Course MQSN: Markovian Queues and Stochastic Networks

Time:	Monday 11.00 - 12.45 (September 9 – November 11) Please note that there is no lecture on 16 September
Location:	All LNMB courses take place on the Campus Utrecht Science Park. Room HFG 611, Hans-Freudenthal building, Budapestlaan 6, 3584 CD Utrecht
Lecturer:	Prof. Dr. Richard J. Boucherie (UT)

Important information

Participants of this course: please see the lecturer's website. There you may find announcements, lecture notes, additional material, slides, old videos, and exercise sets, among other information.

Course description

Complex stochastic systems, like communication systems, computer networks and manufacturing systems, may often be modeled as queueing networks with multiple nodes and/or multiple classes. The performance of these systems may be evaluated in terms of queue lengths, sojourn times or blocking probabilities. This course focuses on basic queueing networks for which performance measures can be obtained in closed form. First, the course focuses on a class of networks where the equilibrium distribution has a so-called product-form solution. Topics include the output theorem, reversibility, partial balance, quasi reversibility and product-form. Examples include Jackson networks, Kelly-Whittle networks, BCMP networks, loss networks and processor sharing networks. Second, the course considers the sojourn time distribution in simple networks. Third, computation of performance measures often requires effcient algorithms. To this end, Mean Value Analysis and approximation techniques will be studied.

Detailed content

reversibility, stationarity, basic queues, output theorem, feedforward networks
partial balance, Jackson network, Kelly-Whittle network, arrival theorem
quasi-reversibility, customer types, BCMP networks, bandwidth sharing networks
blocking, aggregation, decomposition
loss networks, insensitivity via supplementary variables
sojourn time distribution in networks
MVA, AMVA, QNA

Literature

R. Nelson, Probability, Stochastic Processes and Queueing Theory, 1995 : Chapter 10
F.P. Kelly, Reversibility and Stochastic Networks, Wiley, 1979 (available on-line)
R.W. Wolff, Stochastic Modeling and the Theory of Queues, Prentice Hall, 1989.
R.J. Boucherie, N.M. van Dijk (editors), Queueing Networks - A Fundamental Approach, International Series in Operations Research and Management Science Vol 154, Springer, 2011
P. Whittle, Systems in stochastic equilibrium, Wiley, 1986
Handouts, slides and references to relevant additional literature will be made available at the lectures.

Prerequisites

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

Examination

Take home problems.

Address of the lecturer

Prof.dr. R.J. Boucherie
Stochastic Operations Research;
Department of Applied Mathematics;
Faculty of Electrical Engineering, Mathematics, and Computer Science;
University of Twente
P.O. Box 217
NL-7500 AE Enschede
Phone: 053-4893432
Email: r.j.boucherie@utwente.nl