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Poisson Cox Point Processes for Vehicular Networks [article]

Chang-Sik Choi, François Baccelli
2018 arXiv   pre-print
This paper analyzes statistical properties of the Poisson line Cox point process useful in the modeling of vehicular networks.  ...  The point process is created by a two-stage construction: a Poisson line process to model road infrastructure and independent Poisson point processes, conditionally on the Poisson lines, to model vehicles  ...  Subsequently, Poisson line Cox point processes were used to analyze vehicular networks in [6] and to analyze heterogeneous cellular networks in [7] .  ... 
arXiv:1801.04556v2 fatcat:qdgupfwmunfcbb5k4n2iyu5gqq

An Analytical Framework for Coverage in Cellular Networks Leveraging Vehicles [article]

Chang-Sik Choi, François Baccelli
2017 arXiv   pre-print
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 independent planar Poisson point processes.  ...  To produce a tractable model for heterogeneous cellular network with vehicles, we propose the superposition of a stationary Cox point process on lines and a homogeneous planar Poisson point process to  ... 
arXiv:1711.09453v2 fatcat:qk3hc7hsezeqpduxoe4kgt6bz4

Success Probability and Area Spectral Efficiency of a VANET Modeled as a Cox Process [article]

Vishnu Vardhan Chetlur, Harpreet S. Dhillon
2018 arXiv   pre-print
This paper analyzes the performance of a vehicular ad hoc network (VANET) modeled as a Cox process, where the spatial layout of the roads is modeled by a Poisson line process (PLP) and the locations of  ...  nodes on each line are modeled as a 1D Poisson point process (PPP).  ...  Dhillon Abstract-This paper analyzes the performance of a vehicular ad hoc network (VANET) modeled as a Cox process, where the spatial layout of the roads is modeled by a Poisson line process (PLP) and  ... 
arXiv:1804.10298v1 fatcat:3xbdkdya7zdddhphab52khmgqy

Analysis of Vehicular Safety Messaging in Cellular Networks [article]

Chang-sik Choi, Francois Baccelli
2020 arXiv   pre-print
We model the locations of vehicles as a Poisson line Cox point process and the locations of users as a planar Poisson point process.  ...  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.  ...  by an independent Poisson-line Cox point process .  ... 
arXiv:2004.04327v1 fatcat:7lyddccy2va2phe3tsrpxdykq4

On the Load Distribution of Vehicular Users Modeled by a Poisson Line Cox Process [article]

Vishnu Vardhan Chetlur, Harpreet S. Dhillon
2020 arXiv   pre-print
In this letter, we characterize the load on the cellular macro base stations (MBSs) due to vehicular users modeled by a Poisson line Cox process (PLCP).  ...  Modeling the locations of MBSs by a homogeneous 2D Poisson point process (PPP), we first characterize the total chord length distribution of the lines of the Poisson line process (PLP) intersecting the  ...  Thus, under the Palm distribution of the PLCP, the resulting point process of vehicular users Φ v0 is the superposition of Φ v , a 1D PPP Ψ L0 with density λ v along the line L 0 that passes through the  ... 
arXiv:2008.01267v1 fatcat:qfrdk7a2z5fwnontdc3aqwwbwe

An Analysis of LOS Coverage in Vehicular Networks with Roadside Units and Relays [article]

Chang-Sik Choi, François Baccelli
2021 arXiv   pre-print
To account for the spatial relationship between vehicles and RSUs, we use Cox point processes. We assume that the LOS distances from RSUs or relays are independent and exponentially distributed.  ...  As a result, the LOS coverage of those RSUs is extended by the LOS coverage newly provided by the vehicular relays.  ...  Contributions To model the LOS coverage region of vehicular networks, we first model the RSUs and vehicles as Cox point processes on Poisson lines representing the roads.  ... 
arXiv:2110.13436v1 fatcat:m6it33iryjcvtcnrbfxwokpihi

Coverage Analysis of a Vehicular Network Modeled as Cox Process Driven by Poisson Line Process [article]

Vishnu Vardhan Chetlur, Harpreet S. Dhillon
2017 arXiv   pre-print
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 (PPP).  ...  In this paper, we consider a vehicular network in which the wireless nodes are located on a system of roads.  ...  A well-known canonical model in the literature that readily meets this requirement is a Cox process or doubly stochastic Poisson point process [13] , [14] , where the roads in a network are modeled by  ... 
arXiv:1709.08577v1 fatcat:z75uackqvnbhvi2oh4scch6hai

Modeling and Analysis of 2-Tier Heterogeneous Vehicular Networks Leveraging Roadside Units and Vehicle Relays [article]

Chang-Sik Choi, François Baccelli
2022 arXiv   pre-print
We present a two-dimensional analytical model where the spatial dependence between RSUs, vehicle relays, vehicle users, and roads is accurately taken into account through a Cox point process structure.  ...  This paper leverages stochastic geometry to propose a novel framework for the performance analysis of heterogeneous vehicular networks with RSUs, vehicle relays, and vehicle users.  ...  them as Cox point processes generated on the same Poisson line process.  ... 
arXiv:2204.12243v1 fatcat:hijmdtneh5b7fovixznauglg2y

