Analysis of Queues Methods and Applications

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.

Introduction Analysis of Queues: Where, What, and How?Systems Analysis: Key ResultsQueueing Fundamentals and Notations Psychology in Queueing Reference Notes Exercises Exponential Interarrival and Service Times: Closed-Form Expressions Solving Balance Equations via Arc CutsSolving Balance Equations Using Generating Functions Solving Balance Equations Using Reversibility Reference Notes ExercisesExponential Interarrival and Service Times: Numerical Techniques and Approximations Multidimensional Birth and Death ChainsMultidimensional Markov Chains Finite-State Markov ChainsReference Notes Exercises General Interarrival and/or Service Times: Closed-Form Expressions and Approximations Analyzing Queues Using Discrete Time Markov Chains Mean Value Analysis Bounds and Approximations for General Queues Matrix Geometric Methods for G/G/s Queues Other General Queues but with Exact Results Reference Notes Exercises Multiclass Queues under Various Service Disciplines IntroductionEvaluating Policies for Classification Based on Types: Priorities Evaluating Policies for Classification Based on Location: Polling Models Evaluating Policies for Classification Based on Knowledge of Service Times Optimal Service-Scheduling Policies Reference Notes Exercises Exact Results in Network of Queues: Product Form Acyclic Queueing Networks with Poisson Flows Open Jackson Networks Closed Jackson NetworksOther Product-Form Networks Reference Notes Exercises Approximations for General Queueing NetworksSingle-Server and Single-Class General Queueing Networks Multiclass and Multiserver Open Queueing Networks with FCFS Multiclass and Single-Server Open Queueing Networks with PrioritiesReference Notes Exercises Fluid Models for Stability, Approximations, and Analysis of Time-Varying QueuesDeterministic Fluid Queues: An Introduction Fluid Models for Stability Analysis of Queueing Networks Diffusion Approximations for Performance Analysis Fluid Models for Queues with Time-Varying Parameters Reference NotesExercisesStochastic Fluid-Flow Queues: Characteristics and Exact AnalysisIntroductionSingle Buffer with Markov Modulated Fluid Source First Passage Times Reference Notes Exercises Stochastic Fluid-Flow Queues: Bounds and Tail Asymptotics Introduction and Preliminaries Performance Analysis of a Single Queue Multiclass Fluid Queues Reference NotesExercisesAppendix A: Random VariablesAppendix B: Stochastic ProcessesReferencesIndex

Natarajan Gautam