Introduction

Abstract

In this book we present concepts, tools and methodologies for a probabilistic treatment of decentralized spatial telecommunication systems. The ubiquitous ansatz for analyzing such a device-to-device network is by means of a random point process with interactions and additional features. The most fundamental and flexible mathematical model is the Poisson point process (PPP), which has a great degree of independence and admits many explicit calculations for important expectations and functionals. We build on this fundamental structure a variety of network models intended to represent the most important aspects of the telecommunication systems. Among the additional features that we introduce are random environments and interference constraints. Our main focus is based on answering questions about the connectivity of the system, which we will address predominantly in limiting settings of a large number of network participants, both in a typical as well as in an atypical situation. Finally we will introduce models for the space-time evolution of malware in the adhoc network by means of interacting Markov jump processes and analyze the propagation in the presence of some countermeasures.