The Experts below are selected from a list of 21930 Experts worldwide ranked by ideXlab platform
François Baccelli - One of the best experts on this subject based on the ideXlab platform.
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Random Measures, Point Processes, and Stochastic Geometry
2020Co-Authors: François Baccelli, Bartłomiej Błaszczyszyn, Mohamed KarrayAbstract:This book is centered on the mathematical analysis of random structures embedded in the Euclidean space or more general topological spaces, with a main focus on random measures, point processes, and Stochastic Geometry. Such random structures have been known to play a key role in several branches of natural sciences (cosmology, ecology, cell biology) and engineering (material sciences, networks) for several decades. Their use is currently expanding to new fields like data sciences. The book was designed to help researchers finding a direct path from the basic definitions and properties of these mathematical objects to their use in new and concrete Stochastic models. The theory part of the book is structured to be self-contained, with all proofs included, in particular on measurability questions, and at the same time comprehensive. In addition to the illustrative examples which one finds in all classical mathematical books, the document features sections on more elaborate examples which are referred to as models}in the book. Special care is taken to express these models, which stem from the natural sciences and engineering domains listed above, in clear and self-contained mathematical terms. This continuum from a comprehensive treatise on the theory of point processes and Stochastic Geometry to the collection of models that illustrate its representation power is probably the main originality of this book. The book contains two types of mathematical results: (1) structural results on stationary random measures and Stochastic Geometry objects, which do not rely on any parametric assumptions; (2) more computational results on the most important parametric classes of point processes, in particular Poisson or Determinantal point processes. These two types are used to structure the book. The material is organized as follows. Random measures and point processes are presented first, whereas Stochastic Geometry is discussed at the end of the book. For point processes and random measures, parametric models are discussed before non-parametric ones. For the Stochastic Geometry part, the objects as point processes are often considered in the space of random sets of the Euclidean space. Both general processes are discussed as, e.g., particle processes, and parametric ones like, e.g., Poisson Boolean models of Poisson hyperplane processes. We assume that the reader is acquainted with the basic results on measure and probability theories. We prove all technical auxiliary results when they are not easily available in the literature or when existing proofs appeared to us not sufficiently explicit. In all cases, the corresponding references will always be given.
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Adaptive Spatial Aloha, Fairness and Stochastic Geometry
2012Co-Authors: François Baccelli, Chandramani SinghAbstract:This work aims at combining adaptive protocol design, utility maximization and Stochastic Geometry. We focus on a spatial adaptation of Aloha within the framework of ad hoc networks. We consider quasi-static networks in which mobiles learn the local topology and incorporate this information to adapt their medium access probability~(MAP) selection to their local environment. We consider the cases where nodes cooperate in a distributed way to maximize the global throughput or to achieve either proportional fair or max-min fair medium access. In the proportional fair case, we show that nodes can compute their optimal MAPs as solutions to certain fixed point equations. In the maximum throughput case, the optimal MAPs are obtained through a Gibbs Sampling based algorithm. In the max min case, these are obtained as the solution of a convex optimization problem. The main performance analysis result of the paper is that this type of distributed adaptation can be analyzed using Stochastic Geometry in the proportional fair case. In this case, we show that, when the nodes form a homogeneous Poisson point process in the Euclidean plane, the distribution of the optimal MAP can be obtained from that of a certain shot noise process w.r.t. the node Poisson point process and that the mean utility can also be derived from this distribution. We discuss the difficulties to be faced for analyzing the performance of the other cases (maximum throughput and max-min fairness). Numerical results illustrate our findings and quantify the gains brought by spatial adaptation in such networks.
