Diagnosing the coexistence of Poissonity and self-similarity in memory workloads

Abstract

Accurately modeling the inter-arrival distribution is critical for synthesizing memory traces to evaluate performance. The intensity and complexity of memory accesses have increased greatly in modern applications. This motivates us to re-examine two fundamental issues: (1) Can the arrival process of memory accesses in modern workloads still be described as a Poisson process? (2) Do modern memory workloads present self-similarity? Via analyzing SPEC CPU2017, this paper demonstrates the coexistence of both Poissonity and self-similarity in modern memory workloads, which seems to reconcile the contradiction between Poisson and self-similar characteristics. Specifically, memory access intervals at a small time scale, such as milliseconds, approximately follow an exponential distribution and memory accesses are independent of each other. At such time scales, memory access series can be approximated by a Poisson process. For the aggregated process of memory access series at a large time scale, such as several minutes, the non-degenerate structures of the auto-correlation function show the presence of self-similarity in memory workloads. All Hurst parameters estimated are greater than 0.5, confirming the presence of self-similarity.