Dynamic tree algorithms

Annals of Applied Probability

Volumn 20, Issue 1, 2010, Pages 26-51

  Mohamed, Hanène ^a,b   Robert , Philippe ^a,c  

^a LABORATOIRE DES SCIENCES DU CLIMAT ET DE L ENVIRONNEMENT   (France)

^b UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

^c INRIA   (France)

Author keywords

Auto regressive processes; Capetanakis Tsybakov Mikhailov algorithm; Random access networks; Renewal theorems; Tree structures

Indexed keywords

EID: 76449087721     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/09-AAP617     Document Type: Article

References (18)

1. ALDOUS, D. J. (1987). Ultimate instability of exponential back-off protocol for acknowledgement-based transmission control of random access communication channels. IEEE Trans. Inform. Theory 33 219-223. MR880163
2. BERGER, T. (1981). The Poisson multiple-access conflict resolution problem. In Multi-User Communication Systems (G. Longo, ed.). CISM Courses and Lectures 265 1-28. Springer, New York.
3. BERTOIN, J. (2001). Homogeneous fragmentation processes. Probab. Theory Related Fields 121 301-318. MR1867425
4. BERTSEKAS, D. and GALLAGER, R. (1991). Data Networks, 2nd ed. Prentice-Hall, Upper Saddle River, NJ.
5. BOXMA, O.J, DENTENEER, D. and RESING, J. (2003). Delay models for contention trees in closed populations. Performance Evaluation 53 169-185.
6. CAPETANAKIS, J. I. (1979). Tree algorithms for packet broadcast channels. IEEE Trans. Inform. Theory 25 505-515. MR545006
7. EPHREMIDES, A. and HAJEK, B. (1998). Information theory and communication networks: An unconsummated union. IEEE Trans. Inform. Theory 44 2416-2434. MR1658779
8. FAYOLLE, G., FLAJOLET, P. and HOFRI, M. (1986). On a functional equation arising in the analysis of a protocol for a multi-access broadcast channel. Adv. in Appl. Probab. 18 441-472. MR840103
9. FAYOLLE, G., FLAJOLET, P., HOFRI, M. and JACQUET, P. (1985). Analysis of a stack algorithm for random multiple-access communication. IEEE Trans. Inform. Theory 31 244-254. MR793094
10. FLAJOLET, P., GOURDON, X and DUMAS, P. (1995). Mellin transforms and asymptotics: armonic sums. Theoret. Comput. Sci. 144 3-58. MR1337752
11. JANSSEN, A.J.E.M. and DEJONG, M. J. M. (2000). Analysis of contention tree algorithms. IEEE Trans. Inform. Theory 46 217-2.
12. MASSEY, J. L. (1981). Collision-resolution algorithms and random access communication. In
13. Multi-User Communication Systems (G. Longo, ed.). CISM Courses and Lectures 265 73-140. Springer, New York.
14. MATHYS, P. and FLAJOLET, P. (1985). Q-ary collision resolution algorithms in random-access systems with free or blocked channel access. IEEE Trans. Inform. Theory 31 217-243. MR793093
15. MOHAMED, H. and ROBERT, P. (2005). A probabilistic analysis of some tree algorithms. Ann. Appl. Probab. 15 2445-2471. MR2187300
16. TSYBAKOV, B.S. and MIKHAǏLOV, V. A. (1978). Free synchronous packet access in a broadcast channel with feedback. Probl. Inf. Transm. 14 32-59. MR538901
17. TSYBAKOV, B.S. and VVEDENSKAYA, N. D. (1981). Random multiple-access stack algorithm. Probl. Inf. Transm. 16 230-243.
18. VAN VELTHOVEN, J., VAN HOUDT, B and BLONDIA, C. (2006). On the probability of abandonment in queues with limited sojourn and waiting times. Oper. Res. Lett. 34 333-338. MR2204347