On subcube dependability in a hypercube

Jong Kim, Chits R. Das

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

4 Scopus citations

Abstract

In this paper, we present an analytical model for computing the dependability of hypercube systems. The model, referred to as task-based dependability (TBD), is developed under the assumption that a task needs at least an m-cube (m < n) in an n-cube for its execution. Two probabilistic terms are required for computing this dependability. The first is the probability of any x nodes working out of 2n nodes. The second term is a conditional probability that at least a connected m-cube exists among those x working nodes. This term is computed using a recursive expression. Two dependability measures, reliability and availability, are analyzed in this paper. A combinatorial enumeration is used in the reliability analysis, and a machine repairman model is used in the availability analysis to find the first probability. The machine repairman model is modified to capture imperfect coverage and imprecise repair. The TBD model is also extended to find multitask dependability. Numerical results are presented for n-cubes with different task requirements and are validated through extensive simulation. It is observed that an m-cube requirement is highly restrictive compared to the simple 2m-connected node requirement.

Original languageEnglish (US)
Title of host publicationProceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991
PublisherAssociation for Computing Machinery, Inc
Pages111-119
Number of pages9
ISBN (Print)0897913922, 9780897913928
Publication statusPublished - Apr 2 1991
Event1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991 - San Diego, United States
Duration: May 21 1991May 24 1991

Publication series

NameProceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991

Other

Other1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991
CountryUnited States
CitySan Diego
Period5/21/915/24/91

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Software

Cite this

Kim, J., & Das, C. R. (1991). On subcube dependability in a hypercube. In Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991 (pp. 111-119). (Proceedings of the 1991 ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 1991). Association for Computing Machinery, Inc.