Asymptotic Analysis of Stationary Random Tessellations

In the recent decade, methods and models from stochastic geometry and spatial statistics have found widespread applications in analysing and modelling of network structures and have become established alternatives to traditional techniques.This book provides an account of random network techniques. In a first part, random geometric models are introduced. The focus is centred on random tessellations and the study of their asymptotic behaviour. Central limit theorems for a variety of model functionals are derived resulting in asymptotic tests and confidence intervals. Goodness-of-fit is examined through simulation studies and the relevance for practical application in network modelling is demonstrated. In a second part, a project is presented that deals with random modelling of telecommunication networks for cost evaluation and strategic planning. An innovative model fitting technique, based on the minimisation of distance functions, is introduced. Such functions arise from mean value relations of network characteristics and for several random tessellations of the Poisson family explicit expressions are given. This in turn allows for fast and efficient model fitting.