Introduction to Poisson Cluster

What is/are Poisson Cluster?

Poisson Cluster - 3-5) has been extensively observed and shows non-Poisson clustering of bursts over time and a power-law energy distribution6-8. ^[1] Moreover, to capture the dynamic network topology, the Poisson cluster process is employed to model UAV networks. ^[2] Considering the dense hotspot communications, this work employs Poisson point process (PPP) to model the locations of MBSs and PBSs, and uses Poisson cluster process (PCP) to model the ones of UEs and FBSs. ^[3] Using a spatial scan statistic approach, a Poisson cluster analysis method based on a likelihood ratio test and Monte Carlo replications was applied to identify high-risk clusters of a COVID-19-related outcome. ^[4] We consider multiple UAVs to provide user-equipments (UEs) with uplink transmissions, where the distribution of UEs follows the Poisson Cluster process (PCP) and each UAV is dedicated to a specific cluster. ^[5] The Bartlett-Lewis (BL) rectangular pulse model is a type of stochastic model that represents rainfall using a Poisson cluster point process. ^[6] In UAV-enabled mmWave networks, the locations of UAVs are usually modeled by a Poisson point process or a Poisson cluster process in an infinite area. ^[7] In this correspondence, we study the physical layer security in a stochastic unmanned aerial vehicles (UAVs) network from a network-wide perspective, where the locations of UAVs are modeled as a Mat$\acute{\text{e}}$rn hard-core point process (MHCPP) to characterize the minimum safety distance between UAVs, and the locations of users and eavesdroppers are modeled as a Poisson cluster process and a Poisson point process, respectively. ^[8] Specifically, we first establish a general and tractable framework to investigate the performance of mmWave networks using the Poisson cluster process integrated with several features of the mmWave band. ^[9] This study suggests a simple approach to modifying Poisson cluster rectangular pulse rainfall models to resolve this issue. ^[10] The locations of cellular UEs are modeled as a Poisson point process, while the locations of potential D2D UEs are modeled as a Poisson cluster process. ^[11] To this end, we in this paper consider base station (BS) cooperation and analyze user rate and energy efficiency of HetNets based on a Poisson cluster process (PCP). ^[12] The use of Poisson cluster processes to model rainfall time series at a range of scales now has a history of more than 30 years. ^[13] Our proposed non-uniform user distribution model is such that a Poisson cluster process with the cluster centers located at SAs in which SAs have a base station offset with their BSs. ^[14] We introduce clustered millimeter-wave (mmWave) networks with invoking non-orthogonal multiple access (NOMA) techniques, where the NOMA users are modeled as Poisson cluster processes and each cluster contains a base station (BS) located at the center. ^[15] Then, it downscales the generated monthly rainfall to the hourly aggregation level using the Modified Bartlett–Lewis Rectangular Pulse (MBLRP) model, a type of Poisson cluster rainfall model. ^[16] Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). ^[17] Locations of UAVs are modeled as a Poison Point Process (PPP), while locations of UEs are modeled as a Poisson Cluster Process (PCP). ^[18] More specifically, the locations of transceivers in downlink and uplink are modeled through the Poisson point processes and Poisson cluster processes (PCPs), respectively. ^[19] In particular, we model the locations of the IoT devices using a Poisson cluster process and assume that some of the clusters have IoT gateways (GWs) deployed at their centers while the other GWs are deployed independently of the IoT devices. ^[20] To enable efficient transmission in WPC, this paper proposes a PB deployment strategy where the distribution of PBs is subject to a truncated Poisson cluster process (PCP), and develops a two-tier correlated PCP model for the WPC network. ^[21] In particular, we consider a heterogeneous network model with user equipments (UEs) being distributed according to a Poisson cluster process (PCP). ^[22] In this paper, considering the in-band communication, we use the Poisson cluster process (PCP) to model and analyze the heterogeneous cellular and D2D networks. ^[23] Simulation of root water uptake of different 2D root maps