  Edge-connectivity is a classic measure for reliability of a network in the
presence of edge failures. $k$-restricted edge-connectivity is one of the
refined indicators for fault tolerance of large networks. Matching preclusion
and conditional matching preclusion are two important measures for the
robustness of networks in edge fault scenario. In this paper, we show that the
DCell network $D_{k,n}$ is super-$\lambda$ for $k\geq2$ and $n\geq2$,
super-$\lambda_2$ for $k\geq3$ and $n\geq2$, or $k=2$ and $n=2$, and
super-$\lambda_3$ for $k\geq4$ and $n\geq3$. Moreover, as an application of
$k$-restricted edge-connectivity, we study the matching preclusion number and
conditional matching preclusion number, and characterize the corresponding
optimal solutions of $D_{k,n}$. In particular, we have shown that $D_{1,n}$ is
isomorphic to the $(n,k)$-star graph $S_{n+1,2}$ for $n\geq2$.
