Dr Alex Leong Department of Electrical and Electronic Engineering University of Melbourne firstname.lastname@example.org (Lecture Notes adapted from Notes of Dr Feng Li)
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
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)
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
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
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?”
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)
Conditional probability, statistical...