This work studies fixed priority (FP) scheduling of real-time jobs with end-to-end deadlines in a distributed system. Specifically, given a multi-stage pipeline with multiple heterogeneous resources of the same type at each stage, the problem is to assign priorities to a set of real-time jobs with different release times to access a resource at each stage of the pipeline subject to the end-to-end deadline constraints. Note, in such a system, jobs may compete with different sets of jobs at different stages of the pipeline depending on the job-to-resource mapping. To this end, following are the two major contributions of this work. We show that an OPA-compatible schedulability test based on the delay composition algebra can be constructed, which we then use with an optimal priority assignment algorithm to compute a priority ordering. Further, we establish the versatility of pairwise priority assignment in such a multi-stage multi-resource system, compared to a total priority ordering. In particular, we show that a pairwise priority assignment may be feasible even if a priority ordering does not exist. We propose an integer linear programming formulation and a scalable heuristic to compute a pairwise priority assignment. We also show through simulation experiments that the proposed approaches can be used for the holistic scheduling of real-time jobs in edge computing systems.

翻译：本文研究分布式系统中具有端到端截止期限的实时作业的固定优先级调度问题。具体而言，给定一个包含多个异构资源的流水线，且每个阶段存在多个同类资源，问题在于如何为一组具有不同释放时间的实时作业分配优先级，以使其在满足端到端截止期限约束的条件下访问流水线各阶段的资源。注意到，在此类系统中，作业在不同阶段可能与不同的作业集合竞争，其竞争关系取决于作业与资源的映射方式。为此，本文提出以下两项主要贡献：首先，我们证明可以构建一种基于延迟合成代数的、与OPA兼容的可调度性检验方法，并将其与最优优先级分配算法结合，以计算优先级排序；其次，我们论证了在此类多阶段多资源系统中，成对优先级分配相较于全局优先级排序的通用性。特别地，我们证明即使不存在全局优先级排序，成对优先级分配仍可能是可行的。为此，我们提出了一种整数线性规划模型及可扩展的启发式算法来计算成对优先级分配。仿真实验表明，所提方法可有效用于边缘计算系统中实时作业的整体调度。