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François Baccelli and Bartłomiej Błaszczyszyn (2010), "Stochastic Geometry and Wireless Networks: Volume I Theory", Foundations and Trends® in Networking: Vol. 3: No. 3–4, pp 249-449. http://dx.doi.org/10.1561/1300000006

© 2010 F. Baccelli and B. Błaszczyszyn

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**In this article:**

I Classical Stochastic Geometry

1 Poisson Point Process

2 Marked Point Processes and Shot-Noise Fields

3 Boolean Model

4 Voronoi Tessellation

Bibliographical Notes on Part I

II Signal-to-Interference Ratio Stochastic Geometry

5 Signal-to-Interference Ratio Cells

6 Interacting Signal-to-Interference Ratio Cells

7 Signal-to-Interference Ratio Coverage

8 Signal-to-Interference Ratio Connectivity

Bibliographical Notes on Part II

III Appendix: Mathematical Complements

9 Higher Order Moment Measures of a Point Process

10 Stationary Marked Point Processes

11 Fairness and Optimality

12 Lemmas on Fourier Transforms

13 Graph Theoretic Notions

14 Discrete Percolation

References

Table of Mathematical Notation and Abbreviations

Index

Volume I first provides a compact survey on classical stochastic geometry models, with a main focus on spatial shot-noise processes, coverage processes and random tessellations. It then focuses on *signal to interference noise ratio* (SINR) stochastic geometry, which is the basis for the modeling of wireless network protocols and architectures considered in Volume II. It also contains an appendix on mathematical tools used throughout Stochastic Geometry and Wireless Networks, Volumes I and II.

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Preface iii

Preface to Volume I vii Contents of Volume I ix

Part I Classical Stochastic Geometry

1 Poisson Point Process

2 Marked Point Processes and Shot-Noise Fields

3 Boolean Model

4 Voronoi Tessellation

Bibliographical Notes on Part I

Part II Signal-to-Interference Ratio Stochastic Geometry

5 Signal-to-Interference Ratio Cells

6 Interacting Signal-to-Interference Ratio Cells

7 Signal-to-Interference Ratio Coverage

8 Signal-to-Interference Ratio Connectivity

Bibliographical Notes on Part II

Part III Appendix: Mathematical Complements

9 Higher Order Moment Measures of a Point Process

10 Stationary Marked Point Processes

11 Fairness and Optimality

12: Lemmas on Fourier Transforms

13: Graph Theoretic Notions

14: Discrete Percolation

Bibliography

Table of Notation

Index

Stochastic Geometry and Wireless Networks, Volume I: THEORY first provides a compact survey on classical stochastic geometry models, with a main focus on spatial shot-noise processes, coverage processes and random tessellations. It then focuses on signal to interference noise ratio (SINR) stochastic geometry, which is the basis for the modeling of wireless network protocols and architectures considered in Stochastic Geometry and Wireless Networks, Volume II: APPLICATIONS. It also contains an appendix on mathematical tools used throughout Stochastic Geometry and Wireless Networks, Volumes I and II.