skip to main content
10.1145/1146381.1146398acmconferencesArticle/Chapter ViewAbstractPublication PagespodcConference Proceedingsconference-collections
Article

Adversarial queuing on the multiple-access channel

Published: 23 July 2006 Publication History

Abstract

We consider broadcasting on the multiple-access channel when packets are injected continuously. Multiple-access channel is a synchronous system with the properties that a single transmission at a round delivers the message to all nodes, while multiple simultaneous transmissions result in a conflict which prevents delivering messages to any among the recipients. The traditional approach to dynamic broadcasting has been concerned with stability of protocols under suitable stochastic assumptions about injection rates. We study deterministic protocols competing against adversaries restricted by injection rate and burstiness of traffic. Stability means that the number of packets in queues is bounded by a constant in any execution, for a given number of stations, protocol, and adversary. Strong stability denotes the property that the number of queued packets is proportional to the burstiness of traffic, that is, the maximum number of packets an adversary may inject simultaneously. There are three natural classes of protocols we consider. The weakest acknowledgement-based protocols have a station rely on its local clock and on a feedback from the channel during its own attempts of transmissions. Full-sensing protocols allow a station to rely on a global clock and to store the history of all the previous successes/failures of transmissions in the course of an execution. A station running an adaptive protocol can rely on a global clock, may add control bits to be piggybacked on messages, and may store the complete history of the feedback from the channel during an execution. It turns out that there is no adaptive broadcast protocol stable for the injection rate λ = 1 for the multiple-access channel with at least n ≥ 4 stations, even when collision detection is available. We show that a simple full-sensing protocol is universally stable, which means it can handle any constant injection rate λ ‹ 1 in a stable manner. A more involved full-sensing protocol is shown to be both universally stable and strongly-stable for injection rate ρ (n) ≤ 1over>d lg2 n, where d>0 is a sufficiently large constant and n is the number of stations. We show that there is an acknowledgement-based protocol that is strongly stable for injection rate ρ(n)≤ 1<over>d lg2 n, for a sufficiently large constant d0. Regarding the stability of acknowledgement-based protocols, we show that no such a protocol is stable for injection rate ρ(n)> 2<over>1+lg n. This implies that there are no universally stable acknowledgement-based protocols. We show that when collision detection is available, then a simple full-sensing protocol is both universally stable and strongly stable for injection rate ρ(n)≤ 1<over>2 lgn. As a complementary fact, we prove that no adaptive protocol for a channel with collision detection can be strongly stable for the injection rate that satisfies ρ (n) = ω (1<over>log n). This shows that the protocol we give is optimal with respect to injection rates it handles in a strongly stable manner.

References

[1]
N. Abramson, Development of the Alohanet, IEEE Transactions on Information Theory, 31 (1985) 119 -- 123.
[2]
W. Aiello, E. Kushilevitz, R. Ostrovsky, and A. Rosén, Adaptive packet routing for bursty adversarial traffic, Journal of Computer and System Sciences, 60 (2000) 482 -- 509.
[3]
M. Andrews, B. Awerbuch, A. Fernández, T. Leighton, Z. Liu, and J. Kleinberg., Universal-stability results and performance bounds for greedy contention-resolution protocols, Journal of the ACM, 48 (2001) 39 -- 69.
[4]
R. Bar-Yehuda, O. Goldreich, and A. Itai, Efficient emulation of single-hop radio network with collision detection on multi-hop radio network with no collision detection, Distributed Computing, 5 (1991) 67 -- 72.
[5]
M.A. Bender, M. Farach-Colton, S. He, B.C. Kuszmaul, and C.E. Leiserson, Adversarial contention resolution for simple channels, in Proceedings, 17th ACM Symposium on Parallel Algorithms (SPAA), 2005, pp. 325 -- 332.
[6]
A. Borodin, J.M. Kleinberg, P. Raghavan, M. Sudan, and D.P. Williamson, Adversarial queuing theory, Journal of the ACM, 48 (2001) 13 -- 38.
[7]
B.S. Chlebus, L. Gąsieniec, D.R. Kowalski, and T. Radzik, On the wake-up problem in radio networks, in Proceedings, 32nd International Colloquium on Automata, Languages and Programming (ICALP), 2005, LNCS 3580, pp. 347 -- 359.
[8]
B.S. Chlebus, K. Gołąb, and D.R. Kowalski, Broadcasting spanning forests on a multiple-access channel, Theory of Computing Systems, 36 (2003) 711 -- 733.
[9]
B.S. Chlebus, and D.R. Kowalski, A better wake-up in radio networks, in Proc., 23rd ACM Symposium on Principles of Distributed Computing (PODC), 2004, pp. 266 -- 274.
[10]
B.S. Chlebus, D.R. Kowalski, and A. Lingas, The do-all problem in broadcast networks, in Proceedings, 20th ACM Symposium on Principles of Distributed Computing (PODC), 2001, pp. 117 -- 126.
[11]
M. Chrobak, L. Gąsieniec, and D.R. Kowalski, The wake-up problem in multi-hop radio networks, in Proc., 15th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2004, pp. 985 -- 993.
[12]
R.G. Gallager, A perspective on multiaccess channels, IEEE Transactions on Information Theory, 31 (1985) 124 -- 142.
[13]
D. Gamarnik, Stability of contents-adaptive and noncontents-adaptive packet routing policies in adversarial queuing networks, SIAM Journal on Computing, 32 (2003) 371 -- 385.
[14]
L. Gąsieniec, A. Pelc, and D. Peleg, The wakeup problem in synchronous broadcast systems, SIAM Journal on Discrete Mathematics, 14 (2001) 207--222.
[15]
A. Goel, Stability of networks and protocols in the adversarial queuing model for packet routing, Networks, 37 (2001) 219 -- 224.
[16]
L.A. Goldberg, M. Jerrum, S. Kannan and M. Paterson, A bound on the capacity of backoff and acknowledgement-based protocols, SIAM Journal on Computing, 33 (2004) 313 -- 331.
[17]
L.A. Goldberg, P. MacKenzie, M. Paterson, and A. Srinivasan, Contention resolution with constant expected delay, Journal of the ACM, 47 (2000) 1048--1096.
[18]
A.G. Greenberg, and S. Winograd, A lower bound on the time needed in the worst case to resolve conflicts deterministically in multiple-access channels, Journal of the ACM, 32 (1985) 589 -- 596.
[19]
J. Håstad, T. Leighton, and B. Rogoff, Analysis of backoff protocols for multiple-access channels, SIAM Journal on Computing, 25 (1996) 740 -- 774.
[20]
P. Indyk, Explicit constructions of selectors and related combinatorial structures, with applications, in Proc., 13th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2002, pp. 697 -- 704.
[21]
T. Jurdziński, M. Kutyłowski, and J. Zatopiański, Efficient algorithms for leader election in radio networks, in Proceedings, 21th ACM Symposium on Principles of Distributed Computing (PODC), 2002, pp. 51 -- 57.
[22]
T. Jurdziński, and G. Stachowiak, Probabilistic algorithms for the wakeup problem in single-hop radio networks, in Proceedings, 13th Annual International Symposium on Algorithms and Computation (ISAAC), LNCS 2518, 2002, pp. 535 -- 549.
[23]
F.P. Kelly, "Reversibility and Stochastic Networks," 1979, Wiley.
[24]
L. Kleinrock, "Queuing Systems," 1975, Wiley.
[25]
J. Komlós, and A.G. Greenberg, An asymptotically noncontents-adaptive algorithm for conflict resolution in multiple-access channels, IEEE Transactions on Information Theory, 31 (1985) 303 -- 306.
[26]
D.R. Kowalski, On selection problem in radio networks, in Proceedings, 24th ACM Symposium on Principles of Distributed Computing (PODC), 2005, pp. 158 -- 166.
[27]
E. Kushilevitz, and Y. Mansour, An Ω(D log (N/D)) lower bound for broadcast in radio networks, SIAM Journal on Computing, 27 (1998) 702 -- 712.
[28]
N.A. Lynch, Distributed Algorithms, Morgan Kaufmann, 1996.
[29]
R.M. Metcalfe, and D.R. Boggs, Ethernet: distributed packet switching for local computer networks, Communications of the ACM, 19 (1976) 395 -- 404.
[30]
P. Raghavan, and E. Upfal, Stochastic contention resolution with short delays, SIAM Journal on Computing, 28 (1998) 709 -- 719.
[31]
J. Walrand, "An Introduction to Queuing Networks," 1988, Prentice Hall.
[32]
D.E. Willard, Log-logarithmic selection resolution protocols in a multiple-access channel, SIAM Journal on Computing, 15 (1986) 468 -- 477.

