A New View of the Heavy-traffic Limit Theorem for Many-server Queues PDF Download

Author: Glynn, Peter W
Publisher:
ISBN:
Category : Limit theorems (Probability theory)
Languages : en
Pages : 34

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Author: J. Michael Harrison
Publisher:
ISBN:
Category :
Languages : en
Pages : 21

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A single server, two priority queueing system is studied under the heavy traffic condition where the system traffic intensity is either at or near its critical value. An approximation is developed for the transient distribution of the low priority customers' virtual waiting time process. This result is stated formally as a limit theorem involving a sequence of systems whose traffic intensities approach the critical value. (Author).

Author: Ward Whitt
Publisher: Springer Science & Business Media
ISBN: 0387217487
Category : Mathematics
Languages : en
Pages : 616

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Book Description
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

Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 1461300053
Category : Mathematics
Languages : en
Pages : 522

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Book Description
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.

Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 272

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Author: Halldóra Thorsdottir
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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"This thesis considers queueing systems affected by a random environment. The behaviour of these queues is studied under specific asymptotic regimes. Embedding a queueing system in a random environment is a way to add flexibility to a model. This flexibility comes at the cost of increased complexity, in that the already stochastic arrival and service processes are also assumed to have randomly fluctuating parameters governed by the external environment. Here, scalings are applied to impose either a central limit theorem (CLT) type of scaling or a heavy traffic scaling. After speeding up the environment that modulates the Poisson arrivals to an infinite server queue, the arrival process is shown to be asymptotically Poisson with a uniform rate, see Chapter 2. By also speeding up the arrival rates, the scaled and centered queue length converges to a normally distributed random variable. The results are extended in Chapter 3 to a multi-dimensional CLT for an M/G/1 queue with Markov-modulation. Chapter 4 contains a functional CLT for the queue length with modulated arrivals using the martingale CLT to prove weak convergence to an OU process, where the environment moves either faster or slower than the arrival process. In Chapter 5, assuming a fairly general class of service disciplines, it is shown that the workload of an M/G/1 queue with modulated service capacity converges to an exponentially distributed random variable in heavy traffic. A special case of the queue is analysed under the discriminatory processor sharing discipline."--Samenvatting auteur.

Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 9780387952642
Category : Mathematics
Languages : en
Pages : 12

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Book Description
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.

Author: George Yin
Publisher: Springer
ISBN: 3030254984
Category : Mathematics
Languages : en
Pages : 599

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Book Description
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Author: Władysław Szczotka
Publisher:
ISBN:
Category : Queuing theory
Languages : en
Pages : 66

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Author: Gideon Weiss
Publisher: Cambridge University Press
ISBN: 1108415326
Category : Business & Economics
Languages : en
Pages : 447

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Book Description
A graduate text on theory and methods using applied probability techniques for scheduling service, manufacturing, and information networks.