Random Walks in Local Dynamics of Network Losses

TL;DR

This paper models data losses in network nodes using a novel random walk approach, revealing critical transitions and non-Markovian correlations at the threshold of network congestion.

Contribution

It introduces a new random walk model for network losses with unique boundary conditions and analyzes critical behavior and correlations at the transition point.

Findings

Loss rate exhibits a sharp transition at a critical data arrival rate.

At the critical point, loss rate fluctuations become very strong.

Loss rate shows non-Markovian power-law correlations in time.

Abstract

We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt transition from exponentially small to finite losses as the data arrival rate increases. The critical point is characterized by strong fluctuations of the loss rate. Although we consider the packet arrival being a Markovian process, the loss rate exhibits non-Markovian power-law correlations in time at the critical point.