Approximations of functionals of some modulated-poisson Voronoi tessellations with applications to modeling of communication networks

Japan Journal of Industrial and Applied Mathematics

Volumn 22, Issue 2, 2005, Pages 179-204

  Błaszczyszyn, Bartłomiej ^a   Schott, René ^b  

^a UNIVERSITY OF WROC AW   (Poland)

^b LORIA   (France)

Author keywords

Approximation; Communication network; Decomposability; Double stochastic Poisson point process; Modulated Poisson point process; Stochastic geometry; Voronoi tessellation

Indexed keywords

EID: 22544469149     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167437     Document Type: Conference Paper

References (17)

1. F. Baccelli and B. Blaszczyszyn, On a coverage process ranging from the Boolean model to the Poisson-Voronoi tessellation, with applications to wireless communications. Adv. in Appl. Probab., 33 (2001), 293-323.
2. F. Baccelli, B. Blaszczyszyn and P. Mühlethaler, An Aloha protocol for multihop mobile wireless networks. Proc. of ITC Specialist Seminar on Performance Evaluation of Wireless and Mobile Systems, Antwerp, Belgium, 2004.
3. F. Baccelli, B. Blaszczyszyn and F. Tournois, Spatial averages of coverage characteristics in large CDMA networks. Wireless Networks, 8 (2002), 569-586.
4. F. Baccelli, B. Blaszczyszyn and F. Tournois, Downlink capacity and admission/congestion control in CDMA networks. Proc. of IEEE INFOCOM, San Francisco, 2003.
5. F. Baccelli, M. Klein, M. Lebourges and S. Zuyev, Géométrie aléatoire et architecture de réseaux de communication. Annales des Télécommunications, 51 (1996), 158-179. (In French).
6. F. Baccelli, M. Klein, M. Lebourges and S. Zuyev, Stochastic geometry and architecture of communication networks. Telecommunications Systems, 7 (1997), 209-227.
7. F. Baccelli, D. Kofman and J.L. Rougier, Self organizing hierarchical multicast trees and their optimization. Proceedings of IEEE INFOCOM, New York (USA), 1999.
8. F. Baccelli and S. Zuyev, Stochastic geometry models of mobile communication networks. Frontiers in Queueing. Models and Applications in Science and Engineering (ed. J.H. Dshalalow), CRC Press, Boca Raton, 1997, 227-244.
9. B. Blaszczyszyn and R. Schott, Approximate decomposition of some modulated-Poisson Voronoi tessellations. Adv. in Appl. Probab., 35 (2003), 847-862.
10. P.J. Courtois, Decomposability, Queueing and Computer System Applications. Academic Press, New York, 1977.
11. R. Cowan, Properties of ergodic random mosaic processes. Math. Nachr., 97 (1980), 89-102.
12. S. Farinetto and S. Zuyev, Stochastic geometry modeling of hybrid optical networks. Performance Evaluations, 2004, to appear.
13. G. Matheron, Random Sets and Integral Geometry. John Wiley & Sons, London, 1975.
14. J. Mecke, Palm methods for stationary random mosaics. Combinatorial Principles in Stochastic Geometry (ed. R.V. Ambartzumian), Armenian Academy of Sciences Publ., 1980, 124-132.
15. J. Møller, Lectures on Random Voronoi Tessellations. Lecture Notes in Statistics, 87, Springer-Verlag, New York, 1989.
16. A. Okabe, B. Boots and K. Sugihara, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. John Wiley &; Sons, Chichester, 2000.
17. D. Stoyan, W. Kendall and J. Mecke, Stochastic Geometry and its Applications. Wiley, Chichester, 1995.