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A parallel program together with the parallel hardware it is running on isnot only a vehicle to solve numerical problems, it is also a complex systemwith interesting dynamical behavior: resynchronization and desynchronization ofparallel processes, propagating phases of idleness, and the peculiar effects ofnoise and system topology are just a few examples. We propose a physicaloscillator model (POM) to describe aspects of the dynamics of interactingparallel processes. Motivated by the well-known Kuramoto Model, a process withits regular compute-communicate cycles is modeled as an oscillator which iscoupled to other oscillators (processes) via an interaction potential. Insteadof a simple all-to-all connectivity, we employ a sparse topology matrix mappingthe communication structure and thus the inter-process dependencies of theprogram onto the oscillator model and propose two interaction potentials thatare suitable for different scenarios in parallel computing: resource-scalableand resource-bottlenecked applications. The former are not limited by aresource bottleneck such as memory bandwidth or network contention, while thelatter are. Unlike the original Kuramoto model, which has a periodic sinusoidalpotential that is attractive for small angles, our characteristic potentialsare always attractive for large angles and only differ in the short-distancebehavior. We show that the model with appropriate potentials can mimic thepropagation of delays and the synchronizing and desynchronizing behavior ofscalable and bottlenecked parallel programs, respectively.

Physical Oscillator Model for Supercomputing