S-38.143 Queueing THeory (3 cr) L

S-38.143 Queueing Theory (3 cr) L

Course instructions, Fall 2000

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 HUT main building, room U345, starting from the 14th of September, and ending on the 7th of December (12 lectures).

Exercises: Exercises are held in the same place after the lectures, starting from the 21th of September. Solved problems are to be returned to the assistant before exercises.

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 Esa Hyytiä (room SI 209, puh. 4786, email esa.hyytia@tct.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.

Entry: Obligatory enrolling is through TOPI.

Program:
1. Introduction, basic probability theory
2. Some important distributions, transformations, generating function
3. Stochastic processes, Markov chains, Markov processes
4. Poisson-process; Little's result, 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. Priority queues, multidimensional systems
9. M/G/1-queue: PK-formulas for the means
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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