Criticality and Tolerance in Injection Timing in Cup-Stacking Method for Collective Communication

Today’s parallel computers definitely employ a crucial component of interconnection network, in which message packets are used for interchanging information. One of the challenging issues of the network is congestion control. We have proposed a novel method of Cup-Stacking to solve the problem. The Cup-Stacking method splits a large packet into slices, re-shapes the slice by adjusting possible parameters, and injects the slices with an appropriate interval. The method is successful in reducing congestion by pre-scheduling the packet injection timing. However, as a practical system does not always guarantee precise packet timing, we should discuss robustness issues on the delays from the scheduled timing to show the practical usefulness of the proposed method (Cup-Stacking). This paper addresses criticality and tolerance issues for evaluating the delays from the scheduled timing and, then, proposes two evaluation indices to represent expected performance degradation: delay criticality index (DCI) and delay tolerance measure (DTM). The former represents the impact of the injection delay of individual packet and the latter shows the expected performance degradation. Evaluation results in the Cup-Stacking method reveal preferable relationships between DCI and DTM values. Furthermore, the results lead us to a practical guideline in applying the Cup-Stacking method.