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A Stochastic Geometry Model for Cognitive Radio Networks
The Computer Journal, 2011Co-Authors: Tien Viet Nguyen, François BaccelliAbstract:We propose a probabilistic model based on Stochastic Geometry to analyze cognitive radio in a large wireless network with randomly located users sharing the medium with carrier sensing multiple access. Analytical results are derived on the impact of the interaction between primary and secondary users, on their medium access probability, coverage probability and throughput. These results can be seen as the continuation of the theory of priorities in queueing theory to spatial processes. They give insight into the guarantees that can be offered to primary users and more generally on the possibilities offered by cognitive radio to improve the effectiveness of spectrum utilization in such networks.
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Stochastic Geometry and Wireless Networks, Part I: Theory
2009Co-Authors: François Baccelli, Bartlomiej BlaszczyszynAbstract:Stochastic Geometry and Wireless Networks, Part I: Theory first provides a compact survey on classical Stochastic Geometry models, with a main focus on spatial shot-noise processes, coverage processes and random tessellations. It then focuses on signal to interference noise ratio (SINR) Stochastic Geometry, which is the basis for the modeling of wireless network protocols and architectures considered in Stochastic Geometry and Wireless Networks, Part II: Applications. It also contains an appendix on mathematical tools used throughout Stochastic Geometry and Wireless Networks, Parts I and II.
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Stochastic Geometry and wireless networks volume i theory
2009Co-Authors: François Baccelli, Bartllomiej BllaszczyszynAbstract:Volume I first provides a compact survey on classical Stochastic Geometry models, with a main focus on spatial shot-noise processes, coverage processes and random tessellations. It then focuses on signal to interference noise ratio (SINR) Stochastic Geometry, which is the basis for the modeling of wireless network protocols and architectures considered in Volume II. It also contains an appendix on mathematical tools used throughout Stochastic Geometry and Wireless Networks, Volumes I and II.
Hamid Eltom - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Geometry Methods for Modeling Automotive Radar Interference
IEEE Transactions on Intelligent Transportation Systems, 2018Co-Authors: Akram Al-hourani, Robin J. Evans, Sithamparanathan Kandeepan, Bill Moran, Hamid EltomAbstract:As the use of automotive radar increases, performance limitations associated with radar-to-radar interference will become more significant. In this paper we employ tools from Stochastic Geometry to characterize the statistics of radar interference. Specifically, using two different models for vehicle spacial distributions, namely, a Poisson point process and a Bernoulli lattice process, we calculate for each case the interference statistics and obtain analytical expressions for the probability of successful range estimation. Our study shows that the regularity of the geometrical model appears to have limited effect on the interference statistics, and so it is possible to obtain tractable tight bounds for worst case performance. A technique is proposed for designing the duty cycle for random spectrum access which optimizes the total performance. This analytical framework is verified using Monte-Carlo simulations.
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Stochastic Geometry Methods for Modeling Automotive Radar Interference
IEEE Transactions on Intelligent Transportation Systems, 2018Co-Authors: Akram Al-hourani, Robin J. Evans, Sithamparanathan Kandeepan, Bill Moran, Hamid EltomAbstract:As the use of automotive radar increases, performance limitations associated with radar-to-radar interference will become more significant. In this paper, we employ tools from Stochastic Geometry to characterize the statistics of radar interference. Specifically, using two different models for the spatial distributions of vehicles, namely, a Poisson point process and a Bernoulli lattice process, we calculate for each case the interference statistics and obtain analytical expressions for the probability of successful range estimation. This paper shows that the regularity of the geometrical model appears to have limited effect on the interference statistics, and so it is possible to obtain tractable tight bounds for the worst case performance. A technique is proposed for designing the duty cycle for the random spectrum access, which optimizes the total performance. This analytical framework is verified using Monte Carlo simulations.
Akram Al-hourani - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Geometry Methods for Modeling Automotive Radar Interference
IEEE Transactions on Intelligent Transportation Systems, 2018Co-Authors: Akram Al-hourani, Robin J. Evans, Sithamparanathan Kandeepan, Bill Moran, Hamid EltomAbstract:As the use of automotive radar increases, performance limitations associated with radar-to-radar interference will become more significant. In this paper we employ tools from Stochastic Geometry to characterize the statistics of radar interference. Specifically, using two different models for vehicle spacial distributions, namely, a Poisson point process and a Bernoulli lattice process, we calculate for each case the interference statistics and obtain analytical expressions for the probability of successful range estimation. Our study shows that the regularity of the geometrical model appears to have limited effect on the interference statistics, and so it is possible to obtain tractable tight bounds for worst case performance. A technique is proposed for designing the duty cycle for random spectrum access which optimizes the total performance. This analytical framework is verified using Monte-Carlo simulations.
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Stochastic Geometry Methods for Modeling Automotive Radar Interference
IEEE Transactions on Intelligent Transportation Systems, 2018Co-Authors: Akram Al-hourani, Robin J. Evans, Sithamparanathan Kandeepan, Bill Moran, Hamid EltomAbstract:As the use of automotive radar increases, performance limitations associated with radar-to-radar interference will become more significant. In this paper, we employ tools from Stochastic Geometry to characterize the statistics of radar interference. Specifically, using two different models for the spatial distributions of vehicles, namely, a Poisson point process and a Bernoulli lattice process, we calculate for each case the interference statistics and obtain analytical expressions for the probability of successful range estimation. This paper shows that the regularity of the geometrical model appears to have limited effect on the interference statistics, and so it is possible to obtain tractable tight bounds for the worst case performance. A technique is proposed for designing the duty cycle for the random spectrum access, which optimizes the total performance. This analytical framework is verified using Monte Carlo simulations.
Nuggehalli Pavan Santhana Krishna - One of the best experts on this subject based on the ideXlab platform.
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Stochastic Geometry-Based Modeling and Analysis of Citizens Broadband Radio Service System
IEEE Access, 2017Co-Authors: Priyabrata Parida, Harpreet S. Dhillon, Nuggehalli Pavan Santhana KrishnaAbstract:In this paper, we model and analyze a cellular network that operates in the licensed band of the 3.5-GHz spectrum and consists of a licensed and an unlicensed operator. Using tools from Stochastic Geometry, we concretely characterize the performance of this spectrum sharing system. We model the locations of the licensed base stations (BSs) as a homogeneous Poisson point process with protection zones (PZs) around each BS. Since the unlicensed BSs cannot operate within the PZs, their locations are modeled as a Poisson hole process. In addition, we consider carrier sense multiple access with collision avoidance-type contention-based channel access mechanism for the unlicensed BSs. For this setup, we first derive an approximate expression and useful lower bounds for the medium access probability of the serving unlicensed operator BS. Furthermore, by efficiently handling the correlation in the interference powers induced due to correlation in the locations of the licensed and unlicensed BSs, we provide approximate expressions for the coverage probability of a typical user of each operator. Subsequently, we study the effect of different system parameters on area spectral efficiency of the network. To the best of our knowledge, this is the first attempt toward accurate modeling and analysis of a citizens broadband radio service system using tools from Stochastic Geometry.
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WCNC Workshops - Stochastic Geometry Perspective of Unlicensed Operator in a CBRS System
2017 IEEE Wireless Communications and Networking Conference Workshops (WCNCW), 2017Co-Authors: Priyabrata Parida, Harpreet S. Dhillon, Nuggehalli Pavan Santhana KrishnaAbstract:In this work, we model and analyze a cellular system that operates in the licensed band of the 3.5 GHz spectrum and consists of a licensed and an unlicensed operator. Using tools from Stochastic Geometry, we study the co-existence of these networks from the perspective of the unlicensed operator. We model the licensed base station (BS) locations as a homogeneous Poisson point process with protection zones (PZs) around each BS. Since the unlicensed BSs can not operate within PZs, their locations are modeled as a Poisson hole process. In addition, we also consider contention-based channel access mechanism for the unlicensed BSs. We provide useful lower bound for the medium access probability for a typical BS of the unlicensed operator. Further, approximate results for coverage probability are also presented, by effectively handling the correlation in the interference powers induced due to correlation in locations of the licensed and unlicensed BSs. Using the derived expressions, we study the effect of the density of licensed BSs on the average number of active unlicensed BSs per unit area and coverage probability for a typical unlicensed user. To the best of our knowledge, this work presents the first comprehensive Stochastic Geometry-based analysis of the CBRS system.
