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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Customers in service systems act independently in order to maximize their welfare. Yet, each customer’s optimal behavior is affected by acts taken by the system managers and by the other customers. The result is an aggregate “equilibrium” pattern of behavior which may not be optimal from the point of view of society as a whole. Similar observations have been known to economists for a long time, but have been made explicit in the context of queueing theory only after the publication in 1969 of a paper by P. Naor [133]. The scope of queueing theory prior to Naor’s paper is well reflected in a “Letter to the Editor” [103] published in 1964 by W.A. Leeman. It ends with the following excerpt:
It is a bit surprising that in a capitalistic economy, applied queueing theory limits itself to recommendations of administrative measures for the reduction of queues. One might have expected to observe such an approach in a planned economy but not in an economy in which prices and markets play so large a role.
Refael Hassin, Moshe Haviv

Chapter 2. Observable Queues

Abstract
This chapter deals with queueing systems, where an arriving customer observes the length of the queue before making his decisions.
Refael Hassin, Moshe Haviv

Chapter 3. Unobservable Queues

Abstract
In the previous chapter we assumed that actions are selected after observing the queue. In this chapter, we present models where the customers do not observe the queue prior to their actions.
Refael Hassin, Moshe Haviv

Chapter 4. Priorities

Abstract
Priorities are often used in queueing systems as a mechanism for service allocation. By carefully selecting an appropriate system of priorities, both social welfare and profits can be increased.1 This chapter also considers models where customers purchase priority. The rationale behind purchasing priority is twofold: priority enables overtaking ordinary customers who are present upon arrival, and it avoids being overtaken by later-to-arrive priority customers. The latter reason means that as more customers purchase priority, the more inclined an individual should be to do so himself in any given state. In other words, this is an FTC situation.
Refael Hassin, Moshe Haviv

Chapter 5. Reneging and Jockeying

Abstract
This chapter discusses models in which customers react to certain conditions created after they join the queue. Customers may renege from the queue if the expected utility from remaining in the queue becomes negative. This may happen when conditions in the system deteriorate, due to a slow-down in the service rate, an increase in the expected queue length, a decrease in the value of service, or other reasons. Recall that reneging was already mentioned in §2 in a LCFS model where the last in line may renege when a new customer arrives. Another model in which customers react to changes in the state of the system deals with an observable multi-server queue where jockeying from one line to another (probably shorter) is allowed.
Refael Hassin, Moshe Haviv

Chapter 6. Schedules and Retrials

Abstract
This chapter deals with models where customers choose their time of arrival. Such models contain some non-stationary element like known times that a service facility is open, a scheduled (possibly periodic) service, or information about the state of the queue in past instants.1
Refael Hassin, Moshe Haviv

Chapter 7. Competition Among Servers

Abstract
This chapter deals with markets in which servers compete over the customers, usually by posting prices. Most of the models consider a game with two stages; servers act as leaders by announcing prices, and customers follow by selecting servers accordingly. Thus, the model computes customers’ equilibrium for any given set of prices, so that each customer optimizes his own welfare by choosing a server. Then, an equilibrium among the servers is computed, where each server sets a price that maximizes its profits, given the prices of the others. At this stage, the servers assume that for each set of prices, the arrival rates are determined by the corresponding customers’ equilibrium.
Refael Hassin, Moshe Haviv

Chapter 8. Service Rate Decisions

Abstract
This chapter is concerned with models in which the service rate is a decision variable. In most cases, it is the server who determines the service rate, but we also deal with models where this is done by the customers. We also consider in this chapter models where the customer determines the amount of service he obtains.
Refael Hassin, Moshe Haviv

Backmatter

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