Related papers: On the Contact and Nearest-Neighbor Distance Distr…
In this letter, we derive the cumulative density function (CDF) of the nearest neighbor and contact distance distributions of the Matern cluster process (MCP) in R2. These results will be useful in the performance analysis of many…
Inspired by recent applications of point processes to biological nanonetworks, this paper presents a novel variant of a Mat\'ern cluster process (MCP) in which the points located within a certain distance from the cluster centers are…
In this letter, we derive the CDF (cumulative distribution function) of $k$th contact distance (CD) and nearest neighbor distance (NND) of the $n$-dimensional ($n$-D) Mat\'ern cluster process (MCP). We present a new approach based on the…
In this paper we present an analytic framework for formulating the statistical distribution of the nearest neighbour distance in hard-core point processes. We apply this framework to Mat\'{e}rn hard-core point process (MHC) to derive the…
We characterize the statistics of nearest-neighbor and contact distance distributions for Thomas cluster process (TCP), which is a special case of Poisson cluster process. In particular, we derive the cumulative distribution function (CDF)…
This letter characterizes the statistics of the contact distance and the nearest neighbor (NN) distance for binomial point processes (BPP) spatially-distributed on spherical surfaces. We consider a setup of $n$ concentric spheres, with each…
The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are…
This paper develops a stochastic geometry-based approach for the modeling and analysis of single- and multi-cluster wireless networks. We first define finite homogeneous Poisson point processes to model the number and locations of the…
This work focuses on the development of an analytical framework to study a diffusion-assisted molecular communication-based network of nano-machines (NMs) with a clustered initial deployment to detect a target in a three-dimensional (3D)…
The multifractal critical phase (MCP) fundamentally differs from extended and localized phases, exhibiting delocalized distributions in both position and momentum spaces. The investigation on the MCP has largely focused on one-dimensional…
This paper investigates the performance of millimeter wave (mmWave) communications in clustered device-to-device (D2D) networks. The locations of D2D transceivers are modeled as a Poisson Cluster Process (PCP). In each cluster, devices are…
This letter presents a unified analytical framework for internodal distance distributions in 2D and 3D wireless networks, with nodes confined to concentric circular or spherical regions. Four deployment scenarios are considered, covering…
We develop a systematic typical medium dynamical cluster approximation that provides a proper description of the Anderson localization transition in three dimensions (3D). Our method successfully captures the localization phenomenon both in…
Clustering is a very popular network structuring technique which mainly addresses the issue of scalability in large scale Wireless Sensor Networks. Additionally, it has been shown to improve the energy efficiency and prolong the life of the…
This report presents a survey on how to group together in a static way planar nodes, that may belong to a wireless network (ad hoc or cellular). The aim is to identify appropriate methods that could also be applied for Point Processes.…
The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to…
We present a comprehensive approach to the modeling, performance analysis, and design of clustered molecular nanonetworks in which nano-machines of different clusters release an appropriate number of molecules to transmit their sensed…
Clustering is an important concept to reduce the energy consumption and prolonging the life of a wireless sensor network. In heterogeneous wireless sensor network some of the nodes are equipped with more energy than the other nodes. Many…
Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the…
Future mobile networks are converging toward heterogeneous multi-tier networks, where various classes of base stations (BS) are deployed based on user demand. So it is quite necessary to utilize the BSs resources rationally when BSs are…