The emerging edge-hub-cloud paradigm has enabled the development of innovative latency-critical cyber-physical applications in the edge-cloud continuum. However, this paradigm poses multiple challenges due to the heterogeneity of the devices at the edge of the network, their limited computational, communication, and energy capacities, as well as their different sensing and actuating capabilities. To address these issues, we propose an optimal scheduling approach to minimize the overall latency of a workflow application in an edge-hub-cloud cyber-physical system. We consider multiple edge devices cooperating with a hub device and a cloud server. All devices feature heterogeneous multicore processors and various sensing, actuating, or other specialized capabilities. We present a comprehensive formulation based on continuous-time mixed integer linear programming, encapsulating multiple constraints often overlooked by existing approaches. We conduct a comparative experimental evaluation between our method and a well-established and effective scheduling heuristic, which we enhanced to consider the constraints of the specific problem. The results reveal that our technique outperforms the heuristic, achieving an average latency improvement of 13.54% in a relevant real-world use case, under varied system configurations. In addition, the results demonstrate the scalability of our method under synthetic workflows of varying sizes, attaining a 33.03% average latency decrease compared to the heuristic.

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