The extra connectivity, extra conditional diagnosability and t/k-diagnosability of the data center network DCell

Connectivity and diagnosability are two important metrics in evaluating the fault tolerability of a network. The g-extra connectivity and the g-extra conditional diagnosability are both defined under the restraint that every component of the network removing a faulty vertex set has at least g + 1 fault-free vertices. The t / k -diagnosability is an outstanding diagnosis strategy, in which the identified faulty vertex set is allowed to contain at most k fault-free vertices. As a well-known model for a large-scale data center network (DCN) with a server-centric structure, the m-dimensional DCell with n-port switches and t m , n servers, D m , n , has many desirable properties. In this paper, we first investigate the g-extra connectivity of D m , n for 0 ≤ g ≤ n − 1 . Based on this, we establish the g-extra conditional diagnosability of D m , n under the PMC model for 0 ≤ g ≤ n − 1 . Finally, we evaluate the t / k -diagnosability of D m , n under the PMC model for 1 ≤ k ≤ n − 1 .