| Summary: | The revolution that Industrial Control Systems are undergoing is reshaping the traditional network management and it is introducing new challenges. After the advent of network virtualization, an enhanced level of automation has been required to cope with the safety-critical mission of industrial systems and strict requirements for end-to-end latency. In the literature, there have been attempts to automatically solve two strictly interconnected problems for the management of virtual industrial networks: the Virtual Network Function embedding and the time-sensitive flow scheduling problems. However, dealing with these problems separately can lead to unoptimized results, or in the worst case to situations where the latency requirements cannot be satisfied because of a poorly chosen function embedding. In light of these motivations, this paper proposes a formal approach to jointly solve the two problems through an Optimization Satisfiability Modulo Theories formulation. This choice also allows combining two vital features: a formal guarantee of the solution correctness and optimization targeting the minimization of the end-to-end delay for flow scheduling. The feasibility of the proposed approach has been validated by implementing a prototype framework and experimentally testing it on realistic use cases.
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