Stability of the multiple-access channel under maximum broadcast loads

Bogdan S. Chlebus, Dariusz R. Kowalski, Mariusz A. Rokicki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We investigate deterministic broadcasting on multiple-access channels in the framework of adversarial queuing. A protocol is stable when the number of packets stays bounded, and it is fair when each packet is eventually broadcast. We address the question if stability and fairness can be achieved against the maximum injection rate of one packet per round. We study three natural classes of protocols: acknowledgment based, full sensing and fully adaptive. We show that no adaptive protocol can be both stable and fair for the system of at least two stations against leaky-bucket adversaries, while this is achievable against window adversaries. We study in detail small systems of exactly two and three stations attached to the channel. For two stations, we show that bounded latency can be achieved by a full-sensing protocol, while there is no stable acknowledgment-based protocol. For three stations, we show that bounded latency can be achieved by an adaptive protocol, while there is no stable full-sensing protocol. We develop an adaptive protocol that is stable for any number of stations against leaky-bucket adversaries. The protocol has Ο(n 2) packets queued simultaneously, which is proved to be best possible as an upper bound. We show that protocols that do not use queue sizes at stations in an effective way or are greedy by having stations with nonempty queues withhold the channel cannot be stable in systems of at least four stations.

Original languageEnglish (US)
Title of host publicationStabilization, Safety, and Security of Distributed Systems - 9th International Symposium, SSS 2007, Proceedings
Pages124-138
Number of pages15
StatePublished - Dec 1 2007
Externally publishedYes
Event9th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2007 - Paris, France
Duration: Nov 14 2007Nov 16 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4838 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2007
CountryFrance
CityParis
Period11/14/0711/16/07

Keywords

  • Adversarial queuing
  • Deterministic broadcast
  • Fairness
  • Latency
  • Multiple-access channel
  • Stability

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Chlebus, B. S., Kowalski, D. R., & Rokicki, M. A. (2007). Stability of the multiple-access channel under maximum broadcast loads. In Stabilization, Safety, and Security of Distributed Systems - 9th International Symposium, SSS 2007, Proceedings (pp. 124-138). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4838 LNCS).