Cited By

View all
  • (2021)Windowed backoff algorithms for WiFi: theory and performance under batched arrivalsDistributed Computing10.1007/s00446-021-00403-9Online publication date: 13-Sep-2021
  • (2020)Contention Resolution with Message DeadlinesProceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3350755.3400239(23-35)Online publication date: 6-Jul-2020
  • (2018)Scaling Exponential BackoffJournal of the ACM10.1145/327676966:1(1-33)Online publication date: 12-Dec-2018
  • Show More Cited By

Index Terms

  1. Adversarial queuing on the multiple-access channel

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    PODC '06: Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
    July 2006
    230 pages
    ISBN:1595933840
    DOI:10.1145/1146381
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Sponsors

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 23 July 2006

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. adversarial queuing
    2. broadcast
    3. continuous packet injection
    4. multiple-access channel
    5. stability

    Qualifiers

    • Article

    Conference

    PODC06

    Acceptance Rates

    Overall Acceptance Rate 740 of 2,477 submissions, 30%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)3
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 14 Feb 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2021)Windowed backoff algorithms for WiFi: theory and performance under batched arrivalsDistributed Computing10.1007/s00446-021-00403-9Online publication date: 13-Sep-2021
    • (2020)Contention Resolution with Message DeadlinesProceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3350755.3400239(23-35)Online publication date: 6-Jul-2020
    • (2018)Scaling Exponential BackoffJournal of the ACM10.1145/327676966:1(1-33)Online publication date: 12-Dec-2018
    • (2018)SadeDistributed Computing10.1007/s00446-017-0307-131:3(241-254)Online publication date: 1-Jun-2018
    • (2017)Is Our Model for Contention Resolution Wrong?Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3087556.3087584(183-194)Online publication date: 24-Jul-2017
    • (2017)Adaptive packet scheduling over a wireless channel under constrained jammingTheoretical Computer Science10.1016/j.tcs.2017.06.020692:C(72-89)Online publication date: 5-Sep-2017
    • (2016)How to scale exponential backoffProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884482(636-654)Online publication date: 10-Jan-2016
    • (2016)Contention resolution with log-logstar channel accessesProceedings of the forty-eighth annual ACM symposium on Theory of Computing10.1145/2897518.2897655(499-508)Online publication date: 19-Jun-2016
    • (2016)Bounded information dissemination in multi-channel wireless networksJournal of Combinatorial Optimization10.1007/s10878-014-9804-331:3(996-1012)Online publication date: 1-Apr-2016
    • (2016)Information exchange with collision detection on multiple channelsJournal of Combinatorial Optimization10.1007/s10878-014-9713-531:1(118-135)Online publication date: 1-Jan-2016
    • Show More Cited By

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media