Spontaneous Resonances and the Coherent States of the Queuing Networks

TL;DR

This paper investigates a highly connected queuing network where time correlations persist even as the network size grows infinitely, resembling symmetry breaking phenomena in statistical mechanics, with load acting as an inverse temperature.

Contribution

It introduces a model of queuing networks exhibiting spontaneous resonances and persistent correlations, linking network dynamics to concepts from statistical physics.

Findings

Time correlations do not vanish in large networks.

The network exhibits symmetry-breaking-like behavior.

Average load functions as an inverse temperature parameter.

Abstract

We present an example of a highly connected closed network of servers, where the time correlations do not go to zero in the infinite volume limit. This phenomenon is similar to the continuous symmetry breaking at low temperatures in statistical mechanics. The role of the inverse temperature is played by the average load.