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

Distributed, Parallel, and Cluster Computing;Computational Physics