Double declined subnetwork reliability analysis in bubble-sort networks under node fault model

Abstract

The n-dimensional bubble-sort network $B_n$ is a competitive interconnection network that could be used to construct large-scale multiprocessor computer systems. Let p be the reliability of each node in $B_n$ and let $R_{n,n-2}\left(p\right)$ be the $B_{n-2}$-subnetwork reliability (i.e., double declined subnetwork reliability) in $B_n$ under the equiprobability node fault model. In this paper, the bounds on $R_{n,n-2}\left(p\right)$ are derived for $n\ge 4$, and an algorithm is given to further verify the accuracy of the lower and upper bounds. The MTTFs that maintain the healthy state of different numbers of disjoint $B_{n-2}$'s in $B_n$ under different partition patterns are calculated. Simulations are also carried out to verify the MTTFs. Both the theoretical result and the simulating result show that using the flexible partition pattern will make the network more reliable in the sense of double declined subnetwork availability.