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Viktoria Fodor redigerade 20 januari 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
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
Ioannis Glaropoulos redigerade 3 februari 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - 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 redigerade 5 februari 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - slides (pdf)
Lecture 5-7 - 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 redigerade 17 februari 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - slides (pdf)
Lecture 5-7 - slides (pdf)
Lecture 7 (M/M/m//C) - slides (pdf) (new)¶
Lecture 8 - 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 redigerade 20 februari 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - slides (pdf)
Lecture 5-7 - slides (pdf)
Lecture 7 (M/M/m//C) - slides (pdf) (new)
Lecture 8 - slides (pdf)
Lecture 9 - 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 redigerade 24 februari 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - slides (pdf)
Lecture 5-7 - slides (pdf)
Lecture 7 (M/M/m//C) - slides (pdf) (new)
Lecture 8 - slides (pdf)
Lecture 9 - slides (pdf)
Lecture 10 - 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 redigerade 4 mars 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - slides (pdf)
Lecture 5-7 - slides (pdf)
Lecture 7 (M/M/m//C) - slides (pdf) (new)
Lecture 8 - slides (pdf)
Lecture 9 - slides (pdf)
Lecture 10 - slides (pdf) - updated
Lecture 11 - slides (pdf)
Lecture 12 - slides (pdf)
Problems for lecture and recitation 12
Solutions for problems 1 and 2¶
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 redigerade 5 mars 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - slides (pdf)
Lecture 5-7 - slides (pdf)
Lecture 7 (M/M/m//C) - slides (pdf) (new)
Lecture 8 - slides (pdf)
Lecture 9 - slides (pdf)
Lecture 10 - slides (pdf) - updated
Lecture 11 - slides (pdf)
Lecture 12 - slides (pdf)
Problems for lecture and recitation 12
Solutions for problems 1 and 2
Solutions for problems 3 to 5¶
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 redigerade 11 mars 2014
Lecture slides Lecture slides are uploaded a couple of days before the lecture.
Lecture 1: Introduction
Lecture 2 - slides (pdf)
Lecture 3 - slides (pdf)
Lecture 4 - slides (pdf)
Lecture 5-7 - slides (pdf)
Lecture 7 (M/M/m//C) - slides (pdf) (new)
Lecture 8 - slides (pdf)
Lecture 9 - slides (pdf)
Lecture 10 - slides (pdf) - updated
Lecture 11 - slides (pdf)
Lecture 12 - slides (pdf)
Problems for lecture and recitation 12
Solutions for problems 1 and 2
Solutions for problems 3 to 5 - solution 5(a) corrected.
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
Ioannis Glaropoulos redigerade 28 januari 2014
Recitation material
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Detailed Solutions to the exercises (to be updated atbefore each recitation)
Recitation plan
Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems discussed on the recitation.
R1 Probability theory - overview
R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,(5),6)
R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,6)
R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)
R5 M/M/m/m loss system (Ch. 6) + Exercise 5.7
R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2, 7.6 and Ex. 8 from the exam problem set)
R7 M/M/m/S and M/M/m//K (Ch. 8, to be solved on the recitation: Ex. 6.6 and 8.6)
R8 Method of stages (Ch. 9 : 9.1, 9.2, two extra exercise problems)
R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4)
R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.5, exercise 11.3, the problem 2 from the exam in december 2010. )
R11 Queuing networks (Ch. 12: one extra exercise problem, 12.1, 12.3, 12.2 )
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.
Ioannis Glaropoulos redigerade 12 februari 2014
Recitation material
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Detailed Solutions to the exercises (to be updated BEFORE each recitation)
Recitation plan
Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems discussed on the recitation.
R1 Probability theory - overview
R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,(5),6)
R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,6)
R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)
R5 M/M/m/m loss system (Ch. 6) + Exercise 5.7
R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2, 7.6 and Ex. 8 from the exam problem set)
R7 M/M/m/S and M/M/m//K (Ch. 8, to be solved on the recitation: Ex. 6.6 and 8.6)
R8 Method of stages (Ch. 9 : 9.1, 9.2, two extra exercise problems)
R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4)
R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.5, exercise 11.3, the problem 2 from the exam in december 2010. )
R11 Queuing networks (Ch. 12: one extra exercise problem, 12.1, 12.3, 12.2 )
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.
Ioannis Glaropoulos redigerade 13 februari 2014
Recitation material
Problems for all recitations (pdf)
Solutions for all recitations (pdf)
Detailed Solutions to the exercises (to be updated BEFORE each recitation)
Recitation plan
Chapter numbers refer to the problem set chanpter in the course compendium. In same cases we also give the set of problems discussed on the recitation.
R1 Probability theory - overview
R2 Probability theory - problems (Ch. 1, Problems to be considered on the recitation: 2,3,4,(5),6)
R3 Markov chains (Ch. 3, Problems to be considered on the recitation: 2,3,4,6)
R4 Queuing systems (Ch. 4), M/M/1 (Ch. 5)
R5 M/M/m/m loss system (Ch. 6) + Exercise 5.7
R6 M/M/m (Ch. 7, to be solved on the recitation: 7.2, 7.6 and Ex. 8 from the exam problem set)
R7 M/M/m/S and M/M/m//K (Ch. 8, to be solved on the recitation: Ex. 6.6 and 8.6)
R8 Method of stages (Ch. 9 : 9.1, 9.2, two extra exercise problems)
R9 M/G/1 (Ch. 10: 10.1, 10.2, 10.4)
R10 M/G/1 with vacation and priorities (Ch.11: exercise 11.5, exercise 11.3, the problem 2 from the exam in december 2010. )
R11 Queuing networks (Ch. 12: one extra exercise problem, 12.1, 12.3, 12.2 )
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.