Cloud storage exploiting overlay networks is considered to be a scalable and autonomous architecture. While this technology can ensure the security of storage service, it requires addressing the “server breakdown” problem, which may arise due to malicious attacks on servers and mechanical troubles of servers. In existing literature, an overlay network based on bimodal degree distribution was proposed to achieve high connectivity to combat these two types of server breakdown. However, it cannot ensure the high connectivity against physical network disruption that removes numerous nodes from overlay network. To deal with this issue, in this paper, we propose a physical network aware overlay network, in which the neighboring nodes are connected with one another in the overlay. Moreover, the numerical analysis indicates that the proposed system considerably outperforms the conventional system in terms of service availability.