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Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II, Solution as a Hilbert Problem (Classic Reprint) - Tapa blanda
Sinopsis
Excerpt from Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II, Solution as a Hilbert Problem
In this subsection we define the random variables and establish the notation we are using. We assume that the system is initially idle and the first customer's arriving time is the forward recurrence interarrival time. Although this assumption is restrictive for the waiting time distribution, it is not restrictive for the busy period distribution, since the busy period regenerates.
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Excerpt from Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II, Solution as a Hilbert Problem
In this subsection we define the random variables and establish the notation we are using. We assume that the system is initially idle and the first customer's arriving time is the forward recurrence interarrival time. Although this assumption is restrictive for the waiting time distribution, it is not restrictive for the busy period distribution, since the busy period regenerates.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Excerpt from Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II, Solution as a Hilbert Problem
In the first part of this work (bertsimas and Nakazato we presented a method to perform transient and busy period analysis for the mgel/mgem/l queue, where mge is the class of mixed generalized Erlang distributions. Our analysis used the method of stages combined with the separation of variables and root finding techniques together with linear and tensor algebra. We found simple closed form expressions for the Laplace transforms of the queue length and the waiting time distribution under fcfs when the system is initially empty and the busy period distribution. In this paper we extend and generalize these results to the gi/g/l queue with arbitrary distributions. We first formulate the problem as a two di mensional Lindley process and then transform it to a Hilbert factorization problem. We are able to solve explicitly the underlying factorization problem for the cases of gi/r/l and r/g/l queues, where R is the class of distributions with ratio nal Laplace transforms. As a result, we find closed form formulae for the Laplace transforms of the waiting time and busy period distribution.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Transient and Busy Period Analysis of the GiG1 Queue Part II, Solution as a Hilbert Problem Classic Reprint
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781333735326
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Transient and Busy Period Analysis of the GiG1 Queue Part II, Solution as a Hilbert Problem Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781333735326
Cantidad disponible: 15 disponibles
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Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II
Impresión bajo demandaLibrería: Forgotten Books, London, Reino Unido
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Paperback. Condición: New. Print on Demand. This book contributes to the fields of probability theory and queueing theory by presenting a mathematically rigorous approach to analyzing the transient behavior of the GI/G/1 queue. The GI/G/1 queue represents a queue with general inter-arrival times and general service times. By formulating the problem as a two-dimensional Lindley process and transforming it to a Hilbert factorization problem, the author derives closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. These results extend and generalize previous findings for specific queueing models and provide valuable insights into the behavior of queues with arbitrary distributions. The author employs advanced mathematical techniques, including the method of stages, separation of variables, root finding, and linear and tensor algebra, to achieve these solutions. The book is suitable for researchers, graduate students, and practitioners in the fields of operations research, applied probability, and queueing theory who seek a comprehensive understanding of transient queueing analysis. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781333735326_0
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TRANSIENT & BUSY PERIOD ANALYS
Librería: moluna, Greven, Alemania
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Condición: New. KlappentextrnrnExcerpt from Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II, Solution as a Hilbert ProblemIn this subsection we define the random variables and establish the notation we are using. We assume that the syste. Nº de ref. del artículo: 2148078298
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