generated by a Poisson cluster process shows the effectiveness of the derived approximation for clustered roots. ^[24] In this paper, we jointly consider the downlink simultaneous wireless information and power transfer (SWIPT) and uplink information transmission in unmanned aerial vehicle (UAV)-assisted millimeter wave (mmWave) cellular networks, in which the user equipment (UE) locations are modeled using Poisson cluster processes (e. ^[25] We exploit a new topology to model the network, where the node locations of LoRa follow a Poisson cluster process while other coexisting radio modules follow a Poisson point process. ^[26] Poisson–Poisson cluster processes (PPCPs) are a class of point processes exhibiting attractive point patterns. ^[27] In particular, we consider a heterogeneous network model with user equipments (UEs) being distributed according to a Poisson cluster process (PCP). ^[28] A stochastic geometry approach is applied to model the considered N-NOMA scenario as a Poisson cluster process, based on which insightful closed-form or quasi closed-form analytical expressions for outage probabilities and ergodic rates are obtained. ^[29] The methodology is then used to improve the ability of Poisson cluster models to simulate hourly rainfall series that mimic the statistical behavior of the observed ones. ^[30] For such realistic hotspots’ deployment, to exploit the coupling between user equipments (UEs) and base stations (BSs), we model the geographical centers of UE hotspots as independent PPP around which UEs, P-BSs and F-BSs are scattered and form independent and non-homogeneous Poisson cluster processes (PCPs). ^[31] To adopt this approach, we derive the void probability for different Poisson cluster processes (PCP), in particular, Matérn cluster process (MCP) and Thomas cluster process (TCP), which is defined as the probability of having no children point of PCP in a given distance. ^[32] We model Tweet clusters as a Poisson Cluster Process. ^[33] To enable efficient transmission and overcome the doubly-near-far problem in WPC, this paper proposes a PB deployment strategy where the distribution of PBs is subject to a truncated Poisson cluster process (PCP), and analytically investigates the performance of WPC in terms of the SNR outage probability. ^[34] A tractable three-dimensional (3D) spatial model is proposed for evaluating the average downlink performance of UAV networks at mmWave bands, where the locations of UAVs and users are randomly distributed with the aid of a Poisson cluster process. ^[35] In this paper, we propose an analytical framework to investigate the integrated Sub-6GHz-mmWave cellular networks, in which the Sub-6GHz base stations (BSs) are modeled as a Poisson point process, and the mmWave BSs are clustered following a Poisson cluster process in traffic hotspots. ^[36] In this paper, we propose a multi-tier mmWave cellular framework where sub-6 GHz macro BSs (MBSs) are assumed as a Poisson point process (PPP) and small-cell BSs (SBSs), operating on either mmWave or sub-6 GHz, follows non-uniform Poisson cluster point (PCP) model. ^[37] Therefore, we further approximate the point process formed by active RF-powered nodes with a fitted Poisson cluster process, which is shown to provide a good approximation of the success probability in the information transmission. ^[38] In contrast, a Poisson cluster process (PCP) proves more realistic for the deployment of BSs. ^[39] A numerical study is carried out on a real population of aquatic birds together with an artificial population generated by Poisson cluster process. ^[40] To be specific, by modeling the D2D underlay cellular network as a Poisson cluster process (PCP), we derive exact expressions for the coverage outage probabilities (COP) and secrecy outage probabilities (SOP), respectively, for both the cellular users (CU) and D2D users (DU). ^[41] We study the asymptotic distribution of the total claim amount for marked Poisson cluster models. ^[42] We then compared our derived distance decay relationships to theoretical expectations obtained from a Poisson Cluster Process, known to match well with empirical distance decay relationships at local scales. ^[43] In this paper, the users in the network are assumed to be a set of uniformly distributed users and clustered users, which are modeled according to HPPP and Poisson cluster process (PCP), respectively. ^[44]

