## Stochastic Geometry and Wireless Networks, Volume 1This volume bears on wireless network modeling and performance analysis. The aim is to show how stochastic geometry can be used in a more or less systematic way to analyze the phenomena that arise in this context. It first focuses on medium access control mechanisms used in ad hoc networks and in cellular networks. It then discusses the use of stochastic geometry for the quantitative analysis of routing algorithms in mobile ad hoc networks. The appendix also contains a concise summary of wireless communication principles and of the network architectures considered in the two volumes. |

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### Contents

Preface | 1 |

Marked Point Processes and ShotNoise Fields | 43 |

Boolean Model | 71 |

Voronoi Tessellation | 91 |

Bibliographical Notes on Part I | 103 |

Interacting SignaltoInterference Ratio Cells | 131 |

SignaltoInterference Ratio Coverage | 137 |

SignaltoInterference Ratio Connectivity | 155 |

Bibliographical Notes on Part II | 165 |

Stationary Marked Point Processes | 175 |

Fairness and Optimality | 181 |

Graph Theoretic Notions | 189 |

199 | |

206 | |

### Common terms and phrases

Assume assumption ball bond percolation Boolean model bounded capacity functional Chapter closed sets conditional distribution Consider constant convergence Corollary coverage process deﬁned Deﬁnition denote density diﬀerent distribution function edge equal ergodic Euclidean space Example ﬁrst ﬁxed formula given graph hoc network homogeneous BM homogeneous Poisson p.p. i.m. Poisson p.p. independently marked inﬁnite connected component intensity measure Laplace transform Lebesgue measure Lemma locally ﬁnite marked p.p. marked point process nodes non-negative Note OPL function p.p. with intensity parameter path-loss Poisson p.p. Poisson point process Proof Proposition radius random closed set random variable Rayleigh fading Remark response function satisﬁed Section shot-noise SINR cell SINR coverage site percolation spherical grains square integrable stationary p.p. stochastic geometry subset suﬃciently Theorem tion transmitters typical cell vector volume fraction Voronoi cell Voronoi tessellation wireless network