Probabilistic Methods for Spatial Multihop Communication Systems

Abstract

We present and comment some recent modeling and results from stochastic geometry about the functionality of spatial communication networks with a multihop system of message transmissions. Our novel approaches concern connectivity on random street systems, frustration probabilities for service quality under constraints with regard to interference and capacity, and a new model of random message routing. Our main focus is on the description of the influence of spatial aspects, predominantly the locations of all the users. As a leading mathematical tool, we introduce the probabilistic theory of large deviations to the study of such systems in a high-density situation.