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 cellular 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 cellular wireless networks.
Point processes, Poisson processes, cox processes, stationary point processes, Palm theory, cellular wireless networks, coverage probability.
Intercultural skills | Communication skills | ✔ Specialist skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Lectures with a blackboard. The document of each lecture will be uploaded to the OCW-i.
Course schedule | Required learning | |
---|---|---|
Class 1 | Preliminaries: Measures and Integrals | Define measures, integrals and probability |
Class 2 | Point processes and their intensity measures | Define point processes and their intensity measures |
Class 3 | Distribution of point processes | Characterize the probability distribution of point processes |
Class 4 | Poisson point processes | Define the Poisson point processes |
Class 5 | Some properties of Poisson point processes | Reveal some properties of Poisson point processes |
Class 6 | Random measures and Cox point processes | Define random measures and Cox point processes |
Class 7 | Determinantal point processes | Define determinantal point processes |
Class 8 | Stationary point processes | Reveal some properties of stationary point processes |
Class 9 | Marked point processes and Palm probability | Define marked point processes and the Palm probability measure |
Class 10 | Basic formulas of Palm theory | Show some basic formulas of Palm theory |
Class 11 | Basic properties of stationary point processes | Show some basic properties of stationary point processes using the Palm calculus |
Class 12 | Application to cellular networks | Introduce the spatial point process model of cellular wireless networks |
Class 13 | Coverage probability of a cellular network model: The case of a Poisson-based model | Derive the coverage probability of Poisson-based model of cellular networks |
Class 14 | Coverage probability of a cellular network model: The cases of non-Poisson based models | Derive the coverage probability of non-Poisson-based model of cellular networks |
Class 15 | TBA | TBA |
None.
[1] F. Baccelli and B. Blaszczyszyn. "Stochastic geometry and wireless networks, Volume I: Theory." Foundations and Trends in Networking, vol. 3, pp. 249-449, 2009.
[2] F. Baccelli and B. Blaszczyszyn. "Stochastic geometry and wireless networks, Volume II: Applications." Foundations and Trends in Networking, vol. 4, pp. 1-312, 2009.
[3] D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods. Springer, 2003.
[4] D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes, Volume II: General Theory and Structure. Springer, 2008.
[5] G. Last and M. Penrose. Lectures on the Poisson Process. Cambridge University Press, 2017.
Reports.
Understanding of the related courses above (you do not have to take these courses if you understand the contents of them).