Truncated Poisson Cluster

To enable efficient transmission in WPC, this paper proposes a PB deployment strategy where the distribution of PBs is subject to a truncated Poisson cluster process (PCP), and develops a two-tier correlated PCP model for the WPC network. ^[1] To enable efficient transmission and overcome the doubly-near-far problem in WPC, this paper proposes a PB deployment strategy where the distribution of PBs is subject to a truncated Poisson cluster process (PCP), and analytically investigates the performance of WPC in terms of the SNR outage probability. ^[2]

poisson cluster proces

Moreover, to capture the dynamic network topology, the Poisson cluster process is employed to model UAV networks. ^[1] Considering the dense hotspot communications, this work employs Poisson point process (PPP) to model the locations of MBSs and PBSs, and uses Poisson cluster process (PCP) to model the ones of UEs and FBSs. ^[2] We consider multiple UAVs to provide user-equipments (UEs) with uplink transmissions, where the distribution of UEs follows the Poisson Cluster process (PCP) and each UAV is dedicated to a specific cluster. ^[3] In UAV-enabled mmWave networks, the locations of UAVs are usually modeled by a Poisson point process or a Poisson cluster process in an infinite area. ^[4] In this correspondence, we study the physical layer security in a stochastic unmanned aerial vehicles (UAVs) network from a network-wide perspective, where the locations of UAVs are modeled as a Mat$\acute{\text{e}}$rn hard-core point process (MHCPP) to characterize the minimum safety distance between UAVs, and the locations of users and eavesdroppers are modeled as a Poisson cluster process and a Poisson point process, respectively. ^[5] Specifically, we first establish a general and tractable framework to investigate the performance of mmWave networks using the Poisson cluster process integrated with several features of the mmWave band. ^[6] The locations of cellular UEs are modeled as a Poisson point process, while the locations of potential D2D UEs are modeled as a Poisson cluster process. ^[7] To this end, we in this paper consider base station (BS) cooperation and analyze user rate and energy efficiency of HetNets based on a Poisson cluster process (PCP). ^[8] Our proposed non-uniform user distribution model is such that a Poisson cluster process with the cluster centers located at SAs in which SAs have a base station offset with their BSs. ^[9] Owing to its flexibility in modeling real-world spatial configurations of users and base stations (BSs), the Poisson cluster process (PCP) has recently emerged as an appealing way to model and analyze heterogeneous cellular networks (HetNets). ^[10] Locations of UAVs are modeled as a Poison Point Process (PPP), while locations of UEs are modeled as a Poisson Cluster Process (PCP). ^[11] In particular, we model the locations of the IoT devices using a Poisson cluster process and assume that some of the clusters have IoT gateways (GWs) deployed at their centers while the other GWs are deployed independently of the IoT devices. ^[12] To enable efficient transmission in WPC, this paper proposes a PB deployment strategy where the distribution of PBs is subject to a truncated Poisson cluster process (PCP), and develops a two-tier correlated PCP model for the WPC network. ^[13] In particular, we consider a heterogeneous network model with user equipments (UEs) being distributed according to a Poisson cluster process (PCP). ^[14] In this paper, considering the in-band communication, we use the Poisson cluster process (PCP) to model and analyze the heterogeneous cellular and D2D networks. ^[15] Simulation of root water uptake of different 2D root maps generated by a Poisson cluster process shows the effectiveness of the derived approximation for clustered roots. ^[16] We exploit a new topology to model the network, where the node locations of LoRa follow a Poisson cluster process while other coexisting radio modules follow a Poisson point process. ^[17] In particular, we consider a heterogeneous network model with user equipments (UEs) being distributed according to a Poisson cluster process (PCP). ^[18] A stochastic geometry approach is applied to model the considered N-NOMA scenario as a Poisson cluster process, based on which insightful closed-form or quasi closed-form analytical expressions for outage probabilities and ergodic rates are obtained. ^[19] We model Tweet clusters as a Poisson Cluster Process. ^[20] To enable efficient transmission and overcome the doubly-near-far problem in WPC, this paper proposes a PB deployment strategy where the distribution of PBs is subject to a truncated Poisson cluster process (PCP), and analytically investigates the performance of WPC in terms of the SNR outage probability. ^[21] A tractable three-dimensional (3D) spatial model is proposed for evaluating the average downlink performance of UAV networks at mmWave bands, where the locations of UAVs and users are randomly distributed with the aid of a Poisson cluster process. ^[22] In this paper, we propose an analytical framework to investigate the integrated Sub-6GHz-mmWave cellular networks, in which the Sub-6GHz base stations (BSs) are modeled as a Poisson point process, and the mmWave BSs are clustered following a Poisson cluster process in traffic hotspots. ^[23] Therefore, we further approximate the point process formed by active RF-powered nodes with a fitted Poisson cluster process, which is shown to provide a good approximation of the success probability in the information transmission. ^[24] In contrast, a Poisson cluster process (PCP) proves more realistic for the deployment of BSs. ^[25] A numerical study is carried out on a real population of aquatic birds together with an artificial population generated by Poisson cluster process. ^[26] To be specific, by modeling the D2D underlay cellular network as a Poisson cluster process (PCP), we derive exact expressions for the coverage outage probabilities (COP) and secrecy outage probabilities (SOP), respectively, for both the cellular users (CU) and D2D users (DU). ^[27] We then compared our derived distance decay relationships to theoretical expectations obtained from a Poisson Cluster Process, known to match well with empirical distance decay relationships at local scales. ^[28] In this paper, the users in the network are assumed to be a set of uniformly distributed users and clustered users, which are modeled according to HPPP and Poisson cluster process (PCP), respectively. ^[29]

