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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.
A comprehensive guide to the concepts and applications of queuing theory and traffic theory Network Traffic Engineering: Models and Applications provides an advanced level queuing theory guide for students with a strong mathematical background who are interested in analytic modeling and performance assessment of communication networks. The text begins with the basics of queueing theory before moving on to more advanced levels. The topics covered in the book are derived from the most cutting-edge research, project development, teaching activity, and discussions on the subject. They include applications of queuing and traffic theory in: LTE networks Wi-Fi networks Ad-hoc networks Automated vehicles Congestion control on the Internet The distinguished author seeks to show how insight into practical and real-world problems can be gained by means of quantitative modeling. Perfect for graduate students of computer engineering, computer science, telecommunication engineering, and electrical engineering, Network Traffic Engineering offers a supremely practical approach to a rapidly developing field of study and industry.
The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arrival and service times, characteristics of fluid queues, modifications of retrial queueing systems and finite-source retrial queues with random breakdowns, repairs and customers’ collisions. Some recent tendencies in the asymptotic analysis include the average and diffusion approximation of Markov queueing systems and networks, the diffusion and Gaussian limits of multi-channel queueing networks with rather general input flow, and the analysis of two-time-scale nonhomogenous Markov chains using the large deviations principle. The book also analyzes transient behavior of infinite-server queueing models with a mixed arrival process, the strong stability of queueing systems and networks, and applications of fast simulation methods for solving high-dimension combinatorial problems.
This book covers ideas, methods, algorithms, and tools for the in-depth study of the performance and reliability of dependable fault-tolerant systems. The chapters identify the current challenges that designers and practitioners must confront to ensure the reliability, availability, and performance of systems, with special focus on their dynamic behaviors and dependencies. Topics include network calculus, workload and scheduling; simulation, sensitivity analysis and applications; queuing networks analysis; clouds, federations and big data; and tools. This collection of recent research exposes system researchers, performance analysts, and practitioners to a spectrum of issues so that they can address these challenges in their work.
Based on the careful analysis of several hundred publications, this book uniformly describes basic methods of analysis and critical results of the theory of retrial queues. Chapters discuss: analysis of single-server retrial queues, including stationary and transient distribution of the number in the system, busy period, waiting time process, limit theorems, stochastic inequalities, traffic measurement multiserver retrial queues - ergodicity, explicit formulas, algorithmic solutions, limit theorems, approximations advanced single-server and multiserver retrial queues - models with priority subscribers, non-ersistent subscribers, finite source queues Lecturers, researchers, and students in probability, statistics, operations research, telecommunications, and computer systems modeling analysis will find Retrial Queues to be an invaluable resource.
This book constitutes the proceedings of the 14th International Conference on Queueing Theory and Network Applications, QTNA 2019, held in Ghent, Belgium, in August 2019.The 23 full papers included in this volume were carefully reviewed and selected from 49 initial submissions. The papers are organized in topical sections on Retrial Queues; Controllable Queues; Strategic Queues; Queueing Networks; Scheduling Policies; Multidimensional Systems; and Queueing Models in Applications.
I. The single server queue GIIG/1 1 1. 1 Definitions 1 1. 2 Regenerative processes 2 1. 3 The sequence n 1,2, . . . 4 = !::!n' 1. 4 The process t dO,co)} 11 {~t' The process t dO,co)} 1. 5 15 {~t' Applications to the GIIG/1 queue 1. 6 16 The average virtual waiting time during a busy 17 cycle ii. Little's formula 17 iii. The relation between the stationary distributions 18 of the virtual and actual waiting time iv. The relation between the distribution of the idle 20 period and the stationary distribution of the actual waiting time v. The limiting distribution of the residual service 24 time £. , -pw vi. The relation for ~ rn E{e -n} 25 n=O 1. 7 Some notes on chapter I 27 II. The M/G/K system 31 2. 1 On the stationary distribution of the actual and virtua131 waiting time for the M/G/K queueing system 2. 2 The M/G/K loss system 36 2. 3 Proof of Erlang's formula for the M/G/K loss system 43 i. Proof for the system MIMI'" 45 ii. Proof for the system M/G/co 47 VI iii. Proof fol' the MIG IK los s system III. The M/G/1 system 3. 1 Introduction 71 (K) 3. 2 Downcrossings of the ~t -process 74 3. 3 The distribution of the supremum of the virtual waiting 75 • (00) d' b 1 tlme ~t urlng a usy cyc e i. The exit probability 76 ii.
Written with computer scientists and engineers in mind, this book brings queueing theory decisively back to computer science.
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.
This book constitutes revised selected papers of the 19th International Conference on Information Technologies and Mathematical Modelling, ITMM 2020, named after A.F. Terpugov, held in Tomsk, Russia, in December 2020. The 31 full papers presented in this volume were carefully reviewed and selected from 82 submissions. The conference covers various aspects of information technologies, focusing on queueing theory, stochastic processes, Markov processes, renewal theory, network performance equation and network protocols.