This paper proposes a framework to analyze an emerging wireless architecture where vehicles collect data from devices. Using stochastic geometry, the devices are modeled by a planar Poisson point process. Independently, roads and vehicles are modeled by a Poisson line process and a Cox point process, respectively. For any given time, a vehicle is assumed to communicate with a roadside device in a disk of radius @math centered at the vehicle, which is referred to as the coverage disk. We study the proposed network by analyzing its short-term and long-term behaviors based on its space and time performance metrics, respectively. As short-term analysis, we explicitly derive the signal-to-interference ratio distribution of the typical vehicle and the area spectral efficiency of the proposed network. As long-term analysis, we derive the area fraction of the coverage disks and then compute the latency of the network by deriving the distribution of the minimum waiting time of a typical device to be covered by a disk. Leveraging these properties, we analyze various trade-off relationships and optimize the network utility. We further investigate these trade-offs using comparison with existing cellular networks.
However, modeling the locations of vehicles as a planar Poisson point process is inaccurate since almost surely no more than two points can be found on a line in the planar Poisson point process @cite_21 , and yet the locations of vehicles exhibit a linear pattern when they are on the same straight road. In order to address the location dependencies, a Poisson-line Cox model was proposed in @cite_26 , where roads and vehicles are conditionally generated in the Euclidean plane. More recently, this model was further studied in @cite_9 @cite_33 @cite_45 to derive the signal-to-interference ratio (SIR) distribution of various links between vehicles and mobiles on the plane. These papers analyzed the typical network performance by considering an instantaneous snapshot of the network geometry, under the Palm distribution of the vehicle point process. This paper uses the same approach to characterize short-term performance properties such as the distribution of the SIR and the area spectral efficiency.
@cite_26 @cite_33 @cite_9 @cite_21 @cite_45
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This paper analyzes an emerging architecture of cellular network utilizing both planar base stations uniformly distributed in the Euclidean plane and base stations located on roads. An example of this architecture is that where, in addition to conventional planar cellular base stations and users, vehicles also play the role of both base stations and users. A Poisson line process is used to model the road network and, conditionally on the lines, linear Poisson point processes are used to model the vehicles on the roads. The conventional planar base stations and users are modeled by the independent planar Poisson point processes. We use Palm calculus to investigate the statistical properties of a typical user in such a network. Specifically, this paper discusses two different Palm distributions, with respect to the user point processes depending on its type: planar or vehicular. We derive the distance to the nearest base station, the association of the typical users, and the coverage probability of the typical user. Furthermore, we provide a comprehensive characterization of coverage of all possible cellular transmissions in this setting, namely, vehicle-to-vehicle, vehicle-to-infrastructure, infrastructure-to-vehicle, and infrastructure-to-infrastructure. In this paper, we consider a vehicular network in which the wireless nodes are located on a system of roads. We model the roadways, which are predominantly straight and randomly oriented, by a Poisson line process (PLP) and the locations of nodes on each road as a homogeneous 1D Poisson point process. Assuming that each node transmits independently, the locations of transmitting and receiving nodes are given by two Cox processes driven by the same PLP. For this setup, we derive the coverage probability of a typical receiver, which is an arbitrarily chosen receiving node, assuming independent Nakagami- @math fading over all wireless channels. Assuming that the typical receiver connects to its closest transmitting node in the network, we first derive the distribution of the distance between the typical receiver and the serving node to characterize the desired signal power. We then characterize coverage probability for this setup, which involves two key technical challenges. First, we need to handle several cases as the serving node can possibly be located on any line in the network and the corresponding interference experienced at the typical receiver is different in each case. Second, conditioning on the serving node imposes constraints on the spatial configuration of lines, which requires careful analysis of the conditional distribution of the lines. We address these challenges in order to characterize the interference experienced at the typical receiver. We then derive an exact expression for coverage probability in terms of the derivative of Laplace transform of interference power distribution. We analyze the trends in coverage probability as a function of the network parameters: line density and node density. We also provide some theoretical insights by studying the asymptotic characteristics of coverage probability. We study signal-to-interference plus noise ratio (SINR) percolation for Cox point processes, i.e., Poisson point processes with a random intensity measure. SINR percolation was first studied by in the case of a two-dimensional Poisson point process. It is a version of continuum percolation where the connection between two points depends on the locations of all points of the point process. Continuum percolation for Cox point processes was recently studied by Hirsch, Jahnel and Cali. We study the SINR graph model for a stationary Cox point process in two or higher dimensions. We show that under suitable moment or boundedness conditions on the path-loss function and the intensity measure, this graph has an infinite connected component if the spatial density of points is large enough and the interferences are sufficiently reduced (without vanishing). This holds in all dimensions larger than 1 if the intensity measure is asymptotically essentially connected, and in two dimensions also if the intensity measure is only stabilizing but the connection radius is large. A prominent example of the intensity measure is the two-dimensional Poisson-Voronoi tessellation. We show that its total edge length in a given square has some exponential moments. We conclude that its SINR graph has an infinite cluster if the path-loss function is bounded and has a power-law decay of exponent at least 3. In this paper we propose a new method for the extraction of roads from remotely sensed images. Under the assumption that roads form a thin network in the image, we approximate such a network by connected line segments. To perform this task, we construct a point process able to simulate and detect thin networks. The segments have to be connected, in order to form a line-network. Aligned segments are favored whereas superposition is penalized. These constraints are enforced by the interaction model (called the Candy model). The specific properties of the road network in the image are described by the data term. This term is based on statistical hypothesis tests. The proposed probabilistic model can be written within a Gibbs point process framework. The estimate for the network is found by minimizing an energy function. In order to avoid local minima, we use a simulated annealing algorithm, based on a Monte Carlo dynamics (RJMCMC) for finite point processes. Results are shown on SPOT, ERS and aerial images.