poisson cluster process

The use of Poisson cluster processes to model rainfall time series at a range of scales now has a history of more than 30 years. ^[1] We introduce clustered millimeter-wave (mmWave) networks with invoking non-orthogonal multiple access (NOMA) techniques, where the NOMA users are modeled as Poisson cluster processes and each cluster contains a base station (BS) located at the center. ^[2] More specifically, the locations of transceivers in downlink and uplink are modeled through the Poisson point processes and Poisson cluster processes (PCPs), respectively. ^[3] In this paper, we jointly consider the downlink simultaneous wireless information and power transfer (SWIPT) and uplink information transmission in unmanned aerial vehicle (UAV)-assisted millimeter wave (mmWave) cellular networks, in which the user equipment (UE) locations are modeled using Poisson cluster processes (e. ^[4] Poisson–Poisson cluster processes (PPCPs) are a class of point processes exhibiting attractive point patterns. ^[5] For such realistic hotspots’ deployment, to exploit the coupling between user equipments (UEs) and base stations (BSs), we model the geographical centers of UE hotspots as independent PPP around which UEs, P-BSs and F-BSs are scattered and form independent and non-homogeneous Poisson cluster processes (PCPs). ^[6] To adopt this approach, we derive the void probability for different Poisson cluster processes (PCP), in particular, Matérn cluster process (MCP) and Thomas cluster process (TCP), which is defined as the probability of having no children point of PCP in a given distance. ^[7]

poisson cluster model

The methodology is then used to improve the ability of Poisson cluster models to simulate hourly rainfall series that mimic the statistical behavior of the observed ones. ^[1] We study the asymptotic distribution of the total claim amount for marked Poisson cluster models. ^[2]

poisson cluster point

The Bartlett-Lewis (BL) rectangular pulse model is a type of stochastic model that represents rainfall using a Poisson cluster point process. ^[1] In this paper, we propose a multi-tier mmWave cellular framework where sub-6 GHz macro BSs (MBSs) are assumed as a Poisson point process (PPP) and small-cell BSs (SBSs), operating on either mmWave or sub-6 GHz, follows non-uniform Poisson cluster point (PCP) model. ^[2]