Analysis of contention tree algorithms

The Capetanakis-Tsybakov-Mikhailov (1978, 1979) contention tree algorithm provides an efficient scheme for multiaccessing a broadcast-communication channel. This paper studies the statistical properties of multiple-access contention tree algorithms with ternary feedback for an arbitrary degree of node. The particular quantities under investigation are the number of levels required for a random contender to have successful access, as well as the number of levels and the number of contention frames required to provide access for all contenders. Through classical Fourier analysis approximations to both the average and the variance are calculated as a function of the number of contenders n. It is demonstrated that in the limit of large n these quantities do not converge to a fixed mode, but contain an oscillating term as well.

[1]  Edward G. Tiedemann,et al.  Multiple access reservation , 1999 .

[2]  Philippe Flajolet,et al.  Q -ary collision resolution algorithms in random-access systems with free or blocked channel access , 1985, IEEE Trans. Inf. Theory.

[3]  Wenxin Xu.  Distributed queueing random access protocols for a broadcast channel , 1991, SIGCOMM 1993.

[4]  M.J.M. de Jong,et al.  Analytic properties of contention tree-algorithms , 1998, 1998 Information Theory Workshop (Cat. No.98EX131).

[5]  J. Capetanakis,et al.  Generalized TDMA: The Multi-Accessing Tree Protocol , 1979, IEEE Trans. Commun..

[6]  John Capetanakis,et al.  Tree algorithms for packet broadcast channels , 1979, IEEE Trans. Inf. Theory.

[7]  Gabriel Ruget,et al.  Some Tools for the Study of Channel-Sharing Algorithms , 1981 .

[8]  Michael A. Kaplan,et al.  Analytic properties of multiple-access trees , 1985, IEEE Trans. Inf. Theory.

[9]  Norman M. Abramson,et al.  Development of the ALOHANET , 1985, IEEE Trans. Inf. Theory.

[10]  Wenxin Xu,et al.  A Distributed Queueing Random Access Protocol for a Broadcast Channel , 1993, SIGCOMM.

[11]  Robert G. Gallager,et al.  A perspective on multiaccess channels , 1984, IEEE Trans. Inf. Theory.

[12]  GUY FAYOLLE,et al.  Analysis of a stack algorithm for random multiple-access communication , 1985, IEEE Trans. Inf. Theory.

[13]  B. Hajek,et al.  On the delay in a multiple access system with large propagation delay , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[14]  Toby Berger,et al.  Delay analysis of interval-searching contention resolution algorithms , 1985, IEEE Trans. Inf. Theory.

[15]  J. Massey.  Collision-Resolution Algorithms and Random-Access Communications , 1981 .

[16]  L. Kleinrock,et al.  Packet Switching in Radio Channels: Part I - Carrier Sense Multiple-Access Modes and Their Throughput-Delay Characteristics , 1975, IEEE Transactions on Communications.

[17]  Toby Berger,et al.  The Poisson Multiple-Access Conflict Resolution Problem , 1981 .