This course will provide an introduction to the tools and techniques needed to construct and analyze performance models of computer systems, distributed systems, and communication networks.

Both traditional methods (discrete and continuous time (in particular absorbing) Markov chains, renewal theory, queues in isolation, networks of queues, matrix geometric theory, stochastic scheduling, etc.) and "modern" approaches (fluid models, mean-field theory, differential stochastic equations-based models, etc.) will be presented.

Numerous real-life situations will be addressed, including the modeling of a number of network communication protocols, the analysis of search engines, the modeling of TCP, measurement-based modeling, etc.

The goal is to teach fundamentals with a long half-life.

**Prerequisites:** An undergraduate level course on probability theory. Only very elementary knowledge on computer systems, distributed systems and communication networks required.

**Student workload:** Material will be presented by the instructor (slides for all lectures and lecture notes covering a fraction of the class).

** Evaluation:** Homework assignments (optional) and in-class final exam (mandatory).

Three homeworks will be posted on this site along the course of this class (students will be notified in due time). The final grade, F, will be obtained as F=max(F1, ...,F8) where

- F_1 = mark at the final exam
- F_2 = 0.7*F_1 + 0.1*(HW1+HW2+HW3)
- F_2 = 0.8*F_1 + 0.2*(HW1+HW2)
- F_2 = 0.8*F_1 + 0.2*(HW1+HW3)
- F_4 = 0.8*F_1 + 0.2*(HW2+HW3)
- F_5 = 0.9*F_1 + 0.1*HW1
- F_6 = 0.9*F_1 + 0.1*HW2
- F_7 = 0.9*F_1 + 0.1*HW3

** Instructor:** Philippe Nain

Inria Senior Research Scientist

Email: philippe.nain@inria.fr

Homepage

If you want to meet me, please send me an email.

**Class schedule**

~~Lecture 1 - Sep. 11, 1:30pm-3:30pm - amphi B~~

~~ Lecture 2 - Sep. 25, 9:30am-11:30am (new schedule) - room 316, LIP 3rd floor~~

~~ Lecture 3 - Sep. 25, 1:30pm-3:30pm - room 435, 4rd floor~~

~~ Lecture 4 - Oct. 9, 1:30pm-3:30pm - room 316C~~

~~Lecture 5 - Oct. 12, 3:45pmm-5:45pm - room B2, 4th floor~~

~~Lecture 6 - Oct. 16, 1:30pm-3:30pm - room 394 LIP 3rd floor - near Amphi B~~

~~Lecture 7 - Oct. 19, 3:45pm-5:45pm - Amphi B ~~

~~Lecture 8 - Nov. 6, 1:30pm-3:30pm - room 316C~~

~~Lecture 9 - Nov. 9, 3:45pm-5:45pm - room B2, 4th floor~~

~~Lecture 10 - Nov. 13, 1:30pm-3:30pm - room 316C~~

~~Lecture 11 - Dec. 11, 1:30pm-3:30pm - room 316C~~

~~In-class final exam: Dec. 18, 1pm-3:30pm (amphi Schrödinger)~~

**Lecture notes: **here

**Homework assignments:**

Homework1, Solution-homework1

Homework2,
Solution-homework2

Homework3, Solution-homework3

Exam, Solution-exam

**Slides & class material:**

Lecture 1

Lecture 2

Lecture 3,
Slides PageRank,
Slides Wifi,
Paper G. Bianchi

Lecture 4

Lecture 5,
Slides Aloha protocol,
Paper N. Abramson ("THE ALOHA SYSTEM: Another alternative for computer
communications")

Lecture 6

Lecture 7,
Paper Jackson product-form queueing networks,
Paper BCMP product-form queueing networks

Lecture 8

Lecture 9

Lecture 10,
Paper Ott et al., Paper Padhye et al.

Lecture 11,
Paper Misra al.