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.