Haghighi Aliakbar Montazer - Delayed and Network Queues

Copyright 2016 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com.

Library of Congress Cataloging-in-Publication Data:

Names: Haghighi, Aliakbar Montazer, author. | Mishev, D. P. (Dimiter P.), author.

Title: Delayed and network queues / Aliakbar Montazer Haghighi, Prairie View A&M University, member of Texas A&M University System, Prairie View, Texas, USA, Dimitar P. Mishev, Prairie View A&M University, member of Texas A&M University System, Prairie View, Texas.

Description: Hoboken, New Jersey : John Wiley & Sons, 2016. | Includes bibliographical references and index.

Identifiers: LCCN 2016015749 (print) | LCCN 2016020734 (ebook) | ISBN 9781119022138 (cloth) | ISBN 9781119022145 (pdf) | ISBN 9781119022152 (epub)

Subjects: LCSH: Routing (Computer network management)-Mathematics. | Computer networks--Mathematical models. | Telecommunication--Traffic. | Queuing networks (Data transmission)

Classification: LCC TK5105.5487 .H34 2016 (print) | LCC TK5105.5487 (ebook) | DDC 004.601/51982-dc23

LC record available at https://lccn.loc.gov/2016015749

I have always appreciated my lovely wife, Shahin Hamidi, for putting up with me during our about 45 years of marriage. A significant part of what was supposed to be our quality time together, I have squandered in research and publication. Fully aware of her involuntary sacrifice, I have always devoted my scholarly work and achievement to her, along with others.

This volume (my 4th in English Language) is also in her honor which she has consented to gracefully share with my late parents, Roghayyeh Jafari and Mohammad Ali Montazer-Haghighi. I am confident, yet continue to pray, that both remain in the peaceful and merciful hands of the Almighty Allah in whom they lived their lives.

To Allah we belong and to HIM we will return

Aliakbar Montazer Haghighi
Houston, Texas, USA
December 31, 2015

I would like to dedicate the book to my wife, Tatiana, for her patience and encouragement, to my children Elizabeth, Antoan and Ilia, and to my brother Iordan and his family.

Dimitar P. Mishev
Houston, Texas, USA
December 31, 2015

Queueing theory is considered a part of Operations Research, in which the concept of stochastic processes is widely applied. With advancements in manufacturing and production systems, public transportation, logistics, and health care, in this era of technological development made possible by wireless communication and the Internet, performance evaluation of such systems is best accomplished by modeling the system as a network of queues. A network of queues is applied to model a real-world system when a set of resources is shared by some components of the system. Thus, queueing network modeling is a methodology for the analysis of systems such as computer systems. Many examples of networks of queues that appear in our day-to-day lives sometimes go unnoticed. The assembly of an automobile in a car manufacturing plant is a simple example.

In the 1960s, the computer industry was not very aware of the need of queueing network analysis; instead, the time sharing idea was used in the data processing industry. The networks only became fashionable by the end of that decade. New challenges developed in the 1970s and continued when the wireless communication system was studied in the 1980s and has still continued to the present time. By now, the algorithms for evaluating queueing network models are well developed and the mathematical sophistication to analyze systems such as computer systems is not so essential.

However, for long, the networks were based on the assumption of reliable nodes. Breaking down the nodes soon proved the assumption unrealistic in both the Internet and wireless and the industry such as production lines and the automobile industry. This fact is, indeed, a source of delay in the performance analysis of network of queues. This delay is different from the standard waiting time in a service line. Because of the importance of delay that not only affects the time delay but also being an economic factor in a production line, for instance, we have allocated part of to discuss the unreliability of networks.

This book is an attempt to present some queueing models and networks of queues with delay, in a style that is between a monograph and a textbook. We also hope that it will satisfy the need of a handbook for researchers and practitioners.

The principal audience of the book are senior undergraduates, masters and doctorate students, as well as professionals and researchers in the mathematical sciences, stochastic processes, operations research, and engineering. The materials included in the book should also be of interest to those involved in computer network performance analysis. These materials actually instruct the application of queueing network models as tools to assist in the answering of questions on cost and performance that arise throughout the life of a computer system. Our intention is to provide enough information that readers can fully understand the essential aspects of queues with delay and networks of queues with unreliable nodes that may cause delay. We have omitted numerical examples for some models as the development of the fundamentals of models are sufficiently detailed to understand them.

We have included results of some recent research studies to ensure the contents of the book are current enough for all uses.