Time sensitive networks (TSNs) enable deterministic real-time communication over Ethernet networks. According to IEEE 802.1Qbv standards, TSN switches use gates between queues and their corresponding egress ports to facilitate timing-deterministic communications. Management of switch resources, such as queues, has a significant impact on the schedulability of real-time flows. In this paper, we look into the theoretical foundation of queue management in TSN switches. We prove that the queue assignment problem for real-time flows on time sensitive networks under static priority scheduling is NP-hard in the strong sense, even if the number of queues per port is 3. Then we formulate the problem as a satisfiability modulo theories (SMT) specification. Besides, we propose a worst case response time analysis and a fast heuristic algorithms by eliminating scheduling conflicts. Experiments with randomly generated workload demonstrate the effectiveness of our algorithms for queue assignment of real-time flows.

时间敏感网络（TSN）支持通过以太网进行确定性的实时通信。根据IEEE 802.1Qbv标准，TSN交换机在队列及其相应的出口之间使用门来促进时序确定性通信。交换机资源（例如队列）的管理对实时流的可调度性具有重大影响。在本文中，我们研究了TSN交换机中队列管理的理论基础。我们证明，即使每个端口的队列数为3，静态优先级调度下对时间敏感的网络上实时流的队列分配问题也具有NP-hard的强烈意义，然后将该问题表示为可满足性模理论（SMT）规范。除了，通过消除调度冲突，我们提出了最坏情况下的响应时间分析和快速启发式算法。随机生成的工作负载的实验证明了我们的算法对实时流的队列分配的有效性。