An Elementary Introduction to Queueing Systems

✍ Scribed by Wah Chun Chan

• Publisher: World Scientific Publishing Company
• Year: 2014
• Tongue: English
• Leaves: 116
• Category: Library

✦ Synopsis

The book aims to highlight the fundamental concepts of queueing systems. It starts with the mathematical modeling of the arrival process (input) of customers to the system. It is shown that the arrival process can be described mathematically either by the number of arrival customers in a fixed time interval, or by the interarrival time between two consecutive arrivals. In the analysis of queueing systems, the book emphasizes the importance of exponential service time of customers. With this assumption of exponential service time, the analysis can be simplified by using the birth and death process as a model. Many queueing systems can then be analyzed by choosing the proper arrival rate and service rate. This facilitates the analysis of many queueing systems. Drawing on the author's 30 years of experience in teaching and research, the book uses a simple yet effective model of thinking to illustrate the fundamental principles and rationale behind complex mathematical concepts. Explanations of key concepts are provided, while avoiding unnecessary details or extensive mathematical formulas. As a result, the text is easy to read and understand for students wishing to master the core principles of queueing theory

✦ Table of Contents

Content: Chapter 1
Modeling of Queueing Systems
1.1 Mathematical Modeling
1.2 The Poisson Input Process
1.3 Superposition of Independent Poisson Processes
1.4 Decomposition of a Poisson Process
1.5 The Exponential Interarrival Time Distribution
1.6 The Markov Property or Memoryless Property
1.7 Relationship Between the Poisson Distribution and the Exponential Distribution
1.8 The Service Time Distribution
1.9 The Residual Service Time Distribution
1.10 The Birth and Death Process
1.11 The Outside Observer's Distribution and the Arriving Customer's Distribution
Review --
Chapter 2Queueing Systems with Losses
2.1 Introduction
2.2 The Erlang Loss System
2.3 The Erlang Loss Formula
Review --
Chapter 3
Queueing Systems Allowing Waiting
3.1 Introduction
3.2 The Erlang Delay System
3.3 The Distribution Function of the Waiting Time
3.4 Little's Formula
Review --
Chapter 4
The Engset Loss and Delay Systems
4.1 Introduction
4.2 The Engset Loss System
4.3 The Arriving Customer's Distribution for the Engset Loss System
4.4 The Offered Load and Carried Load in the Engset Loss System
4.5 The Engset Delay System. 4.6 The Waiting Time Distribution Function for the Engset Delay System4.7 The Mean Waiting Time in the Engset Delay System
4.8 The Offered Load and Carried Load in the Engset Delay System
Review --
Chapter 5
Queueing Systems with a Single Server
5.1 Introduction
5.2 The M/M/1 Queue
5.3 The M/G/1 Queue and the Pollaczek-Khinchin Formula for the Mean Waiting Time
5.4 The M/G/1 Queue with Vacations
5.5 The M/G/1 Queue with Priority Discipline
(A) The HOL Non-Preemptive Priority System
(B) The Preemptive Priority System
5.6 The GI/M/1 Queue. (A) The Probability of Waiting and the Mean Waiting Time(B) The Waiting Time Distribution Function

✦ Subjects

Queuing theory;Queuing theory -- Mathematical models