Stochastic Geometry and Wireless Networks Volume I

This monograph surveys recent results on the use of stochastic geometry for the performance analysis of large wireless networks. It is structured in two volumes. Volume I focuses on stochastic geometry and on the evaluation of spatial averages within this context. It contains two main parts, one on classical stochastic geometry (point processes, Boolean models, percolation, random tessellations, shot noise fields, etc.) and one on a new branch of stochastic geometry which is based on information theoretic notions, such as signal to interference ratios, and which is motivated by the modeling of wireless networks. This second part revisits several basic questions of classical stochastic geometry such as coverage or connectivity within this new framework. Volume II - Applications (see http://hal.inria.fr/inria-00403040) bears on more practical wireless network modeling and performance analysis. It leverages the tools developed in Volume I to build the time-space framework needed for analyzing the phenomena which arise in these networks. The first part of Volume II focuses on medium access control protocols used in mobile ad hoc networks and in cellular networks. The second part bears on the analysis of routing algorithms used in mobile ad hoc networks. For readers with a main interest in wireless network design, the monograph is expected to offer a new and comprehensive methodology for the performance evaluation of large scale wireless networks. This methodology consists in the computation of both time and space averages within a unified setting which inherently addresses the scalability issue in that it poses the problems in an infinite domain/population case. For readers with a background in applied probability, this monograph is expected to provide a direct access to an emerging and fast growing branch of spatial stochastic modeling.