Performance Bounds for Modeling NUMA Architectures

Scalable, multi-processor, computing systems in which memories are logically shared but physically distributed exhibit non-uniform memory access (NUMA) times. Modeling such systems presents special difficulties. Closed queuing networks, in which some servers provide exponentially distributed service and others provide deterministic (constant) service, offer the desired level of model representation, but such mixed networks remain analytically intractable. This paper shows that the throughput of any such mixed network is necessarily bounded below by the throughput of a purely exponential-server network and bounded above by the throughput of a purely deterministic-server network. In particular, replacing any deterministic server by an exponential server of the same mean will not increase throughput. Since fast techniques exist for solving purely exponential and purely deterministic networks, performance bounds are at hand.