Multiple Channel Queues in Heavy Traffic, II: Sequences, Networks, and Batches
Multiple Channel Queues in Heavy Traffic, II: Sequences, Networks, and Batches

Author: Stanford University. Applied Mathematics and Statistics Laboratory

Publisher:

Published: 1969

Total Pages: 38

ISBN-13:

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Sequences of queueing facilities with r parallel arrival channels and s parallel service channels are studied under the conditions of heavy traffic: the associated sequences of traffic intensities approaching a limit greater than or equal to one. Weak convergence is obtained for sequences of random functions induced in D(0,1) by the basic queueing processes. Sequences of queueing systems in heavy traffic which are networks of the facilities described above are also investigated. Furthermore, customers are allowed to arrive and be served in batches.

Heavy Traffic Analysis of Controlled Queueing and Communication Networks
Heavy Traffic Analysis of Controlled Queueing and Communication Networks

Author: Harold Kushner

Publisher: Springer Science & Business Media

Published: 2013-11-21

Total Pages: 522

ISBN-13: 1461300053

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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.

Multiple Channel Queues in Heavy Traffic, IV: Law of the Iterated Logarithm
Multiple Channel Queues in Heavy Traffic, IV: Law of the Iterated Logarithm

Author: Stanford University. Department of Operations Research

Publisher:

Published: 1969

Total Pages: 56

ISBN-13:

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The queueing system considered consist of r. independent arrival channels and s independent service channels. These systems are assumed to be in heavy traffic, that is, the traffic intensity is greater than or equal to 1. Functional laws of the iterated logarithm are obtained for the queue length, departure, load, and waiting time processes. As immediate corollaries, the ordinary laws of the iterated logarithm are obtained for these processes. Finally, as an application of the functional law of the iterated logarithm, a limit theorem is obtained for the fraction of time the queue length process is above a given function. (Author).

Mathematical Methods in Queueing Theory
Mathematical Methods in Queueing Theory

Author: A. B. Clarke

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 371

ISBN-13: 3642808387

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On May 10-12, 1973 a Conference on Mathematical Methods in Graph Theory was held at Western Michigan University in Kalamazoo. The theme of this Conference was recent advances in the application of analytic and algebraic methods to the analysis of queues and queueing networks. In addition some discussion was given to statistical analy ses in queues, control problems and graphical methods. A total of 83 individuals from both industry and academic estab lishments participated in the Conference. A list of these partici pants can be found on page 373. A total of 18 papers were presented, with sUbstantial time being devoted to their informal discussion. This volume constitutes the proceedings of the Conference, and includes all papers presented. TABLE OF CONTENTS MARCEL F. NEUTS The Markov Renewal Branching Process • 1 RALPH L. DISNEY and W. PETER CHERRY Some Topics in Queueing Network Theory 23 JULIAN KEILSON Convexity and Complete Monotonicity in Queueing Distributions and Associated Limit Behavior . • • • • • . . • • • •• • • 45 G. F. NEWELL Graphical Representation of Queue Evolution for Multiple-Server Systems • . • • • • • • • • • • 63 N. U. PRABHU Wiener-Hopf Techniques in Queueing Theory 81 / IAJOS TAKACS Occupation Time Problems in the Theory of Queues 91 TAPAN P. BAGCHI and J. G. C. TEMPLETON Some Finite waiting Space Bulk Queueing Systems 133 U.

Applied and Computational Control, Signals, and Circuits
Applied and Computational Control, Signals, and Circuits

Author: Biswa Nath Datta

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 298

ISBN-13: 1461514711

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Applied and Computational Control, Signals, and Circuits: Recent Developments is an interdisciplinary book blending mathematics, computational mathematics, scientific computing and software engineering with control and systems theory, signal processing, and circuit simulations. The material consists of seven state-of-the-art review chapters, each written by a leading expert in that field. Each of the technical chapters deals exclusively with some of the recent developments involving applications and computations of control, signals and circuits. Also included is a Chapter focusing on the newly developed Fortran-based software library, called SLICOT, for control systems design and analysis. This collection will be an excellent reference work for research scientists, practicing engineers, and graduate level students of control and systems, circuit design, power systems and signal processing.

Performance Analysis of ATM Networks
Performance Analysis of ATM Networks

Author: Demetres D. Kouvatsos

Publisher: Springer

Published: 2013-06-05

Total Pages: 573

ISBN-13: 0387353534

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Over recent years, a considerable amount of effort has been devoted, both in industry and academia, towards the performance modelling, evaluation and prediction of Asynchronous Transfer Mode (ATM) networks. This book describes recent advances in ATM networks reflecting the state-of-the-art technology and research achievements worldwide. In addition, it provides a fundamental source of reference in the ATM field. Research topics discussed in detail include: Traffic Modelling and Characterisation; Routing; Switch and Multiplexer Models; Call Admission Control (CAC); Congestion Control; Resource Allocation; Quality of Service (QoS); Tools and Techniques. This volume contains recently extended refereed papers of the 5th International Workshop on Performance Modelling and Evaluation of ATM Networks, which was sponsored by the International Federation for Information Processing (IFIP) and held in Ilkley, UK in July 1997. Performance Analysis of ATM Networks continues the tradition established by the first three IFIP volumes on the subject, and it is ideal for personnel in computer/communication industries as well as academic and research staff in computer science and electrical engineering.

Diffusion Approximation for Tandem Queues in Heavy Traffic
Diffusion Approximation for Tandem Queues in Heavy Traffic

Author: Stanford University. Department of Operations Research

Publisher:

Published: 1977

Total Pages: 42

ISBN-13:

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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).