Machine generated contents note: 1.Introduction -- 1.1.Analysis of Queues: Where, What, and How? -- 1.1.1.Where Is This Used? The Applications -- 1.1.2.What Is Needed? The Art of Modeling -- 1.1.3.How Do We Plan to Proceed? Scope and Methods -- 1.2.Systems Analysis: Key Results -- 1.2.1.Stability and Flow Conservation -- 1.2.2.Definitions Based on Limiting Averages -- 1.2.3.Asymptotically Stationary and Ergodic Flow Systems -- 1.2.4.Little's Law for Discrete Flow Systems -- 1.2.5.Observing a Flow System According to a Poisson Process -- 1.3.Queueing Fundamentals and Notations -- 1.3.1.Fundamental Queueing Terminology -- 1.3.2.Modeling a Queueing System as a Flow System -- 1.3.3.Relationship between System Metrics for G/G/s Queues -- 1.3.3.1.G/G/s/K Queue -- 1.3.4.Special Case of M/G/s Queue -- 1.4.Psychology in Queueing -- Reference Notes -- Exercises -- 2.Exponential Interarrival and Service Times: Closed-Form Expressions -- 2.1.Solving Balance Equations via Arc Cuts --

Contents note continued: 2.1.1.Multiserver and Finite Capacity Queue Model (M/M/s/K) -- 2.1.2.Steady-State Analysis -- 2.1.3.Special Cases -- 2.2.Solving Balance Equations Using Generating Functions -- 2.2.1.Single Server and Infinite Capacity Queue (M/M/1) -- 2.2.2.Retrial Queue with Application to Local Area Networks -- 2.2.3.Bulk Arrival Queues (M[X]/M/1) with a Service System Example -- 2.2.4.Catastrophic Breakdown of Servers in M/M/1 Queues -- 2.3.Solving Balance Equations Using Reversibility -- 2.3.1.Reversible Processes -- 2.3.2.Properties of Reversible Processes -- 2.3.3.Example: Analysis of Bandwidth-Sensitive Traffic -- Reference Notes -- Exercises -- 3.Exponential Interarrival and Service Times: Numerical Techniques and Approximations -- 3.1.Multidimensional Birth and Death Chains -- 3.1.1.Motivation: Threshold Policies in Optimal Control -- 3.1.2.Algorithm Using Recursively Tridiagonal Linear Equations -- 3.1.3.Example: Optimal Customer Routing --

Contents note continued: 3.2.Multidimensional Markov Chains -- 3.2.1.Quasi-Birth-Death Processes -- 3.2.2.Matrix Geometric Method for QBD Analysis -- 3.2.3.Example: Variable Service Rate Queues in Computer Systems -- 3.3.Finite-State Markov Chains -- 3.3.1.Efficiently Computing Steady-State Probabilities -- 3.3.1.1.Eigenvalues and Eigenvectors -- 3.3.1.2.Direct Computation -- 3.3.1.3.Using Transient Analysis -- 3.3.1.4.Finite-State Approximation -- 3.3.2.Example: Energy Conservation in Data Centers -- Reference Notes -- Exercises -- 4.General Interarrival and/or Service Times: Closed-Form Expressions and Approximations -- 4.1.Analyzing Queues Using Discrete Time Markov Chains -- 4.1.1.M/G/1 Queue -- 4.1.2.G/M/1 Queue -- 4.2.Mean Value Analysis -- 4.2.1.Explaining MVA Using an M/G/1 Queue -- 4.2.2.Approximations for Renewal Arrivals and General Service Queues -- 4.2.3.Departures from G/G/1 Queues -- 4.3.Bounds and Approximations for General Queues --

Contents note continued: 4.3.1.General Single Server Queueing System (G/G/1) -- 4.3.2.Multiserver Queues (M/G/s, G/M/s, and G/G/s) -- 4.3.3.Case Study: Staffing and Work-Assignment in Call Centers -- 4.3.3.1.TravHelp Calls for Help -- 4.3.3.2.Recommendation: Major Revamp -- 4.3.3.3.Findings and Adjustments -- 4.4.Matrix Geometric Methods for G/G/s Queues -- 4.4.1.Phase-Type Processes: Description and Fitting -- 4.4.2.Analysis of Aggregated Phase-Type Queue (Σ PHi/PH/s) -- 4.4.3.Example: Application in Semiconductor Wafer Fabs -- 4.5.Other General Queues but with Exact Results -- 4.5.1.M/G/[∞] Queue: Modeling Systems with Ample Servers -- 4.5.2.M/G/1 Queue with Processor Sharing: Approximating CPUs -- 4.5.3.M/G/s/s Queue: Telephone Switch Application -- Reference Notes -- Exercises -- 5.Multiclass Queues under Various Service Disciplines -- 5.1.Introduction -- 5.1.1.Examples of Multiclass Systems -- 5.1.2.Preliminaries: Little's Law for the Multiclass System --

