3rd year course at Ecole Polytechnique on “Networks: distributed control and emerging phenomena”

Lecture notes (in french for now) available here

Slides

  • Lecture 1 Introduction and random access protocols. Mathematical tools: Markov chains
  • Lecture 2 Scheduling in switches and wireless routers with max-weight and backpressure policies. Mathematical tools: stability via Foster-Lyapunov criterion
  • Lecture 3 Network bandwidth allocation, principles and algorithms. Mathematical tools: convex optimization, ordinary differential equations
  • Lecture 4 Susceptible-Infective-Removed epidemics. Mathematical tools: random graphs, Poisson approximation, Chernoff bounds
  • Lecture 5 Community detection via spectral methods. Mathematical tools: spectra of symmetric matrices, control of their perturbations
  • Lecture 6 Power-law random graphs and small-world “navigable” graphs. Mathematical tools: coupling constructions, Azuma-Hoeffding inequality
  • Lecture 7 Poisson processes and their basic properties
  • Lecture 8 Some examples of queueing networks. Mathematical tools: Markov jump processes
  • Lecture 9 Susceptible-Infective and Susceptible-Infective-Susceptible epidemics; impact of graph topology on their potency

Exercises