Course AlQT: Algorithmic Methods in Queueing Theory

Time:	Monday 13.15 – 15.00. In case there is a shared lunch, this shifts to 14.00-15.45.
Period:	November 21 - December 19 (2022) and January 30 - February 27 (2023)
Location varies per week:	All LNMB courses are on the Campus Utrecht Science Park. January 30 : Buys Ballot building, room 005 February 6 : Buys Ballot building, room 065 February 13 : Buys Ballot building, room 065 February 20 : Buys Ballot building, room 083 February 27 : Minnaert building, room 014 Details about online facilities for students follow upon registration.
Lecturers:	Prof.dr. R.D. van der Mei (VU Amsterdam, CWI) and Dr. S. Kapodistria (Eindhoven University of Technology)

Course description:
(for participants of this course: see the lecturer's website)

This course focusses on algorithmic aspects of queueing theory, and builds on the basic queueing models treated in the Master course Queueing Theory. Typically, queueing systems can be described by appropriately defined Markov processes. The course starts by treating numerical methods to solve the steady-state and transient behavior of (finite state) Markov processes. Attention is also devoted to the construction of (error) bounds on the steady-state distribution. Then the course introduces elements that enrich the basic queueing models, such as Renewal Phase-type arrival processes, and phase-type service times. Inclusion of such elements usually results in multi-dimensional Markov processes on a strip (i.e., one in finite dimension). Techniques to analyse the steady-state distribution of Markov processes on a strip include: spectral expansion, matrix-analytic and generating function techniques. Further, the course addresses several techniques to analyse Markov processes with two (or more) infinite dimensions, such as the compensation method, the power series method and the generating function (or boundary value) method. Finally, topics such as the (numerical) inversion of generating functions and Laplace transforms are discussed.

Detailed content:
- Direct and iterative methods for the solution of the equilibrium equations
- Markov processes on a strip: M/M/1-type models, G/M/1-type models, and M/G/1-type models
- Matrix-analytic methods
- Spectral expansion
- Generating function (or boundary value) method
- Compensation method
- Power series method
- Numerical inversion of generating functions and Laplace transforms

Literature:
Handouts, slides and references will be made available at the lectures (see webpage).

Prerequisites:
The participants should have followed courses in probability theory, stochastic processes. and queueing theory.

Examination:
Take home problems.

Address of the lecturer:
Dr. S. Kapodistria
Dept. of Mathematics & Computer Science, Eindhoven University of Technology
P.O. Box 513, 5600 MB Eindhoven
Phone: 040-2475825
E-mail: s.kapodistria@tue.nl

Prof.dr. R.D. van der Mei
Faculty of Sciences, Department of Mathematics, Vrije Universiteit Amsterdam
De Boelelaan 1081a, 1081HV Amsterdam
Phone: 020-5987628
E-mail: mei@few.vu.nl