Although a significant number of satellites are deemed essential for facilitating diverse applications of satellite networks, aerial platforms are emerging as excellent alternatives for enabling reliable communications with fewer satellites. In scenarios with sparse satellite networks, aerial platforms participate in downlink communications, serving effectively as relays and providing comparable or even superior coverage compared to a large number of satellites. This article explores the role of aerial platforms in assisting downlink communications, emphasizing their potential as an alternative to dense satellite networks. First, we account for the space-time interconnected movement of satellites in orbits by establishing a stochastic geometry framework based on an isotropic satellite Cox point process. Using this model, we evaluate space-and-time performance metrics, such as the number of orbits, the number of communicable satellites, and the connectivity probability, primarily assessing the geometric impact of aerial platforms. Subsequently, we analyze signal-to-noise ratio (SNR) coverage probability, end-to-end throughput, and association delay. Through examination of these performance metrics, we explicitly demonstrate how aerial platforms enhance downlink communications by improving various key network performance metrics that would have been achieved only by many satellites, thereby assessing their potential as an excellent alternative to dense satellite networks.

This work develops an analytical framework for downlink low Earth orbit (LEO) or medium Earth orbit (MEO) satellite communications, leveraging tools from stochastic geometry. We propose a tractable approach to the analysis of such satellite communication systems, accounting for the fact that satellites are located on circular orbits. We accurately incorporate this geometric property of LEO or MEO satellite constellations by developing a Cox point process model that jointly produces orbits and satellites on these orbits. Our work contrasts with previous modeling studies that presumed satellite locations to be entirely random, thereby overlooking the fundamental fact that satellites are jointly positioned on orbits. Employing this Cox model, we analyze the network performance experienced by users located on Earth. Specifically, we evaluate the no-satellite probability of the proposed network and the Laplace transform of the interference created by such a network. Using it, we compute its SIR (signal-to-interference) distribution, namely its coverage probability. By presenting fundamental network performance as functions of key parameters, this model allows one to assess the statistical properties of downlink LEO or MEO satellite communications and can thus be used as a system-level design tool to operate and optimize forthcoming complex LEO or MEO satellite networks.

Reconfigurable intelligent surfaces (RISs) provide alternative routes for reflected signals to network users, offering numerous applications. This paper explores an innovative approach of strategically deploying RISs along road areas to leverage various propagation and blockage conditions present in cellular networks with roads. To address the local network geometries shown by such networks, we use a stochastic geometry framework, specifically the Cox point processes, to model the locations of RISs and vehicle users. Then, we define the coverage probability as the chance that either a base station or an RIS is in line of sight (LOS) of the typical user and that the LOS signal has a signal-to-noise ratio (SNR) greater than a threshold. We derive the coverage probability as a function of key parameters such as RIS density and path loss exponent. We observe that the network geometry highly affects the coverage and that the proposed RIS deployment effectively leverages the underlying difference of attenuation and blockage, significantly increasing the coverage of vehicle users in the network. With experimental results addressing the impact of key variables to network performance, this work serves as a versatile tool for designing, analyzing, and optimizing RIS-assisted cellular networks with many vehicles.

Reaching all regions of Earth, low Earth orbit (LEO) satellites can harvest delay-tolerant data from remotely located users on Earth without ground infrastructure. This work aims to assess a data harvest network architecture where users generate data and LEO satellites harvest data from users when passing by. By developing a novel stochastic geometry Cox point process model that simultaneously generates orbits and the motion of LEO satellite harvesters on them, we analyze key performance indices of such a network by deriving the following: (i) the average fraction of time that the typical user is served by LEO satellite harvesters, (ii) the average amount of data uploaded per each satellite pass, (iii) the maximum harvesting capacity of the proposed network model, and (iv) the delay distribution in the proposed network. These key metrics are given as functions of key network variables such as λ the mean number of orbits and μ the mean number of satellites per orbit. Providing rich comprehensive analytical results and practical interpretations of these results, this work assesses the potential of the delay-tolerant use of LEO satellites and also serves as a versatile framework to analyze, design, and optimize delay-tolerant LEO satellite networks.

Low Earth Orbit (LEO) satellite networks connect millions of devices on Earth and offer various services, such as data communications, remote sensing, and data harvesting. As the number of services increases, LEO satellite networks will continue to grow, and many LEO satellite network operators will share the same spectrum resources. We aim to examine the coexistence of such a future heterogeneous LEO satellite network by proposing a tractable spatial model and analyzing the basic performance of downlink communications. We model a heterogeneous LEO satellite network as Cox point processes, ensuring satellites are located on various orbits. Then, we analyze two different access technologies for such a heterogeneous satellite network: closed access and open access. For both cases, we derive the coverage probability and prove that the coverage probability of the open access scenario outperforms that of the closed access, and this coverage enhancement applies to all users. By providing essential network performance statistics as key distributional parameters and by presenting the fact that the Cox point process approximates a forthcoming future constellation with slight variation, the developed framework and analysis will serve as a tractable instrument to design, evaluate, and optimize heterogeneous LEO satellite networks with numerous constellations.

