To Queue or Not to Queue

The literature on equilibrium behavior of customers and servers in queuing systems is rich. However, there is no comprehensive survey of this field. Moreover, what has been published lacks continuity and leaves many issues uncovered. One of the main goals of this book is to review the existing literature under one cover. Other goals are to edit the known results in a unified manner, classify them and identify where and how they relate to each other, and fill in some gaps with new results. In some areas we explicitly mention open problems. We hope that this survey will motivate further research and enable researchers to identify important open problems. The models described in this book have numerous applications. Many examples can be found in the cited papers, but we have chosen not to include applications in the book. Many of the ideas described in this book are special cases of general principles in Economics and Game Theory. We often cite references that contain more general treatment of a subject, but we do not go into the details. we have highlighted the results For each topic covered in the book, that, in our opinion, are the most important. We also present a brief discussion of related results. The content of each chapter is briefly de scribed below. Chapter 1 is an introduction. It contains basic definitions, models and solution concepts which will be used frequently throughout the book.

From the reviews:

"The book enriches the literature on equilibrium of customers and servers in queuing systems, and it reviews the existing literature. On the other hand, it edits the known results in a unified way, and mentions some open problems. The book presents a fresh introduction to queuing theory. The nice book is welcome in the realm of queuing world." (Anatolij Dvurecenskij, Zentralblatt MATH, Vol. 1064 (15), 2005)

Autorentext
Moshe Haviv is a Professor of Statistics and Department Head at the Hebrew University in Jerusalem, Israel. He received his B.Sc. in Mathematics at Tel Aviv University, and his M.A. in Administrative Sciences and Ph.D. in Operations Research/Management Science both at Yale University. His research interests include Operations Research, Queueing Models, decision making and strategic behavior in queues, Markov decision processes, and large Markov chains. He is a member of the Center for Rationality at the Hebrew University, and is a visiting professor (summers) in Operations Management and Econometrics at the University of Sydney.

Klappentext

To Queue Or Not To Queue: Equilibrium Behavior in Queueing Systems focuses on the highly interesting, practical viewpoint of customer behavior and its effect on the performance of the queueing system. The book's objectives are threefold: (1) It is a comprehensive survey of the literature on equilibrium behavior of customers and servers in queueing systems. The literature is rich and considerable, but lacks continuity. This book will provide the needed continuity and cover some issues that have not been adequately treated. (2) In addition, it will examine the known results of the field, classify them and identify where and how they relate to each other. (3) And finally, it seeks to fill a number of the gaps in the literature with new results while explicitly outlining open problems in other areas. With this book, it is the authors' paramount purpose is to motivate further research and to help researchers identify new and interesting open problems.

Inhalt

1. Introduction.- 1.1 Basic concepts.- 1.2 Threshold strategies.- 1.3 Costs and objectives.- 1.4 Queueing theory preliminaries.- 1.5 A shuttle example.- 1.6 Non-stochastic models.- 2. Observable Queues.- 2.1 Naor's model.- 2.2 The LCFS-PR model.- 2.3 Social optimization.- 2.4 Profit maximization.- 2.5 Heterogeneous customers.- 2.6 Non-FCFS queues without reneging.- 2.7 Discounting.- 2.8 State dependent pricing.- 2.9 Waiting for the right server.- 2.10 Non-exponential service requirements.- 2.11 Related literature.- 3. Unobservable Queues.- 3.1 Identical customers.- 3.2 Observable vs. unobservable queues.- 3.3 Heterogeneous service values.- 3.4 Heterogeneous service values and time costs.- 3.5 Customers know their demand.- 3.6 Finite buffer.- 3.7 Multi-server models.- 3.8 Queueing networks.- 3.9 Related literature.- 4. Priorities.- 4.1 Observable queues.- 4.2 Unobservable queues.- 4.3 Discriminatory processor sharing.- 4.4 Incentive compatible prices.- 4.5 Bribes and auctions.- 4.6 Class decision.- 4.7 Related literature.- 5. Reneging and Jockeying.- 5.1 Reneging in observable queues.- 5.2 Reneging in unobservable queues.- 5.3 Jockeying.- 5.4 Related literature.- 6. Schedules and Retrials.- 6.1 Waiting time auctions.- 6.2 ?/M/1.- 6.3 Arrivals to scheduled batch service.- 6.4 Retrials.- 6.5 Related literature.- 7. Competition among Servers.- 7.1 Unobservable queues with heterogeneous time values.- 7.2 Unobservable queues with heterogeneous values of service.- 7.3 Observable queues.- 7.4 Price and priority competition.- 7.5 Search among competing servers.- 7.6 Information based competition.- 7.7 Related literature.- 8. Service Rate Decisions.- 8.1 Heterogeneous service values.- 8.2 Service rate at a fixed price.- 8.3 Bribes and auctions.- 8.4 Asymmetric information.- 8.5Observable vs. unobservable queues.- 8.6 Co-production.- 8.7 Competition among servers.- 8.8 Capacity expansion.- 8.9 Related literature.