Related papers: Poisson Cox Point Processes for Vehicular Networks
The Poisson point process (PPP) is not always a realistic model for the locations of vehicles along a road, because it does not account for the safety distance a driver maintains from the vehicle ahead. In this paper, we model the…
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple…
We investigate continuum percolation for Cox point processes, that is, Poisson point processes driven by random intensity measures. First, we derive sufficient conditions for the existence of non-trivial sub- and super-critical percolation…
We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing…
Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…
The Mat\'ern hard-core processes are classical examples for point process models obtained from (marked) Poisson point processes. Points of the original Poisson process are deleted according to a dependent thinning rule, resulting in a…
In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or…
A Neyman-Scott process is a special case of a Cox process. The latent and observable stochastic processes are both Poisson processes. We consider a deep Neyman-Scott process in this paper, for which the building components of a network are…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
Many network architectures exist for learning on meshes, yet their constructions entail delicate trade-offs between difficulty learning high-frequency features, insufficient receptive field, sensitivity to discretization, and inefficient…
We introduce the binomial line process (BLP), a novel spatial stochastic model for the characterization of streets in the statistical evaluation of wireless and vehicular networks. Existing stochastic geometry models for streets, e.g.,…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions…
We present an efficient and robust numerical model for simulation of electrokinetic phenomena in porous networks over a wide range of applications including energy conversion, desalination, and lab-on-a-chip systems. Coupling between fluid…
In this paper, we consider a Riemannian manifold $M$ and the Poisson-Voronoi tessellation generated by the union of a fixed point $x_0$ and a Poisson point process of intensity $\lambda$ on $M$. We obtain asymptotic expansions up to the…
We consider spatial stochastic models, which can be applied e.g. to telecommunication networks with two hierarchy levels. In particular, we consider two Cox processes concentrated on the edge set of a random tessellation, where the points…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
We present a simple model reproducing the long-range autocorrelations and the power spectrum of the web traffic. The model assumes the traffic as Poisson flow of files with size distributed according to the power-law. In this model the…
We present methodology for estimating the stochastic intensity of a doubly stochastic Poisson process. Statistical and theoretical analyses of traffic traces show that these processes are appropriate models of high intensity traffic…