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Author: J. Michael Harrison Publisher: ISBN: Category : Languages : en Pages : 21
Book Description
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: J. Michael Harrison Publisher: ISBN: Category : Languages : en Pages : 21
Book Description
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: Harold Kushner Publisher: Springer Science & Business Media ISBN: 1461300053 Category : Mathematics Languages : en Pages : 522
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: Ward Whitt Publisher: ISBN: Category : Queuing theory Languages : en Pages : 436
Book Description
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).
Author: Martin Ira Reiman Publisher: ISBN: Category : Limit theorems (Probability theory) Languages : en Pages : 114
Book Description
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.
Author: Harold Kushner Publisher: Springer Science & Business Media ISBN: 9780387952642 Category : Mathematics Languages : en Pages : 12
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: J. Michael Harrison
Author: J. Michael Harrison
Author: John Allen Hooke
Author: Sanjay Mithal
Author: Harold Kushner
Author: Ward Whitt
Author: Luiz Felipe Martins
Author: Martin Ira Reiman
Author: International Business Machines Corporation. Research Division
Author: Sreekantan S. Nair
Author: Harold Kushner