diffusion process (continuous strong Markov process) whose state space S is the non-negative quadrant. On the interior of S, the process behaves as an ordinary vector Brownian Motion, and it reflects instantaneously at each boundary surface (axis). At one axis, the reflection is normal, but at the other axis it has a tangential component as well. The generator of Z is calculated. It is shown that the limit distribution F is the solution of a first passage problem for a certain dual diffusion process Z*. The generator of Z* is calculated, and the analytical theory of Markov process is used to derive a partial differential equation (with boundary conditions) for the density f of F. Necessary and sufficient conditions are found for f to be separable (for the limit distribution to have independent components).
Book Synopsis Diffusion Approximation for a Processor Sharing Queue in Heavy Traffic by : Hans Christian Gromoll
Download or read book Diffusion Approximation for a Processor Sharing Queue in Heavy Traffic written by Hans Christian Gromoll and published by . This book was released on 2001 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Heavy Traffic Analysis of Controlled Queueing and Communication Networks by : Harold Kushner
Download or read book Heavy Traffic Analysis of Controlled Queueing and Communication Networks written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the first books in the timely and important area of heavy traffic analysis of controlled and uncontrolled stochastics networks, by one of the leading authors in the field. The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest.
Book Synopsis Approximate Behavior of Tandem Queues by : G.F. Newell
Download or read book Approximate Behavior of Tandem Queues written by G.F. Newell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following monograph deals with the approximate stochastic behavior of a system consisting of a sequence of servers in series with finite storage between consecutive servers. The methods employ deterministic queueing and diffusion approximations which are valid under conditions in which the storages and the queue lengths are typically large compared with 1. One can disregard the fact that the customer counts must be integer valued and treat the queue as if it were a (stochastic) continuous fluid. In these approximations, it is not necessary to describe the detailed probability distribution of service times; it suffices simply to specify the rate of service and the variance rate (the variance of the number served per unit time). Specifically, customers are considered to originate from an infinite reservoir. They first pass through a server with service rate ~O' vari ance rate ~O' into a storage of finite capacity c . They then pass l through a server with service rate ~l' variance rate ~l' into a storage of capacity c ' etc., until finally, after passing through an nth server, 2 they go into an infinite reservoir (disappear). If any jth storage become , n , the service at the j-lth server is interrupted full j = 1, 2, and, of course, if a jth storage becomes empty the jth server is inter rupted; otherwise, services work at their maximum rate.
Book Synopsis Heavy Traffic Limits for Multiphase Queues by : Fridrikh Izrailevich Karpelevich
Download or read book Heavy Traffic Limits for Multiphase Queues written by Fridrikh Izrailevich Karpelevich and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyzes several types of queueing systems arising in network theory and communication theory. Karpelevich and Kreinin use numerous methods and results from the theory of stochastic processes. The main emphasis is on problems of diffusion approximation of stochastic processes in queueing systems and on results based on applications of the hydrodynamic limit method. The book will be useful to researchers working in the theory and applications of queueing theory and stochastic processes.
Book Synopsis Diffusion Approximation for a Tandem Queue by : Toshikazu Kimura
Download or read book Diffusion Approximation for a Tandem Queue written by Toshikazu Kimura and published by . This book was released on 1981 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Controlled Diffusion Approximations for Controlled Queueing Systems by : Steven Shreve
Download or read book Controlled Diffusion Approximations for Controlled Queueing Systems written by Steven Shreve and published by . This book was released on 1998 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: Four problem areas were studied. These are: (1) controlled heavy traffic queueing systems, (2) queueing systems with due dates, (3) backward-forward stochastic differential equations, and (4) Ginzburg-Landau equations and evolving interfaces. In areas (1) and (2), diffusion approximations were obtained for queues in heavy traffic. In (3), connections were established between quasi-linear partial differential equations and diffusion processes constructed via a new class of stochastic differential equations. Finally, (4) provides a study of the partial differential equation characterizing vortices in superconducting material in three dimensions.
Book Synopsis Analytic Methods in Applied Probability by : Yu. M. Suhov
Download or read book Analytic Methods in Applied Probability written by Yu. M. Suhov and published by American Mathematical Soc.. This book was released on 2002 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to F. I. Karpelevich, an outstanding Russian mathematician who made important contributions to applied probability theory. The book contains original papers focusing on several areas of applied probability and its uses in modern industrial processes, telecommunications, computing, mathematical economics, and finance. It opens with a review of Karpelevich's contributions to applied probability theory and includes a bibliography of his works. Other articles discuss queueing network theory, in particular, in heavy traffic approximation (fluid models). The book is suitable for graduate students, theoretical and applied probabilists, computer scientists, and engineers.
