Brief announcement: Probabilistic stabilization under probabilistic schedulers

Yukiko Yamauchi, Sébastien Tixeuil, Shuji Kijima, Masafumi Yamashita

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

3 Citations (Scopus)

Abstract

Motivation. Roughly speaking, a weakly stabilizing system S executed under a probabilistic scheduler ρ is probabilistically self-stabilizing, in the sense that any execution eventually reaches a legitimate execution with probability 1 [1-3]. Here ρ is a set of Markov chains, one of which is selected for S by an adversary to generate as its evolution an infinite activation sequence to execute S. The performance measure is the worst case expected convergence time τ S,M when S is executed under a Markov chain M ∈ ρ. Let τ S,ρ = sup Mερ τ S,M. Then S can be "comfortably" used as a probabilistically self-stabilizing system under ρ only if τ S,ρ < ∞. There are S and ρ such that τ S,ρ = ∞, despite that τ S,M < ∞ for any M ∈ ρ. Somewhat interesting is that, for some S, there is a randomised version S* of S such that τ S*,ρ < ∞, despite that τ S,ρ = ∞, i.e., randomization helps. This motivates a characterization of S that satisfies τ S*,ρ < ∞.

Original languageEnglish
Title of host publicationDistributed Computing - 26th International Symposium, DISC 2012, Proceedings
Pages413-414
Number of pages2
DOIs
Publication statusPublished - Nov 9 2012
Event26th International Symposium on Distributed Computing, DISC 2012 - Salvador, Brazil
Duration: Oct 16 2012Oct 18 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7611 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other26th International Symposium on Distributed Computing, DISC 2012
CountryBrazil
CitySalvador
Period10/16/1210/18/12

Fingerprint

Scheduler
Markov processes
Markov chain
Stabilization
S-system
Convergence Time
Randomisation
Performance Measures
Activation
Chemical activation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yamauchi, Y., Tixeuil, S., Kijima, S., & Yamashita, M. (2012). Brief announcement: Probabilistic stabilization under probabilistic schedulers. In Distributed Computing - 26th International Symposium, DISC 2012, Proceedings (pp. 413-414). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7611 LNCS). https://doi.org/10.1007/978-3-642-33651-5_34

Brief announcement : Probabilistic stabilization under probabilistic schedulers. / Yamauchi, Yukiko; Tixeuil, Sébastien; Kijima, Shuji; Yamashita, Masafumi.

Distributed Computing - 26th International Symposium, DISC 2012, Proceedings. 2012. p. 413-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7611 LNCS).

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

Yamauchi, Y, Tixeuil, S, Kijima, S & Yamashita, M 2012, Brief announcement: Probabilistic stabilization under probabilistic schedulers. in Distributed Computing - 26th International Symposium, DISC 2012, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7611 LNCS, pp. 413-414, 26th International Symposium on Distributed Computing, DISC 2012, Salvador, Brazil, 10/16/12. https://doi.org/10.1007/978-3-642-33651-5_34
Yamauchi Y, Tixeuil S, Kijima S, Yamashita M. Brief announcement: Probabilistic stabilization under probabilistic schedulers. In Distributed Computing - 26th International Symposium, DISC 2012, Proceedings. 2012. p. 413-414. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-33651-5_34
Yamauchi, Yukiko ; Tixeuil, Sébastien ; Kijima, Shuji ; Yamashita, Masafumi. / Brief announcement : Probabilistic stabilization under probabilistic schedulers. Distributed Computing - 26th International Symposium, DISC 2012, Proceedings. 2012. pp. 413-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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