D. Aldous, Ultimate instability of exponential back-off protocol for acknowledgment-based transmission control of random access communication channels, IEEE Transactions on Information Theory, vol.33, issue.2, pp.219-223, 1987.
DOI : 10.1109/TIT.1987.1057295

I. John and . Capetanakis, Tree algorithms for packet broadcast channels, IEEE Transactions on Information Theory, vol.25, issue.5, pp.505-515, 1979.

P. Carmona, F. Petit, and M. Yor, On the distribution and asymptotic results for exponential functionals of Lévy processes, Exponential functionals and principal values related to Brownian motion, Rev. Mat. Iberoam, pp.73-130, 1997.

H. Delange, Sur la formule sommatoire de la fonction somme des chiffres, Mathématique XXI, issue.1, pp.31-47, 1975.

V. Dumas, F. Guillemin, and P. Robert, A Markovian analysis of additive-increase multiplicative-decrease algorithms, Advances in Applied Probability, vol.III, issue.01, pp.85-111, 2002.
DOI : 10.1145/122431.122434

A. Ephremides and B. Hajek, Information theory and communication networks: an unconsummated union, IEEE Transactions on Information Theory, vol.44, issue.6, pp.1-20, 1998.
DOI : 10.1109/18.720543

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.3794

P. Flajolet, Approximate counting: A detailed analysis, BIT, vol.21, issue.1, pp.113-134, 1985.
DOI : 10.1007/BF01934993

P. Flajolet, X. Gourdon, and P. Dumas, Mellin transforms and asymptotics: Harmonic sums, Theoretical Computer Science, vol.144, issue.1-2, pp.3-58, 1995.
DOI : 10.1016/0304-3975(95)00002-E

URL : https://hal.archives-ouvertes.fr/inria-00074307

P. Flajolet and P. Jacquet, Analytic models for tree communication protocols, NATO Advance Science Institute Series, Series F: Computer and Systems Sciences, pp.223-234, 1987.

P. Flajolet and N. Martin, Probabilistic counting algorithms for data base applications, Journal of Computer and System Sciences, vol.31, issue.2, pp.182-209, 1985.
DOI : 10.1016/0022-0000(85)90041-8

URL : https://hal.archives-ouvertes.fr/inria-00076244

P. Jacquet and W. Szpankowski, Analytical depoissonization and its applications, Theoretical Computer Science, vol.201, issue.1-2, pp.1-62, 1998.
DOI : 10.1016/S0304-3975(97)00167-9

J. F. Kingman, Poisson processes, Oxford Studies in Probability, 1993.

P. Kirschenhofer, H. Prodinger, and W. Szpankowski, Analysis of a splitting process arising in probabilistic counting and other related algorithms, Random Structures and Algorithms, vol.9, issue.4, pp.379-401, 1996.
DOI : 10.1002/(SICI)1098-2418(199612)9:4<379::AID-RSA3>3.0.CO;2-U

E. Donald and . Knuth, The art of computer programming Sorting and searching, Series in Computer Science and Information Processing, 1973.

N. Litvak and W. R. Van-zwet, On the minimal travel time needed to collect n items on a circle, The Annals of Applied Probability, vol.14, issue.2, pp.881-902, 2004.
DOI : 10.1214/105051604000000152

M. Hosam and . Mahmoud, Evolution of random search trees, Wiley-Interscience Series in Discrete Mathematics and Optimization, 1992.

R. Metcalf and D. Boggs, Ethernet: distributed packet switching for local computer networks, Communications of the ACM, vol.19, issue.7, pp.395-403, 1976.
DOI : 10.1145/360248.360253

H. Mohamed and P. Robert, A probabilistic analysis of some tree algorithms, The Annals of Applied Probability, vol.15, issue.4, 2004.
DOI : 10.1214/105051605000000494

URL : https://hal.archives-ouvertes.fr/inria-00070586

N. Pippenger, An Elementary Approach to Some Analytic Asymptotics, SIAM Journal on Mathematical Analysis, vol.24, issue.5, pp.1361-1377, 1993.
DOI : 10.1137/0524079

P. Robert, Stochastic networks and queues, Stochastic Modelling and Applied Probability Series, 2003.

B. S. Tsybakov and V. A. , Mikha? ?lov, Free synchronous packet access in a broadcast channel with feedback, Problems Inform, pp.32-59, 1978.

. Ph, . Robert, . Inria, and B. P. Domaine-de-voluceau, 78153 Le Chesnay Cedex, France E-mail address: Philippe.Robert@inria.fr URL