Analytical model for computing hypercube availability

Chitaranjan Das, Jong Kim

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

3 Citations (Scopus)

Abstract

An analytical model is presented for computing the availability of an n-dimensional hypercube. The model computes the probability of j connected working nodes in a hypercube by multiplying two probabilistic terms. The firsts term is the probability of x connected nodes (x ≥ j) working out of 2n fully connected nodes. This is obtained from the numerical solution of the well-known machine repairman model, modified to capture imperfect coverage and imprecise repair. The second term, which is the probability of having j connected nodes in a hypercube, is computed from an approximate model of the hypercube. The approximate model, in turn, is based on a decomposition principle, where an n-cube connectivity is computed from a two-cube base model using a recursive equation. The availability model studied here is known as a task-based availability, where a system remains operational as long as a task can be executed on the system. Analytical results for n-dimensional cubes are given for various task requirements. The model is validated by comparing the analytical results with those from simulation.

Original languageEnglish (US)
Title of host publicationDigest of Papers - FTCS (Fault-Tolerant Computing Symposium)
Editors Anon
PublisherPubl by IEEE
Pages530-537
Number of pages8
ISBN (Print)0818619597
StatePublished - 1989
EventNineteenth International Symposium on Fault-Tolerant Computing - Chicago, IL, USA
Duration: Jun 21 1989Jun 23 1989

Other

OtherNineteenth International Symposium on Fault-Tolerant Computing
CityChicago, IL, USA
Period6/21/896/23/89

Fingerprint

Analytical models
Availability
Repair
Decomposition

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture

Cite this

Das, C., & Kim, J. (1989). Analytical model for computing hypercube availability. In Anon (Ed.), Digest of Papers - FTCS (Fault-Tolerant Computing Symposium) (pp. 530-537). Publ by IEEE.
Das, Chitaranjan ; Kim, Jong. / Analytical model for computing hypercube availability. Digest of Papers - FTCS (Fault-Tolerant Computing Symposium). editor / Anon. Publ by IEEE, 1989. pp. 530-537
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Das, C & Kim, J 1989, Analytical model for computing hypercube availability. in Anon (ed.), Digest of Papers - FTCS (Fault-Tolerant Computing Symposium). Publ by IEEE, pp. 530-537, Nineteenth International Symposium on Fault-Tolerant Computing, Chicago, IL, USA, 6/21/89.

Analytical model for computing hypercube availability. / Das, Chitaranjan; Kim, Jong.

Digest of Papers - FTCS (Fault-Tolerant Computing Symposium). ed. / Anon. Publ by IEEE, 1989. p. 530-537.

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

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AB - An analytical model is presented for computing the availability of an n-dimensional hypercube. The model computes the probability of j connected working nodes in a hypercube by multiplying two probabilistic terms. The firsts term is the probability of x connected nodes (x ≥ j) working out of 2n fully connected nodes. This is obtained from the numerical solution of the well-known machine repairman model, modified to capture imperfect coverage and imprecise repair. The second term, which is the probability of having j connected nodes in a hypercube, is computed from an approximate model of the hypercube. The approximate model, in turn, is based on a decomposition principle, where an n-cube connectivity is computed from a two-cube base model using a recursive equation. The availability model studied here is known as a task-based availability, where a system remains operational as long as a task can be executed on the system. Analytical results for n-dimensional cubes are given for various task requirements. The model is validated by comparing the analytical results with those from simulation.

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Das C, Kim J. Analytical model for computing hypercube availability. In Anon, editor, Digest of Papers - FTCS (Fault-Tolerant Computing Symposium). Publ by IEEE. 1989. p. 530-537