PhD students

Expected schedule: 

Meeting on Wednesdays after EP2200 class (week 5 excluded). Most probably we can stay in the same classroom. If not, we come up the the LCN offices in the Q building. The seminars will be ca. one hour long.

Project performed during the second part and after the course. Project ideas presented on seminars 4,5,6, based on maturity.

Material: see link below (for logged in students)

Seminar style:

PhD students present on white board. Students schedule:

1. Sladjana
2. Andreas
3. Yue
4. Vahan 
5. Xiaolin 
6. Peyman

Topics and references:

Gross and Harris, Fundamentals of Queuing Theory. PDF is available through KTH (e.g., go to www.lib.kth.se, and write Gross and Harris in the search field...)

1. Poisson process, in one and two dimensions
Gross and Harris 1.7-1.8
In addition, let us read some sections on spatial Poisson Process and percolation theory here:
Haenggi, M.; Andrews, J.G.; Baccelli, F.; Dousse, O.; Franceschetti, M., "Stochastic geometry and random graphs for the analysis and design of wireless networks," IEEE Journal on Selected Areas in Communications, , vol.27, no.7, pp.1029,1046, September 2009
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5226957
II.A, IV.C are sections that are mostly interesting for us, but the rest is nice too.

2. Analysis of both discrete and continuous time MCs in transient state. Ergodicity and stability, proof of conditions for these.

We read Chapter 1.9 in Gross and Harris. Unfortunately it does not prove the "main theorem" on the existence of stationer solution, that is, Theorem 1.1 a,b,c on page 38. Neither the two other books I looked at. So, if you have time, please check whether you find a proof. I will keep searching too.

Also, please look at the imbedded MC with equation (1.31).  Can we derive the stability condition of the continuous time birth-death process from this?

3. Use of generating function
M/M/1 Gross and Harris, 2.2.2
Bulk arrival: G-H 3.1
Erlang-r example: G-H 3.3.3 (also phase type?)

4. M/G/1 transform forms:
G-H 5.1.2-5.1.5 (seems to me, maybe some other parts are needed too...)

5. Queuing networks, and specifically product form solutions of large markov chains.
Thomas G. Robertazzi​, Computer networks and systems : queuing theory and performance evaluation, chapters 3.3 and 3.4 (lots of examples, you do not need to go through all of them)

6. Advanced topics: Large deviation theory, Palm calculus - this may be changed given preferences
Large deviation: Lewis, An Introduction... (attached): up to page 9 and page 16
Palm theory: Le Boudec, Performance evaluation of computer and communication systems: chapters 7.1, 7.2 (the first two Palm calculus chapters in my first edition)