The book examines the performance and optimization of systems where queueing and congestion are important constructs. Both finite and infinite queueing systems are examined. Many examples and case studies are utilized to indicate the breadth and depth of the queueing systems and their range of applicability. Blocking of these processes is very important and the book shows how to deal with this problem in an effective way and not only compute the performance measures of throughput, cycle times, and WIP but also to optimize the resources within these systems. The book is aimed at advanced undergraduate, graduate, and professionals and academics interested in network design, queueing performance models and their optimization. It assumes that the audience is fairly sophisticated in their mathematical understanding, although the explanations of the topics within the book are fairly detailed. Read more...
Abstract:
The book examines the performance and optimization of systems where queueing and congestion are important constructs. Read more...
Author(s): Smith, J. MacGregor
Series: Springer series in operations research
Publisher: Springer
Year: 2018
Language: English
Tags: Qu
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).
