Markov Chain Methods For Analyzing Complex Transport Networks

TL;DR

This paper introduces a Markov chain-based steady state theory for complex transport networks, enabling effective analysis, design, and fault tolerance assessment of various network types.

Contribution

It presents a unified Markov chain framework for analyzing complex transport networks, including directed and multi-layered systems, with applications in performance evaluation and fault tolerance.

Findings

Markov chains effectively model equilibrium states of transport networks.

Random walks provide meaningful Euclidean embeddings of network graphs.

The framework applies to directed and multi-network systems.

Abstract

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph representations of transport networks allowing for the effective network design, network performance evaluation, embedding, partitioning, and network fault tolerance analysis. Random walks embed graphs into Euclidean space in which distances and angles acquire a clear statistical interpretation. Being defined on the dual graph representations of transport networks random walks describe the equilibrium configurations of not random commodity flows on primary graphs. This theory unifies many network concepts into one framework and can also be elegantly extended to describe networks represented by directed graphs and multiple interacting networks.