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Viktoria Fodor edited 16 December 2012
Please fill in the course evaluation form. Your oppinion will help us to improve the course.¶ Thanks in advance!¶ The l Password: markov.¶
Link to the course evaluation form will be added towards the ed of the course.. ¶
Thanks in advance!¶
Viktoria Fodor edited 11 January 2013
Here you can find several previous exams with solutions. Also, here you will find the solutions of your exam and make-up exam.
If you have received Fx contact the teacher (vfodor@kth.se) as soon as possible. You have the opportunity to complemet to E, but you have to do it within 6 weeks after the Fx has been reported (until ca. end of February for the main exam and end of September for the make-up exam).
The make-up exam is in June, see KTH Schema for date, time, location. Note, that you have to register for the make-up exam.
If you need to complain about the grading, you can submit complaints through STEX. Please ask them about the exact process.
Exam 2012-12-14 Grading (with the number of students with a given grade)¶
A: 45-50 (1) B: 39-44 (6) C: 33-38 (4) D: 27-32 (10) E: 21-26 (13) Fx: 18-20 (2) F: 0-17 (9)¶
Solutions will be published next week.¶
Make-up exam 2012-06-11 Grading (with the number of students with a given grade)
A: 45-50 (0) B: 39-44.5 (1) C: 32-38.5 (4) D: 26-31.5 (1) E: 21-25.5 (2) Fx: 19-20.5 (0) F: 0-18.5 (3)
* Exam (pdf)
* Solution (pdf)
Exam from 2011-12-15 A: 45-50 (0) B: 39-44.5 (4) C: 32-38.5 (4) D: 26-31.5 (5) E: 21-25.5 (5) Fx: 19-20.5 (4) F: 0-18.5 (8, out of these 4 not higher than 10)
* Exam (pdf)
* Solutions (pdf)
Make-up exam from 2011-06-10
* Exam (pdf)
* Solutions (pdf)
Exam from 2010-12-18
* Exam (pdf)
* Solutions (pdf)
Exam from 2004-12-16
* Exam (pdf)
* Solutions (pdf)
Exam from 2009-12-17
* Exam (pdf)
* Solution (pdf)
Viktoria Fodor edited 15 January 2013
Here you can find several previous exams with solutions. Also, here you will find the solutions of your exam and make-up exam.
If you have received Fx contact the teacher (vfodor@kth.se) as soon as possible. You have the opportunity to complemet to E, but you have to do it within 6 weeks after the Fx has been reported (until ca. end of February for the main exam and end of September for the make-up exam).
The make-up exam is in June, see KTH Schema for date, time, location. Note, that you have to register for the make-up exam.
If you need to complain about the grading, you can submit complaints through STEX. Please ask them about the exact process.
Exam 2012-12-14 Grading (with the number of students with a given grade)
A: 45-50 (1) B: 39-44 (6) C: 33-38 (4) D: 27-32 (10) E: 21-26 (13) Fx: 18-20 (2) F: 0-17 (9)
Solutions will be published next week.¶
* Exam
* Solution
Make-up exam 2012-06-11 Grading (with the number of students with a given grade)
A: 45-50 (0) B: 39-44.5 (1) C: 32-38.5 (4) D: 26-31.5 (1) E: 21-25.5 (2) Fx: 19-20.5 (0) F: 0-18.5 (3)
* Exam (pdf)
* Solution (pdf)
Exam from 2011-12-15 A: 45-50 (0) B: 39-44.5 (4) C: 32-38.5 (4) D: 26-31.5 (5) E: 21-25.5 (5) Fx: 19-20.5 (4) F: 0-18.5 (8, out of these 4 not higher than 10)
* Exam (pdf)
* Solutions (pdf)
Make-up exam from 2011-06-10
* Exam (pdf)
* Solutions (pdf)
Exam from 2010-12-18
* Exam (pdf)
* Solutions (pdf)
Exam from 2004-12-16
* Exam (pdf)
* Solutions (pdf)
Exam from 2009-12-17
* Exam (pdf)
* Solution (pdf)
Scheduling staff edited 31 August 2013
[u'TIKTM1', u'TTLSM2', u'TTLTIEMM1TSIA, TIKTM1, TNSSM1', u'TSCRM1', u'TSCRM2', u'TNSTTLSM1', u'TIEMM1TSIA']TTLSM2
Scheduling staff edited 14 September 2013
TIEMM1TSIA, TIKTM1, TNS[u'TIKTM1', u'TTLSM2', u'TTLSM1', u'TSCRM1', u'TSCRM2', TTLu'TNSSM1', TTLSM2u'TIEMM1TSIA']
Scheduling staff edited 4 December 2012
Q1B21, Q13, Q15B22, B23, B24
Flyttad från Q-huset
Viktoria Fodor edited 17 October 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 8 - slides (pdf)
* Lecture 9 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 29 October 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 8 - slides (pdf)
* Lecture 9 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 5 November 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 8 - slides (pdf)
* Lecture 9 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 6 November 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 8 - slides (pdf)
* Lecture 9 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 14 November 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 7 - slides (pdf) (New !!!)
