Message Transfer in a Communication Network

TL;DR

This paper investigates message transfer dynamics in a 2D communication network with regular nodes and randomly placed hubs, revealing how hub density affects travel times and congestion states through statistical analysis.

Contribution

It introduces a detailed analysis of message transfer behavior, including the impact of hub density on travel times and congestion transitions, with novel insights into distribution patterns.

Findings

Average travel time exhibits q-exponential behavior with hub density.

Power-law tail in travel time distribution indicates rapid efficiency gains.

Congestion transition characterized by Gaussian and log-normal waiting time distributions.

Abstract

We study message transfer in a $2-d$ communication network of regular nodes and randomly distributed hubs. We study both single message transfer and multiple message transfer on the lattice. The average travel time for single messages travelling between source and target pairs of fixed separations shows $q-$exponential behaviour as a function of hub density with a characteristic power-law tail, indicating a rapid drop in the average travel time as a function of hub density. This power-law tail arises as a consequence of the log-normal distribution of travel times seen at high hub densities. When many messages travel on the lattice, a congestion-decongestion transition can be seen. The waiting times of messages in the congested phase show a Gaussian distribution, whereas the decongested phase shows a log-normal distribution. Thus, the congested or decongested behaviour is encrypted in the behaviour of the waiting time distributions.