*Mathematics | Program Guide: Waiting Line Models and Systems

A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.

This is a graduate level textbook that covers the fundamental topics in queuing theory. The book has a broad coverage of methods to calculate important probabilities, and gives attention to proving the general theorems. It includes many recent topics, such as server-vacation models, diffusion approximations and optimal operating policies, and more about bulk-arrival and bull-service models than other general texts.

Not only the visible queues in traffic jams, airport check in desks and supermarkets, but the more common invisible queues caused by voice calls and data packets in optical and wireless channels cost time, money and resources. Queuing control plays a crucial role in manufacturing and communication networks around the world. This pioneering approach, using fuzzy control to solve queuing control problems, determines explicit solutions to various types of control in queuing systems. Twenty-one detailed case studies demonstrate an efficient departure from classical techniques and existing practical problems, especially those that are unresponsive to conventional control techniques, are solved with the introduction of this novel approach.

The book presents a coherent treatment of Markov random walks and Markov additive processes together with their applications.

Computer systems design is full of conundrums: *Given a choice between a single machine with speed s, or n machines each with speed s/n, which should we choose? *If both the arrival rate and service rate double, will the mean response time stay the same? *Should systems really aim to balance load, or is this a convenient myth? *If a scheduling policy favors one set of jobs, does it necessarily hurt some other jobs, or are these "conservation laws" being misinterpreted? *Do greedy, shortest-delay, routing strategies make sense in a server farm, or is what's good for the individual disastrous for the system as a whole? *How do high job size variability and heavy-tailed workloads affect the choice of a scheduling policy? *How should one trade off energy and delay in designing a computer system? *If 12 servers are needed to meet delay guarantees when the arrival rate is 9 jobs/sec, will we need 12,000 servers when the arrival rate is 9,000 jobs/sec? Tackling the questions that systems designers care about, this book brings queueing theory decisively back to computer science. The book is written with computer scientists and engineers in mind and is full of examples from computer systems, as well as manufacturing and operations research. Fun and readable, the book is highly approachable, even for undergraduates, while still being thoroughly rigorous and also covering a much wider span of topics than many queueing books. Readers benefit from a lively mix of motivation and intuition, with illustrations, examples, and more than 300 exercises - all while acquiring the skills needed to model, analyze, and design large-scale systems with good performance and low cost. The exercises are an important feature, teaching research-level counterintuitive lessons in the design of computer systems. The goal is to train readers not only to customize existing analyses but also to invent their own.

This book is an efficient introduction to fundamental concepts and principles underlying the behavior of queueing systems and its application to the design of packet-oriented electrical communication systems. Key features of communication systems, such as correlation in packet arrival processes at IP switches and variability in service rates due to fading wireless links are introduced. Numerous exercises embedded within the text and problems at the end of certain chapters that integrate lessons learned across multiple sections are also included.

This monograph presents important research results in the areas of queuing theory, risk theory, graph theory and reliability theory.

An interdisciplinary approach to understanding queueing andgraphical networks In today's era of interdisciplinary studies and researchactivities, network models are becoming increasingly important invarious areas where they have not regularly been used. Combiningtechniques from stochastic processes and graph theory to analyzethe behavior of networks, Fundamentals of StochasticNetworks provides an interdisciplinary approach by includingpractical applications of these stochastic networks in variousfields of study, from engineering and operations management tocommunications and the physical sciences. The author uniquely unites different types of stochastic,queueing, and graphical networks that are typically studiedindependently of each other. With balanced coverage, the book isorganized into three succinct parts: Part I introduces basic concepts in probability and stochasticprocesses, with coverage on counting, Poisson, renewal, and Markovprocesses Part II addresses basic queueing theory, with a focus onMarkovian queueing systems and also explores advanced queueingtheory, queueing networks, and approximations of queueingnetworks Part III focuses on graphical models, presenting an introductionto graph theory along with Bayesian, Boolean, and randomnetworks The author presents the material in a self-contained style thathelps readers apply the presented methods and techniques to scienceand engineering applications. Numerous practical examples are alsoprovided throughout, including all related mathematicaldetails. Featuring basic results without heavy emphasis on provingtheorems, Fundamentals of Stochastic Networks is a suitablebook for courses on probability and stochastic networks, stochasticnetwork calculus, and stochastic network optimization at theupper-undergraduate and graduate levels. The book also serves as areference for researchers and network professionals who would liketo learn more about the general principles of stochasticnetworks.

Performance Analysis of Telecommunications and Local Area Networks presents information on teletraffic engineering, with emphasis on modeling techniques, queuing theory, and performance analysis for the public-switched telephone network and computer communication networks. Coverage includes twisted pair cables and coaxial cables, subscriber loops, multistage network switching, modeling techniques for traffic flow and service time, random access networks, and much more. End-of-chapter problems with solutions are also included.

This book emphasizes the continuous-mapping approach to obtain new stochastic-process limits from previously established stochastic-process limits. The continuous-mapping approach is applied to obtain heavy-traffic-stochastic-process limits for queueing models, including the case in which there are unmatched jumps in the limit process. These heavy-traffic limits generate simple approximations for complicated queueing processes and they reveal the impact of variability upon queueing performance.