To queue or not to queue: equilibrium behavior in queueing systems.
The book enriches the literature on equilibrium of customers and servers in queueing 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 monograph consists of eight chapters. Chapter 1 has introductory character giving the main notions, definitions, and also a simple example of a queue with two servers on which the authors would like to show the beauty of queueing theory problems. Chapter 2 is dedicated to queueing systems when a potential new customer is observing the queue length before making his decision to join the queue or not. Such models are Naor's model, LCFS-PR model, social optimization, profit maximization, heterogeneous customers, discounting, waiting for the right server, and non-exponential service requirements. Chapter 3 deals with the same questions as in the previous chapter not supposing that customers can observe the queue length before making their decision to join the queue or not. The first such models were studied by Edelson and Hildebrand, and the present authors give comparisons of both the approaches. Chapter 4 is devoted to priorities. The book gives an analysis of queues in which customers are looking to his priorities. Such priorities can be done either on the customer's type or on the option of buying priority. Chapter 5 studies queueing models in which customers react to certain conditions created after they join the queue. They can (1) renege from the form of the queue (if the expected utility from remaining part is negative), or (2) jockey from one line to another in multi-server queueing systems. Chapter 6 is dealing with queueing systems in which customers (1) are planning their arrival to the system, or (2) are planning leaving the system temporarily after observing a long queue and retry at a later time. Chapter 7 studies competitions among the servers over the customers, usually by posting the prices. The authors show how prices or priorities or information are used to optimize the game. The last chapter, Chapter 8, deals with queueing models in which the service time is a decision variable. Such a policy is service rate decisions. The main attention is paid to unobservable queues. The book presents a fresh introduction to queueing theory. The authors give only the final formulas necessary for customer/system to optimize his/its strategy. The main accent is posed to equilibrium stages. The nice book is welcome in the realm of queueing world.
scientific article; zbMATH DE number 2038823