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The traditional Internet architecture relies on the best-effort principle, which is not suitable for critical industrial Internet of Things (IIoT) applications such as healthcare systems with stringent quality-of-service (QoS) requirements. In this article, a software-defined network (SDN) based on an analytical parallel routing framework is proposed by using the massive processing power of a graphics processing unit (GPU) for dynamically optimizing multiconstrained QoS parameters in the IIoT. The framework considers three types of QoS applications for smart healthcare traffic: loss-sensitive, delay-sensitive, and jitter-sensitive. A QoS-enabled routing optimization problem is formulated as a max-flow min-cost problem, while a greedy heuristic that dispatches the path calculation task concurrently to the GPU for calculating optimal forwarding paths considering the QoS requirement of each flow is proposed. The results show …