Designing optimal transport networks

TL;DR

This paper explores the optimal design of transport networks with added long-range links, revealing that a specific power-law exponent optimizes efficiency under cost constraints, supported by real-world data.

Contribution

It introduces a cost-constrained model for optimal transport networks and identifies the optimal exponent for link probability distribution, validated by empirical airport network data.

Findings

Optimal exponent for link probability is alpha=d+1 under cost constraints.

Cost constraints alter the optimal navigation strategies compared to unconstrained models.

Empirical data from US airports supports the theoretical optimal exponent.

Abstract

We investigate the optimal design of networks for a general transport system. Our network is built from a regular two-dimensional ($d=2$) square lattice to be improved by adding long-range connections (shortcuts) with probability $P_{ij} \sim r_{ij}^{-\alpha}$, where $r_{ij}$ is the Euclidean distance between sites $i$ and $j$, and $\alpha$ is a variable exponent. We introduce a cost constraint on the total length of the additional links and find optimal transport in the system for $\alpha=d+1$. Remarkably, this condition remains optimal, regardless of the strategy used for navigation, being based on local or global knowledge of the network structure, in sharp contrast with the results obtained for unconstrained navigation using global or local information, where the optimal conditions are $\alpha=0$ and $\alpha=d$, respectively. The validity of our theoretical results is supported by data on the US airport network, for which $\alpha\approx 3.0$ was recently found [Bianconi {\it et al.}, arXiv:0810.4412 (2008)].