Abstract
This paper proposes a new approach for communication networks planning based on stochastic geometry. We first summarize the state of the art in this domain, together with its economic implications, before sketching the main expectations of the proposed method. The main probabilistic tools are point processes and stochastic geometry. We show how several performance evaluation and optimization problems within this framework can actually be posed and solved by computing the mathematical expectation of certain functionals of point processes. We mainly analyze models based on Poisson point processes, for which analytical formulae can often be obtained, although more complex models can also be analyzed, for instance via simulation.
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References
F. Baccelli, M. Klein, M. Lebourges and S. Zuyev, Géométrie aléatoire et architecture de réseaux de communications, Annales des Télécommunications 51 (1996) 158–179.
F. Baccelli, M. Klein and S. Zuyev, Perturbation analysis of functionals of random measures, Adv. Appl. Probab. 27 (1995) 306–325.
F. Baccelli and S. Zuyev, Stochastic geometry models of mobile communication networks, in: Frontiers in Queuing. Models, Methods and Problems, ed. J.H. Dshalalow (CRC Press, 1996) chapter 8, pp. 227–243.
F. Baccelli and S. Zuyev, Poisson-Voronoi spanning trees with applications to the optimization of communication networks, INRIA Report 3040 (November 1996).
M. Curien and N. et Gensollen, Economie de Télécommunications. Ouverture et Réglementation (Economica-ENSPTT, Paris, 1992).
D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes (Springer, New York, 1988).
S. Foss and S. Zuyev, On a certain Voronoi aggregative process related to a bivariate Poisson process, Adv. Appl. Probab. 28 (1996) 965–981.
G. Grahovac and M. Lebourges, A stochastic geometry model of civil engineering infrastructure in the local loop, in: '96 Conference, Sydney, Australia (24-29 November 1996).
J.F.C. Kingman, Poisson Processes, Oxford Studies in Probability (Oxford University Press, 1993).
J. Møller, Lectures on Random Voronoi Tesselations, Lecture Notes in Statistics 87 (Springer, 1994).
L. Muche and D. Stoyan, Contact and chord length distributions of the Poisson Voronoi tesselation, J. Appl. Probab. 29 (1992) 467–471.
A. Okabe, B. Boots and K. Sugihara, Spatial Tesselations, Wiley Series in Probability and Mathematical Statistics (Wiley, 1992).
D. Stoyan, W.S. Kendall and J. Mecke, Stochastic Geometry and its Applications, Wiley Series in Probability and Mathematical Statistics (Wiley, Chichester, 1987).
S. Zuyev, P. Desnogues and H. Rakotoarisoa, Simulations of large telecommunication networks based on probabilistic modeling, J. Electronic Imaging 6(1) (1997) 68–77.
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Baccelli, F., Klein, M., Lebourges, M. et al. Stochastic geometry and architecture of communication networks. Telecommunication Systems 7, 209–227 (1997). https://doi.org/10.1023/A:1019172312328
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DOI: https://doi.org/10.1023/A:1019172312328