6 EC
Semester 2, period 4, 5
5334QLFT6Y
| Owner | Master Mathematics |
| Coordinator | prof. dr. M.R.H. Mandjes |
| Part of | Master Mathematics, year 1Master Stochastics and Financial Mathematics, year 1 |
The course considers various aspects of queueing systems with Levy input, special cases being the classical M/G/1 queue and reflected Brownian motion. Introducing this class of queues as the solution of a Skorokhod problem, we subsequently characterize its stationary and transient distributions. Emphasis is put on the situation that the driving Levy process is spectrally one-sided; for the two-sided Wiener-Hopf theory is treated (but not in full detail). Then various other performance metrics are considered, such as busy periods and the workload correlation function. Explicit tail asymptotics are provided, which are derived by e.g. inversion techniques and change-of-measure arguments. Then the results are extended to networks of queues, e.g., tandems and feedforward networks. The course concludes by discussing applications in communication networks and mathematical finance.
-- Acquiring basic knowledge on Levy-porcesses
-- Conceptual understanding of Levy-driven queues, and the relation to fluctuation theory (e.g. distribution of running maximum)
-- Mastering a variety of techniques that come in useful in this context: transform-based techniques, various types of asymptotics, importance sampling, rate conservation arguments, etc.
-- Analysis of a broad range of performance metrics, such as workload, busy period, etc.
|
Activity |
Number of hours |
|
Lecture |
26 |
|
Zelfstudie |
142 |
The programme does not have requirements concerning attendance (OER-B).
| Item and weight | Details |
|
Final grade | |
|
0.5 (50%) Oral exam | |
|
0.5 (50%) Homework |
Contact the course coordinator to make an appointment for inspection.
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.uva.nl/plagiarism
| Weeknummer | Onderwerpen | Studiestof |
| 1 | Introduction | Ch. 1 |
| 2 | Levy-driven queue, stationary behavior | Ch. 2-3 |
| 3 | Transient behavior | Ch. 3-4 |
| 4 | Heavy traffic | Ch. 5 |
| 5 | Busy period | Ch. 6 |
| 6 | Workload correlation function | Ch. 7 |
| 7 | Asymptotics | Ch. 8 |
| 8 | Transient asymptotics, simulation | Ch. 9-10 |
| 9 | Finite buffer, MAP input | Ch. 11 |
| 10 | Tandem | Ch. 12 |
| 11 | Networks | Ch. 13 |
| 12 | Communication networks | Ch. 14 |
| 13 | Finance, numerics | Ch. 15-16 |
| 14 | ||
| 15 | ||
| 16 |
The schedule for this course is published on DataNose.