The recent deployment of Cyber-Physical Systems (CPS) has emerged as the most promising approach to provide an extensive computational capability for processing and controlling physical entities, which relies on reliable data exchanges among machines in CPS. However, for CPS exploiting public network infrastructures, links in CPS may suffer from a variety of vulnerabilities to harm real-time data exchanges. Providing network resilience for real-time communications consequently becomes the most critical requirement in CPS. Considering the support of multiple communication paths in state-of-the-art network infrastructures, in this paper, we develop a mathematical resource-optimal network resilience design for CPS. In our design, duplicates of timing sensitive data are simultaneously forwarded via multiple communication paths. Therefore, timing constraints are violated only if all communication paths fail to forward data to the destination on time. By analyzing the relationship among the probability of timing constraint violation, the time domain resource allocation, and the number of communication paths (the spatial domain resource allocation), our design leads to the minimum resource usage to support real-time data exchanges in CPS. Our mathematical resource-optimal design solves the most challenging issue of unreliable data exchanges in CPS in the most efficient fashion, to consequently support the maximum number of machines in CPS.
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