I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, Wireless sensor networks: a survey, Computer Networks, vol.38, issue.4, pp.393-422, 2002.
DOI : 10.1016/S1389-1286(01)00302-4

D. Aldous and J. M. Steele, The Objective Method: Probabilistic Combinatorial Optimization and Local Weak Convergence, pp.1-72, 2004.
DOI : 10.1007/978-3-662-09444-0_1

F. Baccelli, K. Tchoumatchenko, and S. Zuyev, Markov paths on the Poisson-Delaunay graph with applications to routeing in mobile networks, Advances in Applied Probability, vol.32, issue.01, pp.1-18, 2000.
DOI : 10.1007/BF02187821

L. E. Baum and M. Katz, Convergence rates in the law of large numbers, Transactions of the American Mathematical Society, vol.120, issue.1, pp.108-123, 1965.
DOI : 10.1090/S0002-9947-1965-0198524-1

N. Bingham, C. Goldie, and J. Teugels, Regular Variation, 1987.
DOI : 10.1017/CBO9780511721434

D. J. Daley, D. Vere, and -. , An introduction to the Theory of Point Processes, 1988.

M. Draief and A. Ganesh, Routing in poisson small-world networks. ArXiv, pp.303-312, 2005.

F. Baccelli and C. Bordenave, The radial spanning tree of a Poisson point process, The Annals of Applied Probability, vol.17, issue.1, 2005.
DOI : 10.1214/105051606000000826
URL : https://hal.archives-ouvertes.fr/inria-00070309

W. Feller, An Introduction to Probability Theory and its Applications, II. Wiley Series in Probability and Mathematical Statistics, 1971.

P. A. Ferrari, C. Landim, and H. Thorisson, Poisson trees, succession lines and coalescing random walks. Annals de L´Institut Henry Poincaré Volume, pp.141-152, 2004.

M. Franceschetti and R. Meester, Navigation in small world networks, a scale-free continuum model. prepint, 2004.

A. Ganesh, A. Kermarrec, and L. Massoulie, Peer-to-peer membership management for gossip-based protocols, IEEE Transactions on Computers, vol.52, issue.2, 2003.
DOI : 10.1109/TC.2003.1176982

A. Ganesh and F. Xue, On the connectivity and diameter of small-world networks, 2005.

S. Gangopadhyay, R. Roy, and A. Sarkar, Random oriented trees : a model of drainage networks, Annals of Applied Probability, vol.14, pp.1242-1266, 2004.

A. Gut, Convergence Rates for Probabilities of Moderate Deviations for Sums of Random Variables with Multidimensional Indices, The Annals of Probability, vol.8, issue.2, pp.298-313, 1980.
DOI : 10.1214/aop/1176994778

C. Howard and C. Newman, Geodesics and spanning trees for euclidean first-passage percolation, Ann. Probab, vol.29, pp.577-623, 2001.

J. M. Kleinberg, The small-world phenomenon, Proceedings of the thirty-second annual ACM symposium on Theory of computing , STOC '00, pp.163-170, 2000.
DOI : 10.1145/335305.335325

Y. B. Ko and N. Vaidya, Location-aided routing (LAR) in mobile ad hoc networks, Proceedings of the 4th annual ACM/IEEE international conference on Mobile computing and networking , MobiCom '98, pp.307-321, 2000.
DOI : 10.1145/288235.288252

E. Kranakis, H. Singh, and J. Urrutia, Compass routing on geometric networks, Proc. 11 th Canadian Conference on Computational Geometry, pp.51-54, 1999.

S. Lee, The central limit theorem for euclidian minimal spanning trees, The Annals of Applied Probability, vol.7, pp.996-1020, 1997.

J. Liebeherr, M. Nahas, and W. Si, Application-layer multicasting with Delaunay triangulation overlays, IEEE Journal on Selected Areas in Communications, vol.20, issue.8, pp.1472-1488, 2002.
DOI : 10.1109/JSAC.2002.803067
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.18.4712

S. Meyn and R. Tweedie, Markov Chains and Stochastic Stability, 1993.

P. Morin, Online routing in Geometric Graphs, 2001.

M. Penrose and A. Wade, Random minimal directed spanning trees and Dickman-type distributions, Advances in Applied Probability, vol.1, issue.03, pp.691-714, 2004.
DOI : 10.1007/PL00009241
URL : http://projecteuclid.org/download/pdfview_1/euclid.aap/1093962229

M. Penrose and J. Yukich, Limit Theory for Random Sequential Packing and Deposition, The Annals of Applied Probability, vol.12, issue.1, pp.272-301, 2001.
DOI : 10.1214/aoap/1015961164

M. Penrose and J. Yukich, Weak laws of large numbers in geometric probability, The Annals of Applied Probability, vol.13, issue.1, pp.277-303, 2003.
DOI : 10.1214/aoap/1042765669

L. Pimentel, Asymptotics for First-Passage Times on Delaunay Triangulations, Combinatorics, Probability and Computing, vol.11, issue.03, 2005.
DOI : 10.1090/S0894-0347-99-00307-0

G. Plaxton, R. Rajaraman, and A. Richa, Accessing nearby copies of replicated objects in a distributed environment, ACM Symposium on Parallel Algorithms and Architectures, pp.311-320, 1997.

J. M. Steele, Probability Theory and Combinatorial Optimization, NSF- CBMS. SIAM, vol.69, 1997.
DOI : 10.1137/1.9781611970029

M. Vahidi-asl and J. Wierman, First-passage percolation on the Vorono? ? tessellation and Delaunay triangulation, Random graphs '87, pp.341-359, 1987.

M. Vahidi-asl and J. Wierman, A shape result for first-passage percolation on the Vorono? ? tessellation and Delaunay triangulation, In Random graphs, vol.2, pp.247-262, 1989.

J. Yukich, Probability Theory of Classical Euclidean Optimization Problems, Lecture Notes in Mathematics, vol.1675, 1998.
DOI : 10.1007/BFb0093472

I. Unité-de-recherche-inria-rocquencourt-domaine-de-voluceau-rocquencourt-bp, Technopôle de Nancy-Brabois -Campus scientifique 615, rue du Jardin Botanique -BP 101 -54602 Villers-lès-Nancy Cedex (France) Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu -35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l'Europe -38330 Montbonnot-St, pp.105-78153, 2004.

I. De-voluceau-rocquencourt, BP 105 -78153 Le Chesnay Cedex (France) http://www.inria.fr ISSN, pp.249-6399