Contents note continued: 5.1.3.Work-Conserving Disciplines for Multiclass G/G/1 Queues -- 5.1.4.Special Case: At Most One Partially Completed Service -- 5.2.Evaluating Policies for Classification Based on Types: Priorities -- 5.2.1.Multiclass M/G/1 with FCFS -- 5.2.2.M/G/1 with Nonpreemptive Priority -- 5.2.3.M/G/1 with Preemptive Resume Priority -- 5.2.4.Case Study: Emergency Ward Planning -- 5.2.4.1.Service Received by Class-1 Patients -- 5.2.4.2.Experience for Class-2 Patients -- 5.2.4.3.Three-Class Emergency Ward Operation -- 5.3.Evaluating Policies for Classification Based on Location: Polling Models -- 5.3.1.Exhaustive Polling -- 5.3.2.Gated Policy -- 5.3.3.Limited Service -- 5.4.Evaluating Policies for Classification Based on Knowledge of Service Times -- 5.4.1.Shortest Processing Time First -- 5.4.2.Preemptive Shortest Job First -- 5.4.3.Shortest Remaining Processing Time -- 5.5.Optimal Service-Scheduling Policies -- 5.5.1.Setting and Classification --

Contents note continued: 5.5.2.Optimal Scheduling Policies in Single Class Queues -- 5.5.3.Optimal Scheduling Policies in Multiclass Queues -- Reference Notes -- Exercises -- 6.Exact Results in Network of Queues: Product Form -- 6.1.Acyclic Queueing Networks with Poisson Flows -- 6.1.1.Departure Processes -- 6.1.2.Superpositioning and Splitting -- 6.1.3.Case Study: Automobile Service Station -- 6.1.3.1.System Description and Model -- 6.1.3.2.Analysis and Recommendation -- 6.2.Open Jackson Networks -- 6.2.1.Flow Conservation and Stability -- 6.2.2.Product-Form Solution -- 6.2.3.Examples -- 6.3.Closed Jackson Networks -- 6.3.1.Product-Form Solution -- 6.3.2.Arrivals See Time Averages (ASTA) -- 6.3.3.Single-Server Closed Jackson Networks -- 6.4.Other Product-Form Networks -- 6.4.1.Open Jackson Networks with State-Dependent Arrivals and Service -- 6.4.2.Open Jackson--Like Networks with Deterministic Routing -- 6.4.3.Multiclass Networks -- 6.4.4.Loss Networks -- Reference Notes --

Contents note continued: Exercises -- 7.Approximations for General Queueing Networks -- 7.1.Single-Server and Single-Class General Queueing Networks -- 7.1.1.G/G/1 Queue: Reflected Brownian Motion--Based Approximation -- 7.1.2.Superpositioning, Splitting, and Flow through a Queue -- 7.1.2.1.Superposition -- 7.1.2.2.Flow through a Queue -- 7.1.2.3.Bernoulli Splitting -- 7.1.3.Decomposition Algorithm for Open Queueing Networks -- 7.1.4.Approximate Algorithms for Closed Queueing Networks -- 7.1.4.1.Bottleneck Approximation for Large C -- 7.1.4.2.MVA Approximation for Small C -- 7.2.Multiclass and Multiserver Open Queueing Networks with FCFS -- 7.2.1.Preliminaries: Network Description -- 7.2.2.Extending G/G/1 Results to Multiserver, Multiclass Networks -- 7.2.2.1.Flow through Multiple Servers -- 7.2.2.2.Flow across Multiple Classes -- 7.2.2.3.Superposition and Splitting of Flows -- 7.2.3.QNA Algorithm -- 7.2.4.Case Study: Network Interface Card in Cluster Computing --

Contents note continued: 7.3.Multiclass and Single-Server Open Queueing Networks with Priorities -- 7.3.1.Global Priorities: Exponential Case -- 7.3.2.Global Priorities: General Case -- 7.3.3.Local Priorities -- 7.3.3.1.MVA-Based Algorithm -- 7.3.3.2.State-Space-Collapse-Based Algorithm -- Reference Notes -- Exercises -- 8.Fluid Models for Stability, Approximations, and Analysis of Time-Varying Queues -- 8.1.Deterministic Fluid Queues: An Introduction -- 8.1.1.Single Queue with a Single Server -- 8.1.2.Functional Strong Law of Large Numbers and the Fluid Limit -- 8.2.Fluid Models for Stability Analysis of Queueing Networks -- 8.2.1.Special Multiclass Queueing Networks with Virtual Stations -- 8.2.2.Stable Fluid Network Implies Stable Discrete Network -- 8.2.3.Is the Fluid Model of a Given Queueing Network Stable? -- 8.3.Diffusion Approximations for Performance Analysis -- 8.3.1.Diffusion Limit and Functional Central Limit Theorem --

