PhD students

Expected schedule: ¶

Meeting on Thursdays after EP2200 class (week 5 excluded)¶

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

Material: see ling below (for logged in students)¶

Seminar style:¶

PhD students present on white board. Students schedule:¶


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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 dimensionsGross and Harris 1.7-1.8In 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 2009http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5226957II.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 functionM/M/1 Gross and Harris, 2.2.2Bulk arrival: G-H 3.1Erlang-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 evaluationState aggregation in large Markov chains (We still need some good reference)¶

6. Advanced topics: Large deviation theory, Palm calculus - this may be changed given preferencesLarge deviation: Lewis, An Introduction... (attached): up to page 9 and page 16Palm 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)¶

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