The Conditional Reliability Evaluation of Data Center Network BCDC

As the number of servers in a data center network (DCN) increases, the probability of server failures is significantly increased. Traditional connectivity is an important metric to measure the reliability of DCN. However, the traditional connectivity of a DCN based on the condition of arbitrary faulty servers is generally lower. Therefore, it is important to increase the connectivity of a DCN by adding some limited conditions for the faulty server set. As a result, $g$-restricted connectivity and $h$-extra connectivity, which are two crucial subjects for a DCN's ability to tolerate faulty servers, were proposed in the literature. In this paper, we study the $g$-restricted connectivity and $h$-extra connectivity of a new server-centric DCN, called BCDC, based on crossed cube with excellent performance. We prove that the $g$-restricted connectivity of BCDC is 4 for $n=3$ and $2n+g(n-2)-2$ for $n\geq 4$, where $0\leq g\leq n-3$, and the $h$-extra connectivity of BCDC is 4 for $n=3$ and $2n+h(n-2)-2$ for $n\geq 4$, where $0\leq h\leq n-3$.