Queuing Theory
Code  Completion  Credits  Range 

A11THO  ZK  2  2+0 
 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. Nonmarkovian 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 timetable has been prepared for this course
 The course is a part of the following study plans: