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On the modelling of wireless communication networks using non-poisson point processes

Tien Viet Nguyen 1 
1 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : Stochastic geometry is a powerful tool to model large wireless networks with high variation of node locations. In this framework, a common assumption is that the node locations form a realization of a Poisson Point Process (PPP). Using available results on the Laplace transform of the Shot Noise processes associating with PPPs, one can obtain closed form expressions of many performance metrics of interest such as the Medium Access Probability (MAP), the Coverage Probability (COP) and the Spatial Density of Throughput (SDT). However, in many wireless network deployments, there is a Carrier Sensing (CS) mechanism to refrain nodes which are too close to each other from transmitting at the same time. In these network, the process of nodes concurrently transmitting at any time does not form a realization of a PPP any more, and this makes the analysis of the network performance a challenging problem. The aim of this dissertation is to study this problem in two directions. In the first direction, we provide a comprehensive stochastic geometry framework based on Point Processes with exclusion to model the transmitting nodes in different types of wireless networks with CS mechanism. The considered networks are Carrier Sensing Multiple Access (CSMA) networks with perfect CS, Cognitive Radio networks where secondary users use Carrier Sensing to detect primary users, and CSMA networks with imperfect CS mechanism. For the first two cases, we provide approximations of the main network performance metrics, namely the MAP, the COP and the SDT. For the last case, we give analytic bounds on the critical spatial density of nodes where CSMA starts to behave like ALOHA (i.e. the process of concurrent transmitting nodes in the network forms a realization of a PPP). Although this phenomenon has been studied earlier by means of simulations, no analytic result was known to the best of our knowledge. In the second direction, we go deeper into the problem of studying the distribution of points patterns of the Point Processes associated with the classical Mat' ern type II and Mat' ern type III models [Mat' ern 68]. These are the two models that are used to model CSMA networks with perfect CS. Although these model were introduced long ago and have many applications in many disciplines, the distribution of the points patterns in their associated Point Processes in general and the Laplace transform of the corresponding Shot Noise processes are still open problems. We prove that the probability generating functional of this Point Process, when properly parameterized, is the unique solution of some systems of differential functional equations. Using these systems of equations, one can get a lower bound and an upper bound on these generating functional. This result can then be applied to the stochastic geometry framework mentioned above to further bridge the gap between analytic mathematical frameworks and practical network deployments.
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Submitted on : Thursday, March 13, 2014 - 10:10:04 AM
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Tien Viet Nguyen. On the modelling of wireless communication networks using non-poisson point processes. Networking and Internet Architecture [cs.NI]. Université Paris-Diderot - Paris VII, 2013. English. ⟨tel-00958663⟩

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