$t/t$ -Diagnosability and $t/k$ -Diagnosability for Augmented Cube Networks

Diagnosability is an important parameter for evaluating the reliability of multiprocessor systems. t/t-diagnosability and t/k-diagnosability are both new indexes for measuring the reliability of a system. An n-dimensional augmented cube network (AQ
_n
) is a variant of an n-dimensional hypercube network. In this paper, we first prove that an n-dimensional augmented cube network is (4n - 8)/(4n - 8)-diagnosable, which implies that the t/t-diagnosability of AQ
_n
is approximately two times larger than its classical t-diagnosability. Some useful properties of AQ
_n
not reported by previous studies are proposed. By employing these new properties, we prove that AQ
_n
is t/k-diagnosable, which implies that the t/k-diagnosability is approximately (k + 1) times larger than 2n - 1, i.e., the t-diagnosability of AQ
_n
, where t = 2(k + 1)n - ((3(k + 1)(k + 2))/2) + 1, k (4n/9) - (13/9), and n > 5.