From Massively Parallel Algorithms and Fluctuating Time Horizons to Non-equilibrium Surface Growth

TL;DR

This paper analyzes a massively parallel discrete-event simulation algorithm by modeling its time horizon as a non-equilibrium surface, revealing its scalability and connection to surface growth physics.

Contribution

It establishes a link between the algorithm's efficiency and surface growth models, demonstrating asymptotic scalability through theoretical and simulation methods.

Findings

The steady-state surface follows the Edwards-Wilkinson model.

The algorithm's efficiency is proportional to the density of local minima.

The approach confirms the algorithm's asymptotic scalability.

Abstract

We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium surface. Monte Carlo simulations and a coarse-grained approximation indicate that the macroscopic landscape in the steady state is governed by the Edwards-Wilkinson Hamiltonian. Since the efficiency of the algorithm corresponds to the density of local minima in the associated surface, our results imply that the algorithm is asymptotically scalable.