This paper investigates the benefits of employing vehicle relays by analyzing the increment of the line-of-sight (LOS) coverage based on vehicle relays to enable high-speed communications between roadside user devices, vehicles, and roadside infrastructure. We characterize a unique spatial relationship between roadside units (RSUs) and vehicles by employing the Cox point processes. Then, the LOS coverage from these RSUs is modeled by a Boolean model on the Cox point process. Assuming vehicle relays provide an additional LOS coverage when they are within the RSU LOS coverage, we quantify the growth of the LOS coverage by separately deriving the mean area fractions of the RSU LOS coverage and RSU-plus-relay LOS coverage, respectively. We explicitly provide the gain in the LOS coverage as an integral formula and show that relays increase the LOS coverage area by nearly 50 percent.

This paper presents a novel spatially consistent approach for addressing blockage and line-of-sight (LOS) paths in highway vehicular networks. We use stochastic geometry to model transmitters, obstacles, and receivers located in three lines, respectively. Then, their geometric interactions characterize the existence of LOS paths. Specifically, the proposed approach focuses on the role of obstacles in blocking one or more LOS paths, which has been overlooked in most statistical models for blockage. Under the proposed framework, we derive the probability that a typical vehicle is in LOS with respect to transmitters. The proposed framework and LOS analysis are important to the LOS-critical applications such as positioning or mmWave communications in vehicular networks.

This article presents a stochastic geometric framework to model and analyze spatially correlated blockage in a vehicular network. First, we model the vehicular obstacles as a Boolean model on a line using stochastic geometry. Then, we represent signal paths from transmitters to receivers as a graph from the transmitter point process to the receiver point process. The blockage of a signal path occurs if and only if any obstacle obstructs the corresponding edge. Since the signal blockage occurs by obstacles, the proposed determination of blockage preserves the spatial correlation of signal paths. Under the proposed framework, we derive the blockage probability of a typical vehicle. In addition, we derive the probability that a typical vehicle is in the line of sight (LOS) with respect to at least one transmitter. The proposed framework and blockage analysis will be instrumental to the analysis of LOS-critical applications such as positioning or mmWave communications in vehicular networks.

This paper concerns the performance of vehicle-to-everything (V2X) communications. More precisely, we analyze the broadcast of safety-related V2X communications in cellular networks where base stations and vehicles are assumed to share the same spectrum and vehicles broadcast their safety messages to neighboring users. We model the locations of vehicles as a Poisson line Cox point process and the locations of users as a planar Poisson point process. We assume that users are associated with their closest base stations when there is no vehicle within a certain distance ρ. On the other hand, users located within a distance ρ from vehicles are associated with the vehicles to receive their safety messages. We quantify the properties of this vehicle-prioritized association using the stochastic geometry framework. We derive the fractions of users that receive safety messages from vehicles. Then, we obtain the expression for the signal-to-interference ratio of the typical user evaluated on each association type. To address the impact of vehicular broadcast on the cellular network, the paper also derives the effective rate offered to the typical user in this setting.

This paper explores an emerging wireless Internet-of-things (IoT) architecture based on unmanned aerial vehicles (UAVs). We consider a network where a fleet of UAVs at a fixed altitude flies on planned trajectories and IoT devices on the ground are scheduled to transmit their data to the UAVs when the latter are nearby. In such a system, the UAVs' motion triggers the uplink transmissions of the IoT devices. As a result, network performance is determined by the geometric and dynamic characteristics of the system. We propose a joint stationary model for UAVs and IoT devices and then evaluate the interference, the coverage probability, and the data rate of the typical UAV. To assess the harvesting capability of the proposed architecture, we derive a formula for the amount of data uploaded from each IoT device to a UAV. We also establish a linear relationship between the UAV coverage and the harvesting capability of the network, which provides insights into the design of the proposed harvesting scheme. In addition, we use our analytical results to numerically show that there exists a trade-off between the uploaded data and the size of the IoT scheduling window. Specifically, for a given UAV and IoT geometry, there exists an optimal scheduling window that maximizes the harvesting capability of the proposed network.

