This course focuses on stochastic processes and its applications. In this year, topics include the theory of point processes and its application to modeling and analysis of wireless networks.
At the end of this course, students will be able to understand the theory of point processes, one of the fundamental class of stochastic processes, and apply it to modeling and performance evaluation of wireless communication networks.
Point processes, Poisson processes, cox processes, stationary point processes, Palm theory, wireless networks, coverage probability.
|✔ Specialist skills
|Critical thinking skills
|✔ Practical and/or problem-solving skills
On-line lectures. The document of each lecture will be uploaded to the OCW-i.
|Preliminaries: Measures and Integrals
|Define measures, integrals and probability
|Point processes and their distributions
|Define point processes and characterize their distributions
|Poisson point processes
|Define the Poisson point processes
|Properties of Poisson point processes
|Reveal some properties of Poisson point processes
|Random measures and Cox point processes
|Define random measures and Cox point processes
|Determinantal point processes
|Define determinantal point processes and reveal their properties
|Define Palm probability
|Stationary point processes
|Reveal some properties of stationary point processes
|Palm theory for stationary point processes
|Study the Palm theory for stationary point processes
|Basic properties of stationary point processes
|Show some basic properties of stationary point processes using the Palm calculus
|Application to cellular networks
|Introduce a spatial point process model of cellular wireless networks
|Coverage probability of cellular network models
|Derive the coverage probability for cellular network models using various point processes
|Application to wireless broadcasting
|Introduce a spatial point process model of wireless broadcasting
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
 F. Baccelli, B. Blaszczyszyn and Mohamed Karray. Random Measures, Point Processes, and Stochastic Geometry. HAL-02460214 (2020)
 G. Last and M. Penrose. Lectures on the Poisson Process. Cambridge University Press, 2017.
Understanding of the related courses above (you do not have to take these courses if you understand the contents of them).