* Lecture 8 - slides (pdf)
* Lecture 9 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 19 November 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 7 - slides (pdf) (New !!!)
* Lecture 8 - slides (pdf) * Lecture 9 - slides (pdf) * Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 21 November 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 7 - slides (pdf)
* Lecture 8 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 26 November 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 7 - slides (pdf)
* Lecture 8 - slides (pdf)
* Lecture 9 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 29 November 2012
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
* Lecture 1 - slides (pdf)
* Lecture 2 - slides (pdf)
* Lecture 3 - slides (pdf)
* Lectures 4-5 - slides (pdf)
* Lectures 5-7 - summary (pdf)
* Lecture 7 - slides (pdf)
* Lecture 8 - slides (pdf)
* Lecture 9 - slides (pdf)
* Lecture 10 - slides (pdf)
* Lecture 11 - slides (pdf)
* Lecture 12 - slides (pdf)
Lecture topics Below we list the approximate lecture topics and the related reading suggestions. (V1:1-3, 5-7 means the Virtamo notes, section 1: pages 1 to 3 and 5 to 7; N1.1-3 means the Nain notes sections 1.1 to 1.3. All ranges are inclusive final page or section).
* Introduction to queuing systems: course overview, queuing systems, stochastic processes recall. Reading: probability theory and transforms - basics (V1:1-21, V2:1-19,V3:1-19, V9:1-7).
* Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
* Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
* M/M/1 (V12:1-12, N2.1).
* M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
* M/M/m - wait system (V12:13-20, N2.3-7).
* M/M/m/*/n - finite population systems (Engset) (V11:1-11).
* Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
* M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
* Priority service and service vacations (V14:1-10, N3).
* Open queuing networks (V15:1-5,9-12, N4.1).
* Course summary
Viktoria Fodor edited 26 November 2012
There is a mandatory small project in the course with submission deadline 2013 January 4. The project has to be performed individually and is graded pass/fail based on the submitted report. Projects with exceptional quality receive 5 extra points that is added to the points achieved at the exam. These extra points are valid only at the first exam, and are not considered at make-up exams.
TWe offer two projects this year. You can find the project description and submission instructions will be published in the first weeks of the courses below.¶
I. Analytic studi of error control in multihop wireless networks.¶
Coming soon.¶
II. Simulating a Spotify Server¶
Project description (pdf)¶
In additon, you will need two data files for this project. They will be added soon.
Viktoria Fodor edited 28 October 2012
Recitation plan
Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems solved on ther ecitation.
R1 Probability theory - overview
R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,5,6) Problems Solutions
R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,5,6)
R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)
R5 M/M/m/m loss system (Ch. 6)
R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2)
R7 M/M/m/S and M/M/m//K (Ch. 8)
R8 Method of stages (Ch. 9 : 9.1, 9.2)
R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4, 10.3)
R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, the problem 2 from the exam in december 2010, exercise 11.1. )
R11 Queuing networks (Ch. 12)
R12 Course summary, example exam problems
Exam problems solved on the recitations
During the second part of the course we will solve an exam problem on most of the recitations, to prepare for the exam. Try to solve the problem on your own before coming to the recitation, then you will benefit more from the discussion there.
Viktoria Fodor edited 31 October 2012
Recitation material¶
Problems for all recitations (pdf)¶
Solutions for all recitations (pdf)¶
Recitation plan
Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems solved on ther recitation.
R1 Probability theory - overview
R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,5,6) Problems Solutions
R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,5,6)
R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)
R5 M/M/m/m loss system (Ch. 6)
R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2)
R7 M/M/m/S and M/M/m//K (Ch. 8)
R8 Method of stages (Ch. 9 : 9.1, 9.2)
R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4, 10.3)
R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.3, the problem 2 from the exam in december 2010, exercise 11.1. )
R11 Queuing networks (Ch. 12)
R12 Course summary, example exam problems
Exam problems solved on the recitations
During the second part of the course we will solve an exam problem on most of the recitations, to prepare for the exam. Try to solve the problem on your own before coming to the recitation, then you will benefit more from the discussion there.