This paper explores an emerging wireless architecture based on unmanned aerial vehicles (UAVs), i.e., drones. We consider a network where UAVs at fixed altitude harvest data from Internet-of-Things (IoT) devices on the ground. Each UAV serves IoT devices within its coverage area. In such a system, the UAVs' motion activates IoT uplink transmissions and so the motion triggers the interference field and determines the network performance. To analyze the performance, we propose a stochastic geometry model. The coverage area of each UAV, referred to as the activation window, is modeled for simplicity as a rectangle where at most one IoT device is scheduled to transmit at any given time. In this setting, we analyze the signal-to-interference and data rate from two typical perspectives, namely from a typical UAV's and from a typical IoT device's points of view.

This paper proposes a framework to analyze a wireless architecture where vehicles collect data from devices. Roads and vehicles are modeled by a Poisson line process and a Cox point process, respectively. At any given time, each vehicle is assumed to communicate with a roadside device in a disk of radius ν centered at the vehicle, which is referred to as the coverage disk. We study these direct communications from roadside devices to vehicles by investigating the network performance in both space and time domains. For the space domain analysis, we explicitly derive the signal-to-interference ratio distribution of the typical vehicle and the area spectral efficiency of the proposed network. For the time domain analysis, we characterize the evolution of the area fraction of the coverage disks over time and then evaluate the minimum association delay of the proposed network by deriving the distribution of the minimum time required for an arbitrarily located roadside device to be covered by a disk. Leveraging the derived network performance, we investigate the optimization of network utility functions given by linear combinations of the performance metrics.

This paper analyzes the coverage probability of a typical user in a cellular network comprised of planar base stations, planar users, vehicular base stations, and vehicular users. Planar base stations and users in the Euclidean space are modeled by independent stationary planar Poisson point processes. Then, conditionally on a stationary Poisson line process, vehicular base stations and vehicular users are modeled by linear Poisson point processes on the lines. Utilizing the Palm distribution of each user point process, we derive the association probability and the coverage probability of each typical user, namely that of the typical planar user and the typical vehicular user. Using the association and coverage expressions, we fully characterize the Shannon rate distributions of all downlink combinations present in the proposed network based on their association types: vehicle-to-vehicle, vehicle-to-planar, planar-to-vehicle, and planar-to-planar.

Disruptive changes are underway in the automotive industry as large-scale platforms based on vehicular fleets are deployed to deliver ride sharing and delivery services. Such platforms can also be leveraged to deliver wireless connectivity services, e.g., large-scale connectivity for the Internet of Things (IoT). This paper examines a network architecture based on a mesh of IoT devices, roadside repositories and vehicular mobile gateways -- referred to as mesh+vehicular. We propose a system-level model to study its relative merits versus conventional infrastructure-based IoT architectures-- referred to as mesh+cellular. The model reflects the salient properties of the architectures including the key interplay among the variability in the network geometries, routing trees, wireless capacity and eventually IoT queue stability.

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.

We propose a new cellular network model that captures both deterministic and random aspects of base station (BS) deployments. Namely, the BS locations are modeled as the superposition of two independent stationary point processes: a random shifted grid with intensity λgand a Poisson point process (PPP) with intensity λp. Grid and PPP deployments are special cases with λp→ 0 and λg→ 0 , with actual deployments in between these two extremes, as we demonstrate with deployment data. Assuming that each user is associated with the BS that provides the strongest average received signal power, we obtain the probability that a typical user is associated with either a grid or PPP BS. Assuming Rayleigh fading channels, we derive the expression for the coverage probability of the typical user, resulting in the following observations. First, the association and the coverage probability of the typical user are fully characterized as functions of intensity ratio ρλ= λp/λg. Second, the user association is biased toward the BSs located on a grid. Finally, the proposed model predicts the coverage probability of the actual deployment with great accuracy.

We propose a new cellular network model that captures both strong repulsion and randomness between base stations. The base stations are modeled by superposition of a random shifted grid with intensity λgfor the grid base stations and an independent Poisson point process with intensity λpfor the random base stations. Assuming that the typical user is associated with the base station that provides the strongest average receive signal power, we derive the association probability of the typical user. In Rayleigh fading channels, the coverage probability of the typical user at the origin is derived.

In this paper, we describe the necessity of VC merging in an edge label switched router (LSR) for scalability, one of the important merits in multi-protocol label switching (MPLS). We introduce the design of a high-speed IP forwarding engine with virtual connection (VC) merging. This forwarding engine largely consists of a segmentation and reassembly (SAR) processing part, a CAM-based IP look-up processing part, a VC-merging part, and a physical line interface part. It provides some desirable characteristics that are described in this paper. We also compare the edge MPLS systems with centralized and distributed forwarding engine architectures, and the good points of the MPLS system with the latter architectures when supporting VC merging.