Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-27T13:27:56.864Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of ${\textit{d}}$-ary tree algorithms with successive interference cancellation

Part of: Markov processes Algorithms - Computer Science Special processes

Published online by Cambridge University Press:  26 February 2024

Quirin Vogel Open the ORCID record for Quirin Vogel [Opens in a new window] ,
Yash Deshpande ,
Cedomir Stefanović  and
Wolfgang Kellerer
Quirin Vogel*
Affiliation:
Technical University of Munich
Yash Deshpande*
Affiliation:
Technical University of Munich
Cedomir Stefanović*
Affiliation:
Aalborg University
Wolfgang Kellerer*
Affiliation:
Technical University of Munich
*
*Postal address: Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Germany. Email address: quirin.vogel@tum.de
**Postal address: Lehrstuhl für Kommunikationsnnetze, School of Computation, Information and Technology, Technical University of Munich, Germany.
****Department of Electronic Systems, Aalborg University, 2450 København SV, Denmark. Email address: cs@es.aau.dk
**Postal address: Lehrstuhl für Kommunikationsnnetze, School of Computation, Information and Technology, Technical University of Munich, Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

We calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the results are new. We furthermore disprove the claim that only the binary tree maximizes throughput. Our method works with many observables and can be used as a blueprint for further analysis.

Keywords

Random accessasymptotic analysisfunctional equationsplitting algorithms

MSC classification

Primary: 68W40: Analysis of algorithms 60J85: Applications of branching processes
Secondary: 68W20: Randomized algorithms 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 31
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andreev, S. Pustovalov, E. and Turlikov, A. (2011). A practical tree algorithm with successive interference cancellation for delay reduction in IEEE 802.16 networks. In Analytical and Stochastic Modeling Techniques and Applications, eds M. Gribaudo, E. Sopin and I. Kochetkova, Springer, New York, pp. 301–315.Google Scholar
Bertsekas, D. and Gallager, R. (1992). Data Networks. Athena Scientific, Nashua, NH.Google Scholar
Capetanakis, J. (1979). Tree algorithms for packet broadcast channels. IEEE Trans. Inf. Theory, 25, 505–515.CrossRefGoogle Scholar
Conway, J. (1978). Functions of One Complex Variable. Springer, New York.CrossRefGoogle Scholar
Drmota, M. (2009). Random Trees: An Interplay between Combinatorics and Probability. Springer, New York.CrossRefGoogle Scholar
Deshpande, Y., Stefanović, C., Gürsu, H. and Kellerer, W. (2022). Corrections to ‘High-throughput random access using successive interference cancellation in a tree algorithm’. IEEE Trans. Inf. Theory 69, 1658–1659.CrossRefGoogle Scholar
Erdélyi, A. and Bateman, H. (1981). Higher Transcendental Functions, Vol. I. Robert E. Krieger Publishing Co., Inc., Malabar, FL.Google Scholar
Evseev, G. and Turlikov, A. (2007). Interrelation of characteristics of blocked RMA stack algorithms. Probl. Inf. Transm. 43, 344–352.CrossRefGoogle Scholar
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. Appl. Prob. 18, 441–472.CrossRefGoogle Scholar
Flajolet, P., Gourdon, X. and Dumas, P. (1995). Mellin transforms and asymptotics: Harmonic sums. Theoret. Comput. Sci. 144, 3–58.CrossRefGoogle Scholar
Holmgren, C. (2012). Novel characteristics of split trees by use of renewal theory. Electron. J. Prob. 17, 1–27.CrossRefGoogle Scholar
Janson, S. and Szpankowski, W. (1997). Analysis of an asymmetric leader election algorithm. Electron. J. Combinatorics 4, R17.CrossRefGoogle Scholar
Knuth, D. (1998), The Art of Computer Programming: Sorting and Searching, Vol. 3. Addison-Wesley Professional, Boston, MA.Google Scholar
König, W. and Kwofie, C. (2023). The throughput in multi-channel (slotted) ALOHA: Large deviations and analysis of bad events. Preprint, arXiv:2301.08180.Google Scholar
König, W. and Shafigh, H. (2022). Multi-channel ALOHA and CSMA medium-access protocols: Markovian description and large deviations. Preprint, arXiv:2212.08588.Google Scholar
Lawler, G. F. and Limic, V. (2010). Random Walk: A Modern Introduction (Cambridge Studies in Advanced Mathematics). Cambridge University Press.CrossRefGoogle Scholar
Massey, J. L. (1981). Collision-resolution algorithms and random-access communications. In Multi-User Communication Systems, ed. G. Longo, Springer, New York, pp. 73–137.CrossRefGoogle Scholar
Mathys, P. (1984). Analysis of random-access algorithms. PhD thesis, ETH Zurich.Google Scholar
Mathys, P. and Flajolet, P. (1985). q-ary collision resolution algorithms in random-access systems with free or blocked channel access. IEEE Trans. Inf. Theory 31, 217–243.CrossRefGoogle Scholar
Molle, M. and Shih, A. (1992). Computation of the packet delay in Massey’s standard and modified tree conflict resolution algorithms with gated access. Technical report CSRI-264. Computer Systems Research Institute, University of Toronto.Google Scholar
Navarro-Ortiz, J. et al. (2020). A survey on 5G usage scenarios and traffic models. IEEE Commun. Surv. Tutorials 22, 905–929.CrossRefGoogle Scholar
Peeters, G. and Van Houdt, B. (2009). On the maximum stable throughput of tree algorithms with free access. IEEE Trans. Inf. Theory 55, 5087–5099.CrossRefGoogle Scholar
Peeters, G. and Van Houdt, B. (2015). On the capacity of a random access channel with successive interference cancellation. In Proc. 2015 IEEE Int. Conf. Communication Workshop (ICCW), pp. 2051–2056.CrossRefGoogle Scholar
Stefanović, C., Deshpande, Y., Gürsu, H. and Kellerer, W. (2021). Tree-algorithms with multi-packet reception and successive interference cancellation. Preprint, arXiv:2108.00906.Google Scholar
Stefanović, C., Gürsu, H., Deshpande, Y. and Kellerer, W. (2020). Analysis of tree-algorithms with multi-packet reception. In Proc. GLOBECOM 2020–2020 IEEE Global Communications Conf., pp. 1–6.CrossRefGoogle Scholar
Wu, Y. et al. (2020). Massive access for future wireless communication systems. IEEE Wireless Commun. 27, 148–156.CrossRefGoogle Scholar
Yu, Y. and Giannakis, G. (2007). High-throughput random access using successive interference cancellation in a tree algorithm. IEEE Trans. Inf. Theory 53, 4628–4639.CrossRefGoogle Scholar