This course will be taught in English. For any questions see me at   https://fu-berlin.webex.com/meet/k.wolter on Tuesday, 21.4.2020 between 12 and 1pm.

Operations of the course:

- lectures will be videos, the material is mostly from the book by William Stewart, which you find in the resources. All lecture videos will be posted at: https://fu-berlin.eu.vbrickrev.com/#/media/all. They will all be tagged 'Markov Chains', in the hope that this will allow you to find them.

- tutorials take place on Thursdays 4:14-5:45pm at https://fu-berlin.webex.com/fu-berlin-en/j.php?MTID=mb08d48f61b55e4794dd9142b50a45931  , the meeting number is 398560, password XSnMV42i65e.

- there will be no tutorial on 21.05.2020

Requirements:

- participate in at least 7 tutorials, be able to present your solution to at least half of the assignments in at least 7 tutorials.

- pass the exam at the end of the semester, which may be written, or oral, depending on the corona rules at FUB.

Any questions can be discussed during the tutorials.

Contents summary:

All videos will be uploaded to the zedat service vbrick, I will tag them with the term 'Markov Chains', which will hopefully help you to find them, once vbrick is populated with lots of videos.

Week 1: Introduction (video: https://fu-berlin.eu.vbrickrev.com/sharevideo/851e3540-442f-4dec-abf0-d4e27f009cd7,  slides in resources),

Lecture 1:

Probability theory primer part 1 (video: https://fu-berlin.eu.vbrickrev.com/sharevideo/b43523af-d9c8-4d36-9fad-083a7a6e4bc4, lecture notes in resources), or https://nextcloud.imp.fu-berlin.de/index.php/s/FAsA6iZMpSyoHAt

Part 2 (video: https://fu-berlin.eu.vbrickrev.com/sharevideo/6bfcfa9c-8944-4236-93e9-abaca3be2b46, lecture1bAnnotated.pdf are the notes in the resources), or https://nextcloud.imp.fu-berlin.de/index.php/s/XDrEeZdH36rBb6D

Lecture 2: (this is a lot of material, next week it will be less)

Part a: https://fu-berlin.eu.vbrickrev.com/sharevideo/20ac4440-51f2-4e70-9584-489480ed83b6 derived random variables or,https://nextcloud.imp.fu-berlin.de/index.php/s/YrGQxqCEeszeA5J.

Part b: https://fu-berlin.eu.vbrickrev.com/sharevideo/499e9a50-8f5c-44d3-9688-2b1c034dd581, distributions and moments of two random variables, or https://nextcloud.imp.fu-berlin.de/index.php/s/9bWS7gXXdGH2QPS

Part c: https://fu-berlin.eu.vbrickrev.com/sharevideo/dc0f842f-9606-4d0f-80ad-9d9f11725d8d, distribution of minima and maxima of several random variables, or https://nextcloud.imp.fu-berlin.de/index.php/s/ny6TT3p2D4MKACb

Week 2:

Lecture 3:

Part a: https://fu-berlin.eu.vbrickrev.com/sharevideo/1d2133bb-ca5d-42c7-8427-c9e52dde7508 discrete probability distributions.  https://nextcloud.imp.fu-berlin.de/index.php/s/64sgW86tXtft5pM

Lecture 4:

Part a: continuous probability distributions, reliability https://fu-berlin.eu.vbrickrev.com/sharevideo/76842793-36f8-46b1-a1a3-ac5cb5211056  or https://nextcloud.imp.fu-berlin.de/index.php/s/Nt27eKeZTTHWfZY

Part b: Phase-type distributions https://fu-berlin.eu.vbrickrev.com/sharevideo/7654dbd2-25a8-4d61-b9d3-7afc4b361ea7  or  https://nextcloud.imp.fu-berlin.de/index.php/s/d5g78B96Qp5No9R

Week 3:

Lecture 5:

Bounds and limit theorems:  https://fu-berlin.eu.vbrickrev.com/sharevideo/8b37bbfd-993c-4d6d-90a7-31d5cd534583   or https://nextcloud.imp.fu-berlin.de/index.php/s/ofyrtwTQ7g6MLn4

Week 4:

Lecture 6: Discrete time Markov chains https://fu-berlin.eu.vbrickrev.com/sharevideo/491d7c88-4eb9-43ce-ac5a-0c465bc67cc5 or https://nextcloud.imp.fu-berlin.de/index.php/s/27LR85BS29A32tJ

Lecture 7: DTMCs, Sojourn times and embedded MCs  https://fu-berlin.eu.vbrickrev.com/sharevideo/305636f9-7698-4994-b91e-cf5b238d9331 or https://nextcloud.imp.fu-berlin.de/index.php/s/w4k7dTT3qgzfczg

Week 5:

Lecture 8: DTMCs Classification of states https://fu-berlin.eu.vbrickrev.com/sharevideo/a74301da-bb72-4781-8bd7-076b60987e0f  or https://nextcloud.imp.fu-berlin.de/index.php/s/EK8S8ySTB4P8twi

Lecture 9: DTMCs, Irreducibility, Potential and Fundamental matrix   https://fu-berlin.eu.vbrickrev.com/sharevideo/fafba7ad-2061-4794-a743-387568f8620f   or  https://nextcloud.imp.fu-berlin.de/index.php/s/sDd7xzxHMAPoWQp

