Queuing Theory

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

Discrete event process, definition, random distribution, and probability. Basic processes, process of revitalisation. Markov process, Markov models, Kendall classification, model M/M/1, models M/M/n. Non-markovian models, model M/C/n, models G/G/n. Models with continuous flow. Serve process, examples Petri net.

Requirements:

Syllabus of lectures:

1.Introduction, queuing model, examples.

2.Discrete event models, definition, form of notation, random distribution, and probability.

3.Basic processes - homogenous, ordinary processes, Poisson process, process of revitalisation.

4.Markov processes, set of Kolmogorov differential equations.

5.Markov model, Kendall classification.

6.Model M/M/1, number of customers, distribution of arrival rate and waiting time in queue, queuing systems.

7.Models M/M/a, stability condition, characteristics of a system, system M/M/Ą, system with a finite time of queuing.

8.Nonmarkovian models, model M/G/a, system with generally distributed service.

9.Model G/G/n.

10.Model with continuous flow.

11.Serve process, introduction. Equilibrium in queuing model.

12.Serve process, examples. Model of an open server.

13.Petri net.

14.Computer simulations.

Syllabus of tutorials:

Study Objective:

Study materials:

Bacceli F., Brémaud P.: Elements of Queuing Theory, Springer - Verlag, Applications of Mathematics 26, 1994

Kleinrock L.: Queuing Systems. orig. John Wiley &Sons, ruský překlad Moskva, 1979

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: