Lectures

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).

1. 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).  
2. Poisson process and Markov chains in continuous time (V7:1-15, V4:1-6, V5:1-8, N1.1).
3. Birth-death process, Poisson process, Markovian queuing model, Little's theorem (V6:1-9, V8:1-7, V9:1-7, N1.2-3)
4. M/M/1 (V12:1-12, N2.1).
5. M/M/m/m - loss system (Erlang) (V10:1-10, N2.4).
6. M/M/m - wait system (V12:13-20, N2.3-7).
7. M/M/m/*/n - finite population systems (Engset) (V11:1-11).
8. Semi-Markovian queuing systems: Er, Hr, method of stages (Kleinrock).
9. M/G/1-system, Pollaczek-Khinchine mean value and transform equations (V13:1-25, N2.8).
10. Priority service and service vacations (V14:1-10, N3).
11. Open queuing networks (V15:1-5,9-12, N4.1).
12. Course summary