To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems

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 to motivate further research and to help researchers identify new and interesting open problems.

Chapter 1 is an introduction. It contains basic definitions, models and solution concepts which will be used frequently throughout the book. This chapter also deals in depth with a seemingly simple model (the shuttle example) which is used to illustrate some of the main themes of this book. Chapter 2 studies the basic model in which customers decide whether or not to join a queue, after observing its length. The differences between individual optimization (Nash Equilibrium), social optimization, and profit maximization are emphasized. Various ways to regulate the queue and induce customers to behave in the socially desired way are discussed. Chapter 3 deals with the same model as Chapter 2 except that customers cannot observe the queue length before they make their decisions. The authors also discuss models with additional features such as: customers know their exact service requirement; the customer population is heterogeneous; the queueing discipline is not first-come first-served. Chapter 4 analyzes queues in which customers differ by their priority levels. In some models priority is set according to the customer's type, in others customers have the option of buying priority. A main issue in models of the latter type is how to select prices that induce customers to buy the right priority level so that the overall welfare is maximized. Chapter 5 is concerned with two types of behavior. In the first, customers have the option to abandon (or renege) the queue after their
waiting conditions deteriorate. In an observable system customers may renege if the queue becomes too congested. In an unobservable system reneging may result from waiting costs that increase in time. The second type of behavior allows customers to jockey among queues and to purchase information about which queue is the shortest. Chapter 6 deals with models in which customers possess information on the state of the queue at a given point in time. Examples are service systems that open and close at given times, scheduled service, and models in which customers may leave the system temporarily after observing a long queue and retry at a later time. Chapter 7 studies competition among service providers who try to attract customers while maximizing their profits. The authors discuss how prices, priorities, and information are used to achieve this goal. Chapter 8 deals with long-run decisions of servers regarding their service rates. A higher rate means better service and helps to attract more customers, but it usually comes at a higher cost to the server.