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.

Waiting in lines is a staple of everyday human life. Without really noticing, we are doing it when we go to buy a ticket at a movie theater, stop at a bank to make an account withdrawal, or proceed to checkout a purchase from one of our favorite department stores. Oftentimes, waiting lines are due to overcrowded, overfilling, or congestion; any time there is more customer demand for a service than can be provided, a waiting line forms. Queuing systems is a term used to describe the methods and techniques most ideal for measuring the probability and statistics of a wide variety of waiting line models. This book provides an introduction to basic queuing systems, such as M/M/1 and its variants, as well as newer concepts like systems with priorities, networks of queues, and general service policies. Numerical examples are presented to guide readers into thinking about practical real-world applications, and students and researchers will be able to apply the methods learned to designing queuing systems that extend beyond the classroom. Very little has been published in the area of queuing systems, and this volume will appeal to graduate-level students, researchers, and practitioners in the areas of management science, applied mathematics, engineering, computer science, and statistics.

This classic work, now available in paperback, concentrates on the basic models of queueing theory. It has a dual aim: to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.

Understand the Strategic Behavior in Queueing SystemsRational Queueing provides one of the first unified accounts of the dynamic aspects involved in the strategic behavior in queues. It explores the performance of queueing systems where multiple agents, such as customers, servers, and central managers, all act but often in a noncooperative manner.T

The definitive guide to queueing theory and its practical applications—features numerous real-world examples of scientific, engineering, and business applications Thoroughly updated and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fifth Edition presents the statistical principles and processes involved in the analysis of the probabilistic nature of queues. Rather than focus narrowly on a particular application area, the authors illustrate the theory in practice across a range of fields, from computer science and various engineering disciplines to business and operations research. Critically, the text also provides a numerical approach to understanding and making estimations with queueing theory and provides comprehensive coverage of both simple and advanced queueing models. As with all preceding editions, this latest update of the classic text features a unique blend of the theoretical and timely real-world applications. The introductory section has been reorganized with expanded coverage of qualitative/non-mathematical approaches to queueing theory, including a high-level description of queues in everyday life. New sections on non-stationary fluid queues, fairness in queueing, and Little’s Law have been added, as has expanded coverage of stochastic processes, including the Poisson process and Markov chains. • Each chapter provides a self-contained presentation of key concepts and formulas, to allow readers to focus independently on topics relevant to their interests • A summary table at the end of the book outlines the queues that have been discussed and the types of results that have been obtained for each queue • Examples from a range of disciplines highlight practical issues often encountered when applying the theory to real-world problems • A companion website features QtsPlus, an Excel-based software platform that provides computer-based solutions for most queueing models presented in the book. Featuring chapter-end exercises and problems—all of which have been classroom-tested and refined by the authors in advanced undergraduate and graduate-level courses—Fundamentals of Queueing Theory, Fifth Edition is an ideal textbook for courses in applied mathematics, queueing theory, probability and statistics, and stochastic processes. This book is also a valuable reference for practitioners in applied mathematics, operations research, engineering, and industrial engineering.

Queueing is an aspect of modern life that we encounter at every step in our daily activities. Whether it happens at the checkout counter in the supermarket or in accessing the Internet, the basic phenomenon of queueing arises whenever a shared facility needs to be accessed for service by a ]arge number of jobs or customers. The study of queueing is important as it gravides both a theoretical background to the kind of service that we may expect from such a facility and the way in which the facility itself may be designed to provide some specified grade of service to its customers. Our study of queueing was basically motivated by its use in the study of communication systems and computer networks. The various computers, routers and switches in such a network may be modelled as individual queues. The whole system may itself be modelled as a queueing network providing the required service to the messages, packets or cells that need to be carried. Application of queueing theory provides the theoretical framework for the design and study of such networks. The purpose of this book is to support a course on queueing systems at the senior undergraduate or graduate Ievels. Such a course would then provide the theoretical background on which a subsequent course on the performance modeHing and analysis of computer networks may be based.

This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are included.

"Vladimir Sorokin’s first published novel, The Queue, is a sly comedy about the late Soviet “years of stagnation.” Thousands of citizens are in line for . . . nobody knows quite what, but the rumors are flying. Leather or suede? Jackets, jeans? Turkish, Swedish, maybe even American? It doesn’t matter–if anything is on sale, you better line up to buy it. Sorokin’s tour de force of ventriloquism and formal daring tells the whole story in snatches of unattributed dialogue, adding up to nothing less than the real voice of the people, overheard on the street as they joke and curse, fall in and out of love, slurp down ice cream or vodka, fill out crossword puzzles, even go to sleep and line up again in the morning as the queue drags on."--Amazon.com.

Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples. In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.