Message transport characteristics in communication networks

TL;DR

This paper investigates message transport dynamics on a 1D ring network with hubs, revealing critical congestion behavior, noise characteristics, and the effects of network modifications on message travel times.

Contribution

It introduces a detailed analysis of message transport on a ring network, highlighting congestion thresholds, noise spectra, and the impact of assortative connections on inter-arrival times.

Findings

Messages accumulate after a critical deposition rate.

Load time-series exhibits 1/f noise.

Travel time distribution is bimodal with congestion and decongestion peaks.

Abstract

We study message transport on a $1-d$ ring of nodes and randomly distributed hubs. Messages are deposited on the network at a constant rate. When the rate at which messages are deposited on the lattice is very high, messages start accumulating after a critical time and the average load per node starts increasing. The power-spectrum of the load time-series shows $1/f$ like noise similar to the scenario of the Internet traffic. The inter-arrival time distribution of messages for the $1-d$ ring network shows stretched exponential behavior, which crosses over to power-law behavior if assortative connections are added to the hubs. The distribution of travel times in a related double ring geometry is shown to be bimodal with one peak corresponding to initial congestion and another peak to later decongestion.