1,364 research outputs found
Gilbert's disc model with geostatistical marking
We study a variant of Gilbert's disc model, in which discs are positioned at
the points of a Poisson process in with radii determined by an
underlying stationary and ergodic random field
, independent of the Poisson process. When
the random field is independent of the point process one often talks about
'geostatistical marking'. We examine how typical properties of interest in
stochastic geometry and percolation theory, such as coverage probabilities and
the existence of long-range connections, differ between Gilbert's model with
radii given by some random field and Gilbert's model with radii assigned
independently, but with the same marginal distribution. Among our main
observations we find that complete coverage of does not
necessarily happen simultaneously, and that the spatial dependence induced by
the random field may both increase as well as decrease the critical threshold
for percolation.Comment: 22 page
Deployment Strategies of Multiple Aerial BSs for User Coverage and Power Efficiency Maximization
Unmanned aerial vehicle (UAV) based aerial base stations (BSs) can provide
rapid communication services to ground users and are thus promising for future
communication systems. In this paper, we consider a scenario where no
functional terrestrial BSs are available and the aim is deploying multiple
aerial BSs to cover a maximum number of users within a certain target area. To
this end, we first propose a naive successive deployment method, which converts
the non-convex constraints in the involved optimization into a combination of
linear constraints through geometrical relaxation. Then we investigate a
deployment method based on K-means clustering. The method divides the target
area into K convex subareas, where within each subarea, a mixed integer
non-linear problem (MINLP) is solved. An iterative power efficient technique is
further proposed to improve coverage probability with reduced power. Finally,
we propose a robust technique for compensating the loss of coverage probability
in the existence of inaccurate user location information (ULI). Our simulation
results show that, the proposed techniques achieve an up to 30% higher coverage
probability when users are not distributed uniformly. In addition, the proposed
simultaneous deployment techniques, especially the one using iterative
algorithm improve power-efficiency by up to 15% compared to the benchmark
circle packing theory
Towards automatic Markov reliability modeling of computer architectures
The analysis and evaluation of reliability measures using time-varying Markov models is required for Processor-Memory-Switch (PMS) structures that have competing processes such as standby redundancy and repair, or renewal processes such as transient or intermittent faults. The task of generating these models is tedious and prone to human error due to the large number of states and transitions involved in any reasonable system. Therefore model formulation is a major analysis bottleneck, and model verification is a major validation problem. The general unfamiliarity of computer architects with Markov modeling techniques further increases the necessity of automating the model formulation. This paper presents an overview of the Automated Reliability Modeling (ARM) program, under development at NASA Langley Research Center. ARM will accept as input a description of the PMS interconnection graph, the behavior of the PMS components, the fault-tolerant strategies, and the operational requirements. The output of ARM will be the reliability of availability Markov model formulated for direct use by evaluation programs. The advantages of such an approach are (a) utility to a large class of users, not necessarily expert in reliability analysis, and (b) a lower probability of human error in the computation
Betti number signatures of homogeneous Poisson point processes
The Betti numbers are fundamental topological quantities that describe the
k-dimensional connectivity of an object: B_0 is the number of connected
components and B_k effectively counts the number of k-dimensional holes.
Although they are appealing natural descriptors of shape, the higher-order
Betti numbers are more difficult to compute than other measures and so have not
previously been studied per se in the context of stochastic geometry or
statistical physics.
As a mathematically tractable model, we consider the expected Betti numbers
per unit volume of Poisson-centred spheres with radius alpha. We present
results from simulations and derive analytic expressions for the low intensity,
small radius limits of Betti numbers in one, two, and three dimensions. The
algorithms and analysis depend on alpha-shapes, a construction from
computational geometry that deserves to be more widely known in the physics
community.Comment: Submitted to PRE. 11 pages, 10 figure
Recursive analysis and estimation for the discrete Boolean random set model
Random sets provide a powerful class of models for images containing randomly placed objects of random shapes and orientation. Those pixels within the foreground are members of a random set realization. The discrete Boolean model is the simplest general random set model in which a Bernoulli point process (called a germ process) is coupled with an independent shape or grain process. A typical realization consists of many overlapping shapes. Estimation in these models is difficult owing to the fact that many outcomes of the process obscure other outcomes. The directional one-dimensional (ID) model, in which random- length line segments emanate to the right from germs on the line, is analyzed via recursive expressions to provide a complete characterization of these discrete models in terms of the distributions of their black and white runlengths. An analytic representation is given for the optimal windowed filter for the signalunion- noise process, where both signal and noise are Boolean models. Several of these results are extended to the nondirectional case where segments can emanate to the left and right. Sufficient conditions are presented for a two-dimensional (2D) discrete Boolean model to induce a one dimensional Boolean model on an intersecting line. When inducement holds, the likelihood of runlength observations of the two-dimensional model is used to provide maximum-likelihood estimation of parameters of the 2D model. The ID directional discrete Boolean model is equivalent to the discrete-time infinite-server queue. Analysis for the Boolean model is extended to provide densities for many random variables of interest in queueing theory
Perfect simulation of spatial processes
This work presents a review of some of the schemes used to perfect sample from spatial processes
Exploiting Randomly-located Blockages for Large-Scale Deployment of Intelligent Surfaces
One of the promising technologies for the next generation wireless networks
is the reconfigurable intelligent surfaces (RISs). This technology provides
planar surfaces the capability to manipulate the reflected waves of impinging
signals, which leads to a more controllable wireless environment. One potential
use case of such technology is providing indirect line-of-sight (LoS) links
between mobile users and base stations (BSs) which do not have direct LoS
channels. Objects that act as blockages for the communication links, such as
buildings or trees, can be equipped with RISs to enhance the coverage
probability of the cellular network through providing extra indirect LoS-links.
In this paper, we use tools from stochastic geometry to study the effect of
large-scale deployment of RISs on the performance of cellular networks. In
particular, we model the blockages using the line Boolean model. For this
setup, we study how equipping a subset of the blockages with RISs will enhance
the performance of the cellular network. We first derive the ratio of the
blind-spots to the total area. Next, we derive the probability that a typical
mobile user associates with a BS using an RIS. Finally, we derive the
probability distribution of the path-loss between the typical user and its
associated BS. We draw multiple useful system-level insights from the proposed
analysis. For instance, we show that deployment of RISs highly improves the
coverage regions of the BSs. Furthermore, we show that to ensure that the ratio
of blind-spots to the total area is below 10^5, the required density of RISs
increases from just 6 RISs/km2 when the density of the blockages is 300
blockage/km^2 to 490 RISs/km^2 when the density of the blockages is 700
blockage/km^2.Comment: Accepted in IEEE Journal on Selected Areas in Communication
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