# Queueing Theory Basics

Topics: Random variable, Cumulative distribution function, Probability theory Pages: 12 (1803 words) Published: January 23, 2013
ELEN90061 Communication Networks Part I
Dr Alex Leong Department of Electrical and Electronic Engineering University of Melbourne asleong@unimelb.edu.au (Lecture Notes adapted from Notes of Dr Feng Li)

Subject Content
 Part I – Applied Queueing Theory

(Lecturer: Dr Alex Leong)

 Part II- The Internet (protocols and

analysis) (Lecturer: Dr Julien Ridoux)

Lectures and Consultations
 Two lectures and one tutorial per week

Monday 10-11 (Th:Architecture-103 [eZone] )  Wednesday 12-1 (Th:Alan Gilbert-Theatre 2 )  Friday 3:15-4:15 (Th:Doug McDonell-309 [Denis Driscoll Theatrette]) 

 Consultation hours – by email appointment  Two workshops (6 hrs each, weeks TBA)

 Assessment: 70% final exam, 15% each for

two workshops

What will we learn?
 How to quantitatively analyze the

performance of simple communication networks (Part I)  How does the internet work (Part II)  Various internet protocols (Part II)

Important Topics
 Introduction to Queueing theory  Basics of queueing theory  Birth-death processes  M/M/1 queue  M/M/m, M/M/ , M/M/m/n and other Markovian queues  Queues with general service times  Networks of queues  Introduction to the Internet  Transport layer  Network layer  Link layer

Knowledge Required
 Probability and stochastic processes

References (Part I)
 Fundamentals of Queueing Theory, 4th

Edition, Donald Gross and Carl Harris  Data Networks, 2nd Edition, Dimitri Bertsekas and Robert Gallager (free)  Queueing Systems Volume 1: Theory, Leonard Kleinrock  Introduction to Queueing Theory, 2nd Edition, Robert Cooper (free)  Introduction to Queueing Theory and Stochastic Teletraffic Models, Moshe Zukerman (free)

Textbooks (Part II)
 Computer Networking: A Top Down

Approach Featuring the Internet, 4th edition. Jim Kurose, Keith Ross Addison-Wesley, 2008.

Textbooks (Part II)
 Data Networks: 2nd edition.

Dimitri Bertsekas, Robert Gallager Prentice-Hall, 1992.

1. Basics of Queueing Theory

Basics of Queueing Theory
 Introduction

 Terminologies
 Notations  Performance measures  Some analysis – Little’s Law

Queues and Delays
 All of us have experienced the annoyance

of having to wait in line.

Banks, restaurants, airports

 Unfortunately, this phenomenon continues

to be common in “high-tech” societies

Call centers, accessing VCE results, launch of Apple products

 We don’t like to wait
 The managers of the establishment at

which we wait don’t like us to wait

Why then is there waiting?
 There is more demand for the service than

there is facility to provide for the service

There may be a shortage of available servers  It may be economically infeasible for a business to provide the level of service necessary to prevent waiting, e.g. bank tellers  Customers interested in “How long do I

have to wait?”  Business owners interested in “How long will the queue be on average?”

Queueing System
 A queueing system can be described as

customers arriving for service, waiting for service and leaving the system after being served.  “Customers” is used in a general sense and does not imply necessarily a human customer An airplane waiting in line to take off  A data packet waiting to be transmitted by a router 

Applications of Queueing theory
 Queueing theory was developed to provide models

to predict the behaviour of systems that attempt to provide service for randomly arising demands.  The earliest problems studied were in telephone traffic congestion. 

 There are many valuable applications of queueing

“The Theory of Probabilities and Telephone Conversations” Erlang, 1909 “Application of the Theory of Probability to Telephone Trunking Problems” Molina, 1927

theory. Examples are traffic flow (vehicles, people, communication), scheduling (jobs on machines, programs on computer)

Knowledge Required
 Conditional probability, statistical...