Periodic messages transfer data from sensors to actuators in cars, planes, and complex production machines. When considering a given routing, the unicast message starts at its source and goes over several dedicated resources to reach its destination. Such unicast message can be represented as a chain of point-to-point communications. Thus, the scheduling of the periodic chains is a principal problem in time-triggered Ethernet, like IEEE 802.1Qbv Time-Sensitive Networks. This paper studies a strongly NP-hard periodic scheduling problem with harmonic periods, task chains, and dedicated resources. We analyze the problem on several levels of generality and complexity and provide the corresponding proofs. We describe a solution methodology to find a feasible schedule that minimizes the chains' degeneracy related to start-to-end latency normalized in the number of periods. We use the local search with the first fit scheduling heuristic, which we warm-start with a constraint programming model. This notably improves the schedulability of instances with up to 100% utilization and thousands (and more) of tasks, with high-quality solutions found in minutes. An efficient constraint programming matheuristic significantly reduces the degeneracy of the found schedules even further. The method is evaluated on sets of industrial-, avionic-, and automotive-inspired instances.

翻译：在汽车、飞机及复杂生产设备中，周期性消息将数据从传感器传输至执行器。当考虑给定路由时，单播消息从其源节点出发，经过多个专用资源到达目标节点。此类单播消息可表示为点对点通信链。因此，周期性链的调度是时间触发以太网（如IEEE 802.1Qbv时间敏感网络）中的核心问题。本文研究具有调和周期、任务链和专用资源的强NP难周期性调度问题。我们在多个泛化层级和复杂度层面上分析该问题，并提供相应证明。我们提出一种求解方法，旨在寻找可行调度方案以最小化链的退化度——该指标通过起始至终端延迟按周期数归一化计算。我们采用首次适应调度启发式局部搜索，并通过约束规划模型进行热启动。该方法显著提升了利用率高达100%、任务量达数千（及以上）实例的可调度性，并在数分钟内获得高质量解。高效的约束规划数学启发式方法进一步显著降低了所得调度方案的退化度。本方法在工业、航空和汽车领域启发的实例集上进行了评估。