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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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