TKK | Tietoverkkolaboratorio | Opetus

**S-38.143 Queueing Theory (3 cr) L
**

**Course instructions, Fall 2003
**

**Course status:** *Queueing theory* is an obligatory course
for the students having teletraffic theory as a major or minor.
The course is also eligible for postgraduate studies.

**Object: ** The course will teach the fundamentals of the traditional
queueing theory, so that the student can apply the mathematical tools
to practical problems. The queueing models can be used to model
different kinds of systems. The examples in the course are primarily taken
from telecommunication systems.

The course serves as an introductory course for the spring course S-38.141 teletraffic theory, which contains applications to the analysis of data communication systems and more advanced queueing models.

**Credits:** 3 credits units.

**Prerequisites:** Recommended courses are
Mat-2.090 (applied probability A)
Mat-2.111 (stochastic processes) and
S-38.145 (introduction to teletraffic theory).

**Lectures:** Lectures are on Thursdays from 2 pm to 4 pm in the
department of electrical and communications engineering, room F201
starting from the 11th of September, and ending on the 27th of November.

**Exercises:** Exercises are held in the same place
after the lectures, starting from the 18th of September. Solved problems are to be
returned to the assistant before exercises.

**Schedule:**

date | 11.9 | 18.9 | 25.9 | 2.10 | 9.10 | 16.10 | 23.10 | 30.10 | 6.11 | 13.11 | 20.11 | 27.11 | 4.12 |

lecture | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | - |

exercises | - | x | x | x | x | x | x | x | x | x | x | x | x |

**Examination:** After the course, the first examination will be on Friday the 12th of December, 13-16 at S5.

**Language:** Both lectures and exercises are held in Finnish. The lecture notes as well as
homework problems will be available in English.

**Teachers:**
The course is lectured by
prof. Jorma Virtamo
(room SE 311, phone 4783,
email jorma.virtamo@hut.fi).
The exercises are held by
Lic.Sc. (Tech.) Esa Hyytiä
(room SE 322, tel 4786,
email esa.hyytia@netlab.hut.fi).

**Completion:** The completion of the course requires solving the homework problems
and passing the examination. At least 30% of the problems must be solved correctly.
Extra points can be obtained by solving more than the required minimum 30% as follows:
50% 1 point, 65% 2 points, 80% 3 points (cf. examination max 30 points).
The extra points do not, however, apply for a failed examination.

**Literature:**

P.G. Harrison, N.M. Patel, Performance Modelling of Communications
Networks and Computer Architectures, Addison-Wesley, 1993 (partly).

Lecture notes.

Queueing theory related material can be found from
Myron Hlynka's queueing theory page.

**Entry: **Obligatory enrolling is through TOPI.

**Contents:**

1. Introduction, basic probability theory, some important distributions,
transformations, generating function

2. Stochastic processes, Markov chains, Markov processes

3. Poisson-process; Little's result,

4. Queueing systems

5. Erlangs loss system ((M/M/m/m-queue)

6. Finite source population, Engsets system

7. M/M/1-queue, M/M/m-queue

8. M/G/1-queue: PK-formulas for the means

9. Priority queues

10. M/G/1-jqueue: the queue length distribution

11. Time reversibility, Burke's theorem, truncation of state space

12. Open (Jacksons) queueing networks; Closed queueing networks, mean value analysis (MVA)

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