在多任务调度中解决非抢占性：确定性和随机性世界中的最优算法
On Resolving Non-Preemptivity in Multitask Scheduling: An Optimal Algorithm in Deterministic and Stochastic Worlds
AI总结：
本文提出NP-SRPT算法，用于在确定性和随机性环境下优化多任务调度的响应时间，证明其在不同模型下的渐近最优性。
摘要：
多处理器系统上多任务作业的高效调度随着计算系统的迅速扩展而变得越来越关键。这种挑战被称为多处理器多任务调度（MPMS），对于优化云计算和深度学习等领域应用的性能和可扩展性至关重要。在本文中，我们研究了在确定性和随机性模型下MPMS问题，其中每个作业由多个任务组成，只有当所有任务完成时才能完成。我们引入了NP-SRPT，这是SRPT算法的一种非抢占性变体，旨在适应具有非抢占性任务的场景。我们的算法在最小化响应时间方面实现了竞争比为ln α + β + 1，其中α代表最大作业工作量与最小作业工作量的比率，β捕捉了最大非抢占性任务工作量与最小作业工作量的比率。我们进一步证明，当处理器数量固定时，该竞争比是阶最优的。对于随机的M/G/N系统，我们证明NP-SRPT在交通强度接近1时实现渐近最优的平均响应时间，假设任务大小分布具有有限支持。此外，渐近最优性在无限任务大小分布下也成立，包括标准的M/M/N模型。最后，我们将分析扩展到未知作业大小的场景，证明非抢占性适应的M-Gittins和M-SERPT策略在广泛作业大小分布中分别实现渐近最优和近最优。实验结果验证了NP-SRPT的有效性。
英文摘要：
The efficient scheduling of multi-task jobs across multiprocessor systems has become increasingly critical with the rapid expansion of computational systems. This challenge, known as Multiprocessor Multitask Scheduling (MPMS), is essential for optimizing the performance and scalability of applications in fields such as cloud computing and deep learning. In this paper, we study the MPMS problem under both deterministic and stochastic models, where each job is composed of multiple tasks and can only be completed when all its tasks are finished. We introduce $\mathsf{NP}$-$\mathsf{SRPT}$, a non-preemptive variant of the SRPT algorithm, designed to accommodate scenarios with non-preemptive tasks. Our algorithm achieves a competitive ratio of $\ln α+ β+ 1$ for minimizing response time, where $α$ represents the ratio of the largest to the smallest job workload, and $β$ captures the ratio of the largest non-preemptive task workload to the smallest job workload. We further establish that this competitive ratio is order-optimal when the number of processors is fixed. For the stochastic $\mathsf{M}$/$\mathsf{G}$/$\mathsf{N}$ system, we prove that $\mathsf{NP}$-$\mathsf{SRPT}$ achieves asymptotically optimal mean response time as the traffic intensity approaches $1$, assuming task size distribution with finite support. Moreover, the asymptotic optimality extends to infinite task size distributions under mild probabilistic assumptions, including the standard $\mathsf{M}$/$\mathsf{M}$/$\mathsf{N}$ model. Finally, we extend the analysis to the setting of unknown job sizes, proving that non-preemptive adaptations of the $\mathsf{M\text{-}Gittins}$ and $\mathsf{M\text{-}SERPT}$ policies achieve asymptotic optimality and near-optimality, respectively, for a broad class of job size distributions. Experimental results validate the effectiveness of $\mathsf{NP}$-$\mathsf{SRPT}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
