Synchronization of Conservative Parallel Discrete Event Simulations on a Small-World Network

TL;DR

This paper investigates how sparse long-range connections in small-world networks influence synchronization in parallel discrete event simulations, revealing a dependence on network shortest paths and surface growth dynamics.

Contribution

It introduces a model analyzing LVT synchronization in PDES on small-world networks, highlighting the role of long-range links and surface growth universality classes.

Findings

Synchronization depends on average shortest path length.

Surface growth analogy explains synchronization dynamics.

Critical exponents vary logarithmically with long-range link fraction.

Abstract

We examine the question of the influence of sparse long-range communications on the synchronization in parallel discrete event simulations (PDES). We build a model of the evolution of local virtual times (LVT) in a conservative algorithm including several choices of local links. All network realizations belong to the small-world network class. We find that synchronization depends on the average shortest path of the network. The time profile dynamics are similar to the surface profile growth, which helps to analyze synchronization effects using a statistical physics approach. Without long-range links of the nodes, the model belongs to the universality class of the Kardar--Parisi--Zhang equation for surface growth. We find that the critical exponents depend logarithmically on the fraction of long-range links. We present the results of simulations and discuss our observations.