Reliability Evaluation of DCell Networks

Recently, the reliability evaluation of data center network (DCN) is important to the design and operation of DCNs. Extra connectivity determination and faulty networks structure analysis are two significant aspects for the reliability evaluation of DCNs. The DCell network is suitable for a massive data centers with high network capacity by only using cheap switches. A k-dimensional DCell built with n-port switches, denoted by D-k,D-n, is an (n + k - 1)-regular graph. In this paper, we firstly prove that the extra-h connectivity of D-k,D-n for n >= 2, kappa(h)(D-k,D-n) = (k - 1)(h + 1) + n if k >= 2 and 0 <= h = n - 1, and kappa(h) (D-k,D-n) = (k - 1)(h + 1) + 2n - 2 if k >= n + 1 and n <= h <= 2n - 1, respectively. What's more, for any faulty node set F subset of V (D-k,D-n) with vertical bar F vertical bar <= kappa(h)(D-k,D-n) - 1, we obtain that there contains a large connected component in D-k,D-n - F, and the rest of small connected components have not more than h nodes in total if k >= 2 and 0 <= h <= n - 1 (resp. k >= n + 1 and n <= h <= 2n - 1). Our result can provide a proper measure for the reliability evaluation of the DCell network when it is used to model the topological structure of a large-scale DCN.