Emilio Leonardi - One of the best experts on this subject based on the ideXlab platform.
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Almost Sure Central Limit Theorems in Stochastic Geometry
Advances in Applied Probability, 2020Co-Authors: Giovanni Luca Torrisi, Emilio LeonardiAbstract:AbstractWe prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals arising in Stochastic Geometry. As a consequence, we provide almost sure central limit theorems for (i) the total edge length of the k-nearest neighbors random graph, (ii) the clique count in random geometric graphs, and (iii) the volume of the set approximation via the Poisson–Voronoi tessellation.
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Almost Sure Central Limit Theorems in Stochastic Geometry
arXiv: Probability, 2019Co-Authors: Giovanni Luca Torrisi, Emilio LeonardiAbstract:We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in Stochastic Geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total edge length of the $k$-nearest neighbors random graph, $(ii)$ the clique count in random geometric graphs, $(iii)$ the volume of the set approximation via the Poisson-Voronoi tessellation.
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New Directions into the Stochastic Geometry Analysis of Dense CSMA Networks
IEEE Transactions on Mobile Computing, 2014Co-Authors: Giusi Alfano, Michele Garetto, Emilio LeonardiAbstract:We consider extended wireless networks characterized by a random topology of access points (APs) contending for medium access over the same wireless channel. Recently, Stochastic Geometry has emerged as a powerful tool to analyze random networks adopting MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows considering also random fading on each link. In this paper, we extend previous Stochastic Geometry models of CSMA networks, developing computationally efficient techniques to obtain throughput distributions, in addition to spatial averages, which permit us to get interesting insights into the impact of protocol parameters and channel variability on the spatial fairness among the nodes. Moreover, we extend the analysis to a significant class of topologies in which APs are not placed according to a Poisson process.
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new insights into the Stochastic Geometry analysis of dense csma networks
International Conference on Computer Communications, 2011Co-Authors: Giusi Alfano, Michele Garetto, Emilio LeonardiAbstract:Stochastic Geometry proves to be a powerful tool for modeling dense wireless networks adopting random MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows to consider also random fading on each link. Existing models of CSMA networks adopting the Stochastic Geometry approach suffer from two important weaknesses: 1) they permit to evaluate only spatial averages of the main performance measures, thus hiding possibly huge discrepancies in the performance achieved by individual nodes; 2) they are analytically tractable only when nodes are distributed over the area according to simple spatial processes (e.g., the Poisson point process). In this paper we show how the Stochastic Geometry approach can be extended to overcome the above limitations, allowing to obtain node throughput distributions as well as to analyze a significant class of topologies in which nodes are not independently placed.
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INFOCOM - New insights into the Stochastic Geometry analysis of dense CSMA networks
2011 Proceedings IEEE INFOCOM, 2011Co-Authors: Giusi Alfano, Michele Garetto, Emilio LeonardiAbstract:Stochastic Geometry proves to be a powerful tool for modeling dense wireless networks adopting random MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows to consider also random fading on each link. Existing models of CSMA networks adopting the Stochastic Geometry approach suffer from two important weaknesses: 1) they permit to evaluate only spatial averages of the main performance measures, thus hiding possibly huge discrepancies in the performance achieved by individual nodes; 2) they are analytically tractable only when nodes are distributed over the area according to simple spatial processes (e.g., the Poisson point process). In this paper we show how the Stochastic Geometry approach can be extended to overcome the above limitations, allowing to obtain node throughput distributions as well as to analyze a significant class of topologies in which nodes are not independently placed.