Week 6

Lecture 10: Random Walk  https://fu-berlin.eu.vbrickrev.com/sharevideo/080d549b-5b74-449a-90a6-a7aa4c9a1a23  or  https://nextcloud.imp.fu-berlin.de/index.php/s/MEDn5Xa7zB9ZSkJ

Lecture 11: Limiting and stationary distributions https://fu-berlin.eu.vbrickrev.com/sharevideo/4ca5c416-0719-4f42-b03a-280b0bdc9f03  or  https://nextcloud.imp.fu-berlin.de/index.php/s/9nqJ8PdEQKr7mwi 

Lecture 12: Reversibility    https://fu-berlin.eu.vbrickrev.com/sharevideo/b81bcc98-97ad-4b8e-bc3f-d4d124e55603   or  https://nextcloud.imp.fu-berlin.de/index.php/s/KjE5LQRsLb62fF3

Lecture 13: Page rank  https://fu-berlin.eu.vbrickrev.com/sharevideo/e65fb743-fcfd-4f27-9098-f2624556993f  or https://nextcloud.imp.fu-berlin.de/index.php/s/5FrkEn7WbsyG5BK

Week 7

Lecture 14: CTMCs  https://fu-berlin.eu.vbrickrev.com/sharevideo/f4e314ae-26fe-47e0-b841-69c97b2ad23f  or https://nextcloud.imp.fu-berlin.de/index.php/s/TJWyDYm64SeMsTf

Week 8

Lecture 15: Renewal processes, PP, uniformisation, stochastic Petri nets https://fu-berlin.eu.vbrickrev.com/sharevideo/6d1cbc1b-9c6c-4791-a6e8-f91454b4e4e0   or  https://nextcloud.imp.fu-berlin.de/index.php/s/n83bq9jyXcFAkcK

Lecture 16:

Petri net tool PIPE2:    https://fu-berlin.eu.vbrickrev.com/sharevideo/6ee2f5c1-4714-4bce-be27-2fe798cb5e03  or  https://nextcloud.imp.fu-berlin.de/index.php/s/Ri7wFbiEsF5Fedm

Lecture 17: Basic queueing theory   https://fu-berlin.eu.vbrickrev.com/sharevideo/bb1a2e24-6f6a-4497-82be-28a3d5d101ed or  https://nextcloud.imp.fu-berlin.de/index.php/s/KWAKz62miegR5m4

Week 9

Lecture 18: Basic queueing theory (Part 2) https://fu-berlin.eu.vbrickrev.com/sharevideo/dacb3026-0717-40e6-96e3-12c6f7aa4e37    https://nextcloud.imp.fu-berlin.de/index.php/s/RqNi3kjSqBb9BN5

Lecture 19: The M/M/1 queue   https://fu-berlin.eu.vbrickrev.com/sharevideo/0a5911f9-0358-41e1-976b-d74e46a99525  or     https://nextcloud.imp.fu-berlin.de/index.php/s/8ZgN3NHRjHRnf9k

Week 10:

Lecture 20: The M/M/m queue https://fu-berlin.eu.vbrickrev.com/sharevideo/a0b7ef7b-19ec-4997-a8d3-5e5a06ce114c   or  https://nextcloud.imp.fu-berlin.de/index.php/s/NSCAF924786HH8L

Lecture 21: The M/M/m/K queue  https://fu-berlin.eu.vbrickrev.com/sharevideo/c7495d8e-6c26-4c81-823c-08cc8aa8f799  or   https://nextcloud.imp.fu-berlin.de/index.php/s/fpMwgD7qYnQQjcW

Week 11:

Lecture 22: The M/G/1 queue  https://fu-berlin.eu.vbrickrev.com/sharevideo/4a625125-ec14-40a2-9c59-b216c06b0e39 or  https://nextcloud.imp.fu-berlin.de/index.php/s/qGPo3NYj3Gj6rTJ

Lecture 23: Queueing networks https://fu-berlin.eu.vbrickrev.com/sharevideo/c0722e9e-6cef-43e4-8021-e9dd1fd50cc8 or  https://nextcloud.imp.fu-berlin.de/index.php/s/q2gWwE9PAbZFYig

Dieser Kurs wird auf englisch gehalten.

Wir beschäftigen uns mit den grundlegenden stochastischen Modellen, die zur Untersuchung der Leistung von Computersystemen häufig benutzt werden. Markov modelle und Warteschlangen werden gerne für die Untersuchung dynamischer Systeme verwendet, z.B. Computer Hardware, Kommunicationsprotokolle, biologische Systeme, Epidemien, Verkehr und digitale Währungen.  Wir werden uns einen raschen Überblick verschaffen.  Betrachtete Themen sind der Geburts- und Todesprozess, der Poissonprozess, verallgemeinerte Markov und semi-Markov prozesse sowie deren Lösungsmethoden. Soweit die Zeit es erlaubt werden wir auch die Hintergründe der diskreten Ereignissimulation ansehen.

Literatur

William Stewart. Probability, Markov Chains, Queues and Simulation. Princeton University Press 2009.