Energy Utilization and Transmission Delay Optimization in Cox VANET networks

Adil Boumaalif, Ouadoudi Zytoune, B. Benhala, K. Mansouri, A. Raihani, M. Qbadou
2022 E3S Web of Conferences  
For that, we model the network as a Cox Line-Point process, and the transmitter as an M/D/1 queue server.  ...  It is shown , via simulations, that through our algorithm, the vehicular transmitter be able to learn its transmit power in an autonomous way, and achieve better performance for the energy utilization  ...  Due to the principally linear nature, roads can be modeled using a Poisson Line Process (PLP) in R 2 that can be deduced from a Poisson Poisson Processes, where instead of points, the undirected lines  ... 
doi:10.1051/e3sconf/202233600066 fatcat:opvjhe4eivhlnijzl4zfpcg25i

Cox Models for Vehicular Networks: SIR Performance and Equivalence

Jeya Pradha Jeyaraj, Martin Haenggi
2020 IEEE Transactions on Wireless Communications  
Specifically, we prove that the Poisson stick process-based vehicular network is equivalent to the Poisson line process-based and Poisson lilypond model-based vehicular networks, and their rotational variants  ...  The street system, in turn, specifies the random intensity measure of a Cox process of vehicles, i.e., vehicles form independent 1D Poisson point processes on each street.  ...  A vehicular point process V ⊂ R 2 is a Cox process with random intensity measure Υ(B) = λ|S ∩ B| 1 . Equivalently, Υ(B) = λ|P 2 ∩ B| 1 since a.s. V ⊂ P 2 .  ... 
doi:10.1109/twc.2020.3023914 fatcat:5dema4ngobfw7jiiymlz44f7tm

Coverage and Rate Analysis of Downlink Cellular Vehicle-to-Everything (C-V2X) Communication [article]

Vishnu Vardhan Chetlur, Harpreet S. Dhillon
2019 arXiv   pre-print
modeled as Cox processes driven by a Poisson line process (PLP) and the locations of cellular macro base stations (MBSs) are modeled as a 2D Poisson point process (PPP).  ...  model inspired by the asymptotic behavior of the Cox process.  ...  From the perspective of vehicular networks, the spatial model that is gaining popularity is the so-called Cox process, where the spatial layout of roads is modeled by a Poisson line process (PLP) and the  ... 
arXiv:1901.09236v1 fatcat:g4si5usnxjcrtmkggfgp7zkdwi

Stochastic Geometry Modeling of Cellular V2X Communication Over Shared Channels [article]

Muhammad Nadeem Sial, Yansha Deng, Junaid Ahmed, Arumugam Nallanathan, Mischa Dohler
2019 arXiv   pre-print
By practically modeling the vehicles on the roads using the doubly stochastic Cox process and the base-stations, we derive new association probabilities, new success probabilities of infrastructure and  ...  (C-V2X) communication networks, standardized in 3rd Generation Partnership Project (3GPP) Release 14, have been recently introduced to cover broader vehicular communication scenarios including vehicle-to-vehicle  ...  as a Cox process on a Poisson line process (PLP).  ... 
arXiv:1804.08409v3 fatcat:xc4riougorcdpowokubh23ajwe

Communication and Computation Assisted Sensing Information Freshness Performance Analysis in Vehicular Networks [article]

Ning Jiang, Shi Yan, Zhuohan Liu, Chunjing Hu, Mugen Peng
2022 arXiv   pre-print
The network interference is analyzed by modeling the VNETs as Cox Poisson Point Process based on stochastic geometry and the closed-form solution of the coverage probability and the expected data rate  ...  The timely sharing of raw sensing information in the vehicular networks (VNETs) is essential to safety.  ...  We model the vehicles and RSUs by the Cox Poisson Point Process (PPP) which is illustrated in Fig. 1(b ).  ... 
arXiv:2204.05995v1 fatcat:edq6unukbrfgtiowqw3gwqijcq

Binomial Line Processes: Distance Distributions [article]

Gourab Ghatak
2021 arXiv   pre-print
We introduce the binomial line process (BLP), a novel spatial stochastic model for the characterization of streets in the statistical evaluation of wireless and vehicular networks.  ...  Existing stochastic geometry models for streets, e.g., Poisson line processes (PLP) and Manhattan line processes (MLP) lack an important aspect of city-wide street networks: streets are denser in the city  ...  [8] studied a generalized framework for Cox models to study vehicular networks.  ... 
arXiv:2108.03804v2 fatcat:rgb57ek5drac7agnq5ums34nta

Radio Resource Dimensioning with Cox Process Based User Location Distribution [article]

Ridha Nasri, Jalal Rachad, Laurent Decreusefond
2019 arXiv   pre-print
We distinguish between the spatial random distribution of indoor users, modeled by a spatial Poisson Point Process (spatial PPP) in a typical area covered by a 5G cell, and the distribution of outdoor  ...  users modeled by a linear PPP generated in a random system of roads modeled according to a Poisson Line Process (PLP).  ...  Such a model is known as Cox point process driven by PLP.  ... 
arXiv:1909.13809v1 fatcat:sden4yr4ljcjfe7xfyypavfpvu
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