Transient and Busy Period Analysis of the Gi/G/1 Queue: Part II, Solution as a Hilbert Problem (Classic Reprint) - Softcover

Bertsimas, Dimitris J.

Softcover

ISBN 10: 1333735324 ISBN 13: 9781333735326

Verlag: Forgotten Books, 2018

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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.

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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.

Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• ISBN 10: 1333735324
• ISBN 13: 9781333735326
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 26
• Kontakt zum Hersteller: Nicht verfügbar