Book Synopsis Probability Towards 2000 by : L. Accardi
Download or read book Probability Towards 2000 written by L. Accardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.
Book Synopsis Weak Convergence Theorems for Queues in Heavy Traffic by : Ward Whitt
Download or read book Weak Convergence Theorems for Queues in Heavy Traffic written by Ward Whitt and published by . This book was released on 1969 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems are proved for unstable queueing systems. The GI/G/1 queue is the primary concern, but the theorems apply to more general systems in which the various independence assumptions are relaxed. Bulk queues, queues with several servers (GI/M/s), queues with a finite waiting room, and dams are also discussed. (Author).
Book Synopsis Stochastic-Process Limits by : Ward Whitt
Download or read book Stochastic-Process Limits written by Ward Whitt and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews
Book Synopsis The Single Server Queue by : J.W. Cohen
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.
Book Synopsis Computer Communications by : American Mathematical Society. Meeting
Download or read book Computer Communications written by American Mathematical Society. Meeting and published by American Mathematical Soc.. This book was released on 1985 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer communications is characterized by rapid technological advances presenting problems of a theoretical nature that are often very difficult to solve. This title constitutes the proceedings of the 1983 AMS Short Course given at Denver, Colorado. It features contributors from a variety of different fields of computer communications.
Book Synopsis Capacity Oriented Analysis and Design of Production Systems by : M.B.M. de Koster
Download or read book Capacity Oriented Analysis and Design of Production Systems written by M.B.M. de Koster and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: In production systems there are often capacity oriented performance objectives, like a desired total throughput, a desired average throughput time and average work in-process. Such performance objectives are expressed in "units of products" rather than in specific product types. This book presents a way of modeling and analyzing production systems so, that such capacity oriented performance criteria can be measured in a simple way. The model consists of three basic elements. 1. The product types in the system are aggregated. 2. The product flow is modeled as being continuous. 3. The machines in the model have a finite number of states. Each state has a phase-type sojourn distribution and an associated production speed. Transitions between the states are determined by an irreducible Markov transition matrix. In the book both the mathematical properties and the practical applicabilities of the model are investigated. The model is extensively analyzed for various layouts, like flow lines, assembly disassembly systems and networks where parallel machines share common buffers. Furthermore various ways of controlling the product flow in the model are investigated, such as Base Stock Control, Workload Control, control by finite buffers and control by the Reorder Point System. An approximation technique is developed for a quick estimation of performance measures like throughput and average work-in-process, for networks with layouts and control techniques like those above-mentioned.
Book Synopsis Stochastic Models in Operations Research by : Daniel P. Heyman
Download or read book Stochastic Models in Operations Research written by Daniel P. Heyman and published by Courier Corporation. This book was released on 2004-01-01 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of a 2-volume set explores the central facts and ideas of stochastic processes, illustrating their use in models based on applied and theoretical investigations. Explores stochastic processes, operating characteristics of stochastic systems, and stochastic optimization. Comprehensive in its scope, this graduate-level text emphasizes the practical importance, intellectual stimulation, and mathematical elegance of stochastic models.
Book Synopsis Perplexing Problems in Probability by : Maury Bramson
Download or read book Perplexing Problems in Probability written by Maury Bramson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harry Kesten has had a profound influence on probability theory for over 30 years. To honour his achievements a number of prominent probabilists have written survey articles on a wide variety of active areas of contemporary probability, many of which are closely related to Kesten's work.
Book Synopsis Queueing Networks in Heavy Traffic by : Martin Ira Reiman
Download or read book Queueing Networks in Heavy Traffic written by Martin Ira Reiman and published by . This book was released on 1977 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principle purpose of this report is to state and prove a limit theorem which justifies a diffusion approximation for general queueing networks. The K-dimensional vector queue length process is investigated for the network. Because of the general form assumed for the interarrival and service distributions, the process has no special structure such as the Markov property. In this generality, the network has proven to be intractable, hence the desire for an approximation. It is possible to define a traffic intensity for each station in the network. Heavy traffic is said to hold when all stations have traffic intensities close to unity. Mathematically, heavy traffic is interpreted through consideration of a sequence of queueing networks indexed (say) by n, each with its own parameters, defined in such a way that the traffic intensity of each station approaches unity as n approaches infinity. The state space of the limit process is the K-dimensional non-negative orthant. On the interior of its state space the process behaves as a multidimensional Brownian motion with an easily computed drift vector and covariance matrix. At each boundary surface the process reflects instantaneously. The directions of reflection are given by a simple expression involving only the routing matrix. After proving that the limit process is a diffusion, its generator is computed, justifying the above description.
