Understanding memory performance in multi-core platforms is a prerequisite to perform optimizations. To this end, this paper presents analytical models based on Stochastic Reward Nets (SRNs) to model and evaluate the memory performance of Non-Uniform Memory Access (NUMA) multi-core architectures. The approach considers the details of the architecture and first proposes a monolithic SRN model that evaluates the memory performance in terms of the mean memory response time. Since the monolithic model incurs a state space explosion with an increasing number of cores and memory controllers, two approximate models are presented that are able to evaluate large-scale NUMA architectures. The SRNs are validated through measurements on two NUMA multi-core platforms, a 64-core AMD Opteron server and a 72-core Intel system. The results demonstrate the ability of the proposed models to accurately compute the mean memory response time on NUMA architectures. The results also provide valuable information that runtime systems and application designers can use to optimize execution of parallel applications on such architectures.

了解多核平台中的内存性能是执行优化的先决条件。为此，本文提出了基于随机奖励网（SRN）的分析模型，以对非统一内存访问（NUMA）多核体系结构的内存性能进行建模和评估。该方法考虑了体系结构的细节，首先提出了一个单片SRN模型，该模型根据平均内存响应时间来评估内存性能。由于单片模型会导致状态空间爆炸，其中内核和存储控制器的数量会增加，因此提出了两个近似模型，它们能够评估大规模NUMA架构。通过在两个NUMA多核平台，一个64核AMD Opteron服务器和一个72核Intel系统上进行测量来验证SRN。结果证明了所提出的模型能够准确计算NUMA架构上的平均内存响应时间。结果还提供了有价值的信息，运行时系统和应用程序设计人员可以使用这些信息来优化此类体系结构上并行应用程序的执行。