Further combinatorial analysis of substar reliability in star networks

Hao Li and Eminjan Sabir ()
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Hao Li: Xinjiang University
Eminjan Sabir: Xinjiang University

Journal of Combinatorial Optimization, 2025, vol. 49, issue 5, No 9, 28 pages

Abstract: Abstract Substar reliability defined as the probability that a fault-free substar of a certain scale is still available in the star network $$S_n$$ S n when the occurrence of faults. The substar reliability is one of the most practical reliability measures because a user in the current star multiprocessors is given a certain substar for the execution of his/her program. Wu and Latifi(Inf. Sci. 178 (2008)) derived upper-bound on the substar reliability of $$S_n$$ S n by analysing the intersection of no more than three substars. Later, Li et al.(IEEE. Trans. Rel. 65 (2016)) derived lower-bound on the substar reliability of $$S_n$$ S n by considering the intersection of no more than four substars. In the paper, we further derive the upper- and lower bounds on the substar reliability of $$S_n$$ S n by taking into account the intersection of no more than five or four substars, respectively. At a result, we obtain more accurate value of the upper-bound on substar reliability of $$S_n$$ S n . The experimental study indicates that both the upper- and lower bounds are very close to approximate results especially for the low value of the node reliability.

Keywords: Substar reliability; Star networks; Probabilistic fault model; Principle of inclusion-exclusion (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01315-1

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