An Introduction to Queueing Systems

by Bose, Sanjay K.

• ISBN13: 9780306467349
• ISBN10: 0306467348
• Format: Hardcover
• Copyright: 2001-12-01
• Publisher: Plenum Pub Corp

Summary

This volume accomplishes the unique task of providing the reader with the analytical fundamentals for both single queues and queueing networks while keeping the description simple enough so that the results may be directly used for modeling and analysis. A very wide range of single-queue models has been covered, while networks are analyzed through a very comprehensive set of approximation algorithms ready to apply in modeling. The text was honed through years of research and teaching, and is an excellent tool for engineers and students who wish to apply queueing methods to study the performance of systems. For the table of contents, solution manual, and sample tests please visit the author's website at http://home.iitk.ac.in/~skb/qbook/qbook.html

Table of Contents

List of Figures	xv
Introduction	1	(8)
Queueing Model Parameters	2	(1)
A Simple Queueing Model	3	(4)
Some Basic Queueing Models	7	(1)
A Summary of the Contents	7	(2)
Basic Queueing Theory: Fundamentals of Analyzing Single Queues	9	(46)
Markov Processes and Markov Chains	9	(6)
Birth-Death Processes	15	(5)
Kendall's Notation for Queues	20	(2)
Little's Result	22	(1)
Equilibrium Solutions for M/M/-/- Queues	23	(11)
Delay Analysis for FCFS M/M/1/∞ and M/M/m/∞ Queues	34	(4)
Departure Process from a M/M/m/∞ Queue	38	(2)
Time Reversibility Property of Irreducible, Aperiodic Markov Chains	40	(1)
The Method of Stages for Solving a M/-/1/∞ FCFS Queue	41	(4)
Queues with Bulk (or Batch) Arrivals	45	(10)
Problems	49	(6)
Analysis of the M/G/1 Queue in Equilibrium: Performance Analysis Using Residual Life and Imbedded Markov Chain Approaches	55	(34)
The Residual Life Approach for Analysing the M/G/1 Queue	57	(7)
The Imbedded Markov Chain Approach for Analysing the M/G/1 Queue	64	(6)
Distributions of Time Spent in System and the Waiting Time Prior to Service in a FCFS M/G/1 Queue	70	(2)
Busy Period Analysis of a M/G/1 Queue	72	(4)
Delay Analysis for a LCFS M/G/1 Queue	76	(3)
The M/D/1 Queue	79	(2)
Alternative Derivation for the Delays in a FCFS M/G/1 Queue	81	(8)
Problems	86	(3)
Advanced Queueing Theory: Vacations, Bulk Arrivals and Priorities in a M/G/1 Queue and the Geo/G/1 Queue	89	(54)
M/G/1 Queue with Vacations	90	(7)
M/G/1 Queue with Only One Vacation after Idle	97	(1)
M/G/1 Queue with Exceptional First Service	98	(3)
M[X]/G/1 Queue - Single Server Queue with Batch Arrivals	101	(5)
Single Server M/G/1 Priority Queues	106	(21)
The Discrete Time Geo/G/1 and Geo[X]/G/1 Queues	127	(16)
Problems	140	(3)
Fundamentals of Queueing Networks: Open and Closed Networks with Product-Form Solutions	143	(50)
Classification of Different Types of Queueing Networks	145	(3)
Probabilistic Routing in a Queueing Network	148	(2)
Open Networks of M/M/m Type Queues and Jackson's Theorem	150	(11)
Extensions to Jackson's Theorem for Other Open Networks	161	(3)
Closed Queueing Networks	164	(8)
Convolution Algorithm for Finding the Normalisation Constant for a Closed Queueing Network	172	(2)
Mean Value Analysis (MVA) Algorithm for a Closed Queueing Network	174	(7)
Analysis of a Sample Closed Network Using Convolution and MVA Algorithms	181	(3)
Norton's Theorem for Closed Queueing Networks	184	(9)
Problems	189	(4)
Advanced Queueing Networks: Approximation Techniques for Open and Closed Queueing Networks	193	(64)
Mixed Queueing Networks	193	(5)
The GI/G/m Approximation for the Approximate Analysis of Open Queueing Networks (the QNA Technique)	198	(13)
Fork/Join Queues in Open and Closed Networks of Infinite Capacity Queues	211	(7)
Models of Blocking in Open and Closed Networks of Finite Capacity Queues	218	(3)
Approximate Analytical Methods for Solving Closed Networks of Finite Capacity Queues	221	(13)
Approximate Analytical Methods for Solving Open Networks of Finite Capacity Queues	234	(23)
Appendix 6.1: The Generalised Exponential Distribution	254	(3)
Simulation Techniques for Queues and Queueing Networks: Basic Principles for the Design of Queueing Simulators	257	(26)
Simulation Model of a Real World System	258	(5)
Discrete Event Simulation	263	(5)
Collecting and Processing Simulator Outputs for Queues	268	(3)
Estimation of Confidence Intervals and Confidence Levels	271	(3)
Transient Behaviour and the Warm-up Interval	274	(1)
Data Collection in Steady State Conditions	275	(8)
Appendix 7.1 Generating Random Numbers	280	(3)
References	283	(2)
Index	285