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Stochastic Geometry and Wireless Networks: Volume I Theory

  • François Baccelli 1
  • Bartłomiej Błaszczyszyn 2

[1]François Baccelli, INRIA & Ecole Normale Supérieure, francois.baccelli@ens.fr [2]Bartłomiej Błaszczyszyn, NRIA & Ecole Normale Superieure and Math. Inst. University of Wrocław,, bartek.blaszczyszyn@ens.fr

Short description

This two-part work provides a compact survey on classical stochastic geometry models, with a main focus on spatial shot-noise processes, coverage processes and random tessellations.

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Table of contents

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

Foundations and Trends® in Networking

(Vol 3, Issue 3–4, 2008, pp 249-449)

DOI: 10.1561/1300000006

Abstract

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.

Table of contents

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
Cover image for Stochastic Geometry and Wireless Networks

Stochastic Geometry and Wireless Networks:

Volume I Theory

200 pages

DOI: 10.1561/9781601982650

E-ISBN: 978-1-60198-265-0

ISBN: 978-1-60198-264-3

Description

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.