Queuing Theory
6H3708
Credits: 5, ECTS Credits: 7,5
Grading: 3, 4, 5
Language: Engelska / English
Time: Period 1, 2006/7
Coordinator
Armin Halilovic
office: 5046
tel. 08-790 4810
www.syd.kth.se/armin
armin@syd.kth.se
Aim
Queuing theory is the basis for dimensioning of telecommunication and
data communication networks and performance evaluation.
After completing the course the students should have basic knowledge
about queuing theory
Content:
Introduction to basics in probability theory.
Markov chains in discrete and continuous time. Birth-death processes. Stability.
Basic concepts in queuing theory. Little’s theorem.
Arrival processes and service time. Traffic intensity. Queuing disciplines.
Utilization.
Waiting systems M/M/m/K/M.
M/M/m loss systems, Erlang, Engset, Bernoulli. Blocking probability
Survey on queuing networks
Prerequisites
Elementary courses in mathematics and mathematical statistics.
Requirements
Written examination (TEN1; 3 cr.).
Passed written assignment (RED1; 2 cr.).
Grading 3, 4, 5.
Required reading
Required reading:
QUEUEING MODELLING FUNDAMENTALS,
Ng Cheee Hock, John Wiley & Sons LTD ISBN 0471968196
RECOMMENDED
READING
--------------------------
Queueing theory books ( FREE ) online
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A little Swedish -English glossary of basic terms in queueing theory
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EXERCISES AND REPETITION BEFORE THE EXAMINATION
1)
Introduction, Discrete -Time Markov chains, Birth-and-Death Process, Poisson
Process
2)
Continuous -Time Markov chains. Q matrix
2b)
Life distributions
3)
M/M/1 system
4)
M/M/1 system
4b)
M/M/m system
5)
M/M/m/K system (m servers, K waiting positions)
6)
M/M/m/K system (m servers, K waiting positions)
7)
M/M/m/K/C system (m servers, K waiting positions, C customers )
8)
ERLANG LOSS SYSTEM (m servers, 0 waiting positions, "unlimited number of customers")
9)
ENGSET LOSS SYSTEM (m servers, 0 waiting positions, C customers, C>m)
10)
BINOMIAL (BERNOULLI) LOSS SYSTEM (m servers, 0 waiting positions, C customers, C<=m )
11)
MIXED PROBLEMS
==================
COMPUTER ASSIGNMENTS (inlämningsuppgifter) , (RED1; 2cr.) :
Assignment
1
Assignment
2
Assignment
3
Assignment
4
Group work: Maximum 2 students can work together on the same assignment.
Date and time for presentation:
Date: 16 Oct 2006, time 15:15- 17:15, room: 5112
Questions related to lab work will be included in the
exam.
====================
TESTS AND BONUS POINTS:
Two "in-class" tests will be organized during the course.
| Date | Time | room | |
| Test1 | 15 Sept 06 | 15:15 | 2105 |
| Test2 | 6 Oct | 10:15 | 5094 |
Every correct solved problem on tests gives you a bonus point that will be added
on to the result on your final written examination.
You can get maximum 4 points per test.
Earned bonus points are valid until 31 Aug 2007.
-------------------------------------
The old tests:
TEST 1:
test 1: 19 Sep 06
TEST 1:
test 1: Sep 05
--------------------------------------
TEST 2A:
test 2A: 6 Oct 06
TEST 2B:
test 2B: 6 Oct 06
TEST 2: test
2: Oct 05
====================
WRITTEN EXAMINATION (TEN1; 3cr.)
INSTRUCTIONS:
Allowed to use : Calculator
You are NOT allowed to use tables of mathematical formulas in the exam.
Use of any communication device is strictly prohibited when taking this examination.
Grading: For each correct solution 4 points will be awarded.
Credit will be given for presentation and methods of solutions.
A maximum of 24 points can be earned. Points can also be deducted for unsubstantiated
answers. At least 12 points are required to pass the exam.
Grading scale : Total points: 24
12 - 17 points are required for the grade 3;
18 - 20 points are required for the grade 4;
21 -24 points are required for the grade 5
There will be a supplementary exam for those students who can manage at least
9 points in the exam.
The supplementary exam will be different from the regularly scheduled exam,
though it will cover the same material
..
The old exams:
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