Course details

# Optimization Methods and Queuing Theory

DPC-TK1 FEEC BUT DTK1 Acad. year 2019/2020 Winter semester

The second part of the unit deals with the Queuing Theory. Various models of single queue systems and queuing networks are derived. The theory is then used by solving practical problems. Students are also introduced into simulation methods that are the only feasible solution method when a theoretical model is not available.

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Subject specific learning outcomes and competences

Learning objectives

Developing awareness of mathematical models of Queuing Theory and their use in solving technical problems including simulation methods.

Prerequisite kwnowledge and skills

Study literature

- POPELA, P.; SKLENÁŘ, J. Optimization. Teaching notes, University of Malta, 2003.
- SKLENÁŘ, J. Dynamic Programming Theory and Applications. Teaching notes, University of Malta, 2008.
- POPELA, P. Nonlinear Programming. Teaching notes, University of Malta, 2003.
- ATTARD, N.; SKLENÁŘ, J. Linear Programming. Teaching notes, University of Malta, 2007.
- SKLENÁŘ, J. Introduction to Integer Linear Programming. Teaching notes, University of Malta, 2007.
- SKLENÁŘ, J. Infinite Horizon Dynamic Programming Models. Teaching notes, University of Malta, 2010.
- POPELA, P. Stochastic Programming. Teaching notes, University of Malta, 2008.
- SKLENÁŘ, J. Queuing Theory. Teaching notes, University of Malta, 2016.
- SKLENÁŘ, J. Queuing Theory - Worksheets. Teaching notes, University of Malta, 2016.

Syllabus of lectures

2. Linear Programming. Theory and Simplex Method.

3. Integer Programming. Solution methods and use of indicator variables in building models that are out of scope of Linear Programming (models with logical conditions, disjunctive constraints, and similar.)

4. Theory of Nonlinear Programming. Convex sets and functions, optimality conditions.

5. Optimization algorithms of Nonlinear Programming and their application.

6. Dynamic Programming with finite horizon. Introduction to recursion, solution of various practical problems by the methods of Dynamic Programming.

7. Introduction to Stochastic Programming. Terminology, basic forms of Deterministic Equivalents and their solution.

8. Introduction to Dynamic Programming with infinite horizon. Terminology, Markov Decision Process, Bellman's equations and their solution.

9. Heuristic optimization algorithms as a method to solve problem of local optima (genetic and similar algorithms based on populations of solutions).

10. Basics of Queuing Theory, introduction to stochastic processes, Poisson process in detail.

11. Models of simple single queue systems (model M/M/1 and similar).

12. Advanced single queue models (M/G/1, G/M/1 and similar). Network models, Jackson theorem.

13. Simulation methods and their use in analysis of queuing systems.

Progress assessment

Controlled instruction