Contents note continued: 8.3.2.Diffusion Approximation for Multiserver Queues -- 8.3.2.1.Fix s, Increase λ -- 8.3.2.2.Fix ρ, Increase λ and s -- 8.3.2.3.Fix β, increase λ and s -- 8.3.3.Efficiency-Driven Regime for Multiserver Queues with Abandonments -- 8.4.Fluid Models for Queues with Time-Varying Parameters -- 8.4.1.Uniform Acceleration -- 8.4.2.Diffusion Approximation -- Reference Notes -- Exercises -- 9.Stochastic Fluid-Flow Queues: Characteristics and Exact Analysis -- 9.1.Introduction -- 9.1.1.Discrete versus Fluid Queues -- 9.1.2.Applications -- 9.1.3.Preliminaries for Performance Analysis -- 9.1.4.Environment Process Characterization -- 9.1.4.1.CTMC Environmental Processes -- 9.1.4.2.Alternating Renewal Environmental Processes -- 9.1.4.3.SMP Environmental Processes -- 9.2.Single Buffer with Markov Modulated Fluid Source -- 9.2.1.Terminology and Notation -- 9.2.2.Buffer Content Analysis --

Contents note continued: 9.2.3.Steady-State Results and Performance Evaluation -- 9.2.4.Examples -- 9.3.First Passage Times -- 9.3.1.Partial Differential Equations and Boundary Conditions -- 9.3.2.Examples -- Reference Notes -- Exercises -- 10.Stochastic Fluid-Flow Queues: Bounds and Tail Asymptotics -- 10.1.Introduction and Preliminaries -- 10.1.1.Inflow Characteristics: Effective Bandwidths and ALMGF -- 10.1.2.Computing Effective Bandwidth and ALMGF -- 10.1.2.1.Effective Bandwidth of a CTMC Source -- 10.1.2.2.Effective Bandwidth of a Semi-Markov Process (SMP) Source -- 10.1.2.3.Effective Bandwidth of a General On/Off Source -- 10.1.3.Two Extensions: Traffic Superposition and Flow through a Queue -- 10.1.3.1.Superposition of Multiple Sources -- 10.1.3.2.Effective Bandwidth of the Output from a Queue -- 10.2.Performance Analysis of a Single Queue -- 10.2.1.Effective Bandwidths for Tail Asymptotics -- 10.2.2.Chernoff Dominant Eigenvalue Approximation --

Contents note continued: 10.2.3.Bounds for Buffer Content Distribution -- 10.3.Multiclass Fluid Queues -- 10.3.1.Tackling Varying Output Capacity: Compensating Source -- 10.3.2.Timed Round Robin (Polling) -- 10.3.3.Static Priority Service Policy -- 10.3.4.Other Policies -- Reference Notes -- Exercises -- Appendix A Random Variables -- A.1.Distribution and Moments -- A.1.1.Discrete Random Variables -- A.1.2.Continuous Random Variables -- A.1.3.Coefficient of Variation -- A.2.Generating Functions and Transforms -- A.2.1.Generating Functions -- A.2.2.Laplace--Stieltjes Transforms -- A.2.3.Laplace Transforms -- A.3.Conditional Random Variables -- A.3.1.Obtaining Probabilities -- A.3.2.Obtaining Expected Values -- A.4.Exponential Distribution -- A.4.1.Characteristics -- A.4.2.Properties -- A.5.Collection of IID Random Variables -- A.5.1.Poisson Process -- A.5.2.Renewal Process -- Reference Notes -- Exercises -- Appendix B Stochastic Processes -- B.1.Discrete-Time Markov Chains --

Contents note continued: B.1.1.Modeling a System as a DTMC -- B.1.2.Transient Analysis of DTMCs -- B.1.3.Steady-State Analysis of DTMCs -- B.2.Continuous-Time Markov Chains -- B.2.1.Modeling a System as a CTMC -- B.2.2.Transient Analysis of CTMCs -- B.2.3.Steady-State Analysis of CTMCs -- B.3.Semi-Markov Process and Markov Regenerative Processes -- B.3.1.Markov Renewal Sequence -- B.3.2.Semi-Markov Process -- B.3.3.Markov Regenerative Processes -- B.4.Brownian Motion -- B.4.1.Definition of Brownian Motion -- B.4.2.Analysis of Brownian Motion -- B.4.3.Ito's Calculus -- Reference Notes -- Exercises.