Appearances of the Birthday Paradox in High Performance Computing

TL;DR

This paper analyzes how random assignment in high performance computing can cause more resource contention than expected, similar to the birthday paradox, impacting system performance.

Contribution

It provides an elementary statistical analysis revealing the birthday paradox phenomenon in processor cache and network port mappings.

Findings

Random assignment increases resource contention beyond initial expectations.

Contention due to coincidences affects system performance.

The analysis highlights the importance of considering probabilistic effects in HPC design.

Abstract

We give an elementary statistical analysis of two High Performance Computing issues, processor cache mapping and network port mapping. In both cases we find that, as in the birthday paradox, random assignment leads to more frequent coincidences than one expects a priori. Since these correspond to contention for limited resources, this phenomenon has important consequences for performance.