The economics of flash vs. disk storage is driving HPC centers to incorporate faster solid-state burst buffers into the storage hierarchy in exchange for smaller parallel file system (PFS) bandwidth. In systems with an underprovisioned PFS, avoiding I/O contention at the PFS level will become crucial to achieving high computational efficiency. In this paper, we propose novel batch job scheduling techniques that reduce such contention by integrating I/O awareness into scheduling policies such as EASY backfilling. We model the available bandwidth of links between each level of the storage hierarchy (i.e., burst buffers, I/O network, and PFS), and our I/O-aware schedulers use this model to avoid contention at any level in the hierarchy. We integrate our approach into Flux, a next-generation resource and job management framework, and evaluate the effectiveness and computational costs of our I/O-aware scheduling. Our results show that by reducing I/O contention for underprovisioned PFSes, our solution reduces job performance variability by up to 33% and decreases I/O-related utilization losses by up to 21%, which ultimately increases the amount of science performed by scientific workloads.

The Torrance-Sparrow model for calculating bidirectional reflection functions contains a geometrical attenuation factor to account for shadowing and occlusions in a hypothetical distribution of grooves on a rough surface. Using an efficient table-based method for determining the shadows and occlusions, we calculate the geometric attenuation factor for surfaces defined by a specific table of bump heights.Diffuse and glossy specular reflection of the environment can be handled in a unified manner by using an integral of the bidirectional reflection function times the environmental illumination, over the hemisphere of solid angle above a surface. We present a method of estimating the integral, by expanding the bidirectional reflection coefficient in spherical harmonics, and show how the coefficients in this expansion can be determined efficiently by reorganizing our geometric attenuation calculation.