Introduction to Queueing Networks: Theory ∩ Practice

Content: Intro
 Preface
 1 Volume Focus and Outline
 2 Software Tools
 Acknowledgments
 Contents
 Acronyms
 1 Introduction G(V, E)
 1.1 Prologue
 1.1.1 Queueing Properties
 1.1.2 Types of Blocking
 1.2 Kendall Notation (A/B/C/D/E/F)
 1.3 Topological Network Design (TND) Problems
 1.3.1 Design Variables
 1.3.2 Example Context
 1.3.3 Performance Variables
 1.3.4 Contextual Variables
 1.3.5 Performance and Optimization Models
 1.4 Principles of Modeling Queueing Networks
 1.4.1 Representation G(V, E)
 1.4.1.1 Decomposition
 1.4.1.2 Aggregation
 1.4.2 Analysis f[(G(V, E)]
 1.4.3 Synthesis G(V, E)* 2.1.2 Stochastic Processes2.2 Little\'s Law
 2.3 Single Queue History
 2.3.1 A.K. Erlang
 2.3.2 The Early Pioneer Years
 2.3.3 Mid-Century
 2.4 Queueing Network History
 2.4.1 Open Queueing Networks
 2.4.2 Closed Queueing Networks
 2.4.3 Mixed Queueing Networks
 2.4.4 Product-Form Networks
 2.4.5 Non-product-Form Networks
 2.4.6 Blocking Networks
 2.4.7 Transportation and Loss Networks
 2.5 Optimization History
 2.5.1 Static Optimal Control
 2.5.2 Optimization Focus
 2.5.3 Optimal Dynamic Control
 3 Mathematical Models and Properties of Queues G(V)
 3.1 Introduction and Motivation. 3.2 Assumptions, Definitions, Notation3.2.1 Definitions
 3.3 Birth-and-Death Process (BD)
 3.3.1 BD Example Hair Salon
 3.4 redProduct Form: Birth-and-Death Queueing Formulas
 3.4.1 M/M/1 Representation
 3.4.2 Sample Path
 3.4.3 Steady-State Equations
 3.4.4 Algorithm
 3.4.5 Example Routing Problem
 3.4.6 M/M/c Representation
 3.4.7 M/M/c Sample Path
 3.4.8 Birth-Death Equations
 3.4.9 M/M/c Algorithm
 3.4.10 M/M/c Examples and Optimization
 3.4.11 M/G/∞ Queue
 3.4.11.1 Example
 3.5 blueNon-product-Form Queues: M/G/1/∞ and Related Queues
 3.5.1 Embedded Markov Process Approach 3.5.2 M/G/1 Generating Function Approach3.5.3 Embedded DTMC Matrix
 3.5.3.1 Probability Distribution
 3.5.3.2 Recursion Approach
 3.5.3.3 Basic Formula for Wq, Lq
 3.5.3.4 M/G/1 Example of Performance
 3.5.3.5 Example: M/D/1/K Model
 3.5.4 M/G/c Approximation Formula
 3.5.5 M/G/c Approximation Formula Example and Optimization
 3.5.6 G/M/1 and G/M/c Queues
 3.5.7 GI/G/c: Approximation Formula
 3.5.7.1 GI/G/c: Approximation Formula Example
 3.6 magentaBlocking Queues: Finite Buffer Queue Models
 3.6.1 M/M/1/K Models
 3.6.2 M/M/1/K Performance Measures
 3.6.2.1 WIP (L)
 3.6.2.2 Cycle Time (W).