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In a distributed computing environment, guaranteeing the hard deadline for real-time messages is essential to ensure schedulability of real-time tasks. Since capabilities of the shared resources for transmission are limited, e.g., the buffer size is limited on network devices, it becomes a challenge to design an effective and feasible resource sharing policy based on both the demand of real-time packet transmissions and the limitation of resource capabilities. We address this challenge in two cooperative mechanisms. First, we design a static routing algorithm to find forwarding paths for packets to guarantee their hard deadlines. The routing algorithm employs a validation-based backtracking procedure capable of deriving the demand of a set of real-time packets on each shared network device, and it checks whether this demand can be met on the device. Second, we design a packet scheduler that runs on network devices to transmit messages according to our routing requirements. We implement these mechanisms on virtual software-defined network (SDN) switches and evaluate them on real hardware in a local cluster to demonstrate the feasibility and effectiveness of our routing algorithm and packet scheduler.