Chapter 4:
Introduction to Queueing Theory and Its Applications
 CONTENTS Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8
 4 Introduction to Queueing Theory and Its Applications 4.1 Questions And Answers In Queueing Theory 4.2 BackGround, Terms, And Some Conventional Notation 4.3 Defining The Quantities Of Interest 4.4 Some Important Relationships In Queueing Theory 4.5 Fundamental Queueing 4.5.1 Response Distance of an Ambulette Revisited 4.6 Functions of Random Variables 4.6.1 Case 1: One Operator, Infinite Number of Lines 4.6.2 Case 2: m Operators, Infinite Number of Lines 4.6.3 Case 3: One Operator, Finite Number of Lines 4.6.4 Case 4: m Operators, Finite Number of Lines 4.6.5 Extensions and Variations 4.7 Spatially Distributed Queues And The M/G/1 Queueing System 4.8 Useful Results For Difficult-To-Analyze Queueing Systems 4.8.1 Why Are M/G/m, G/G/1, and G/G/m Difficult? 4.8.2 M/G/m Queueing Systems with No Waiting Space 4.8.3 G/G/1/1 System 4.8.4 G/G/m Queueing Systems 4.9 Queueing Systems With Priorities 4.9.1 Preemptive and Nonpreemptive Priorities 4.9.2 Important Optimization Result 4.9.3 Nonpreemptive Priorities in a M/M/m System 4.9.4 Preemptive Priorities 4.10 Queueing Networks 4.10.1 Important Property of M/M/m Quueing Systems 4.10.2 State-Transition-Diagram Approach to Networks with Blocking Effects 4.11 Time-Dependent Analysis Of The M/M/m Queueing System *** References *** Problems