The impact of one-way streets on the asymmetry of the shortest commuting routes

TL;DR

This study investigates how one-way streets cause asymmetry in shortest commuting routes, revealing that the asymmetry diminishes with longer routes and is linked to street network correlations.

Contribution

It introduces a quantitative analysis of route asymmetry caused by one-way streets and establishes a theoretical relationship between network structure and route asymmetry.

Findings

Asymmetry amplitude decays as a power law with route length

Fraction of one-way streets in shortest routes decreases with route length

The decay exponents are related through a semi-analytic relation

Abstract

On a daily commute, the shortest route from home to work rarely overlaps completely the shortest way back. We analyze this asymmetry for several cities and show that it exists even without traffic, due to a non-negligible fraction of one-way streets. For different pairs of origin-destination ($\rm OD$), we compute the log-ratio $r=\ln(\ell_{\rm D}/\ell_{\rm O})$, where $\ell_{\rm O}$ and $\ell_{\rm D}$ are the lengths of the shortest routes from $\rm O$ to $\rm D$ and from $\rm D$ to $\rm O$, respectively. While its average is zero, the amplitude of the fluctuations decays as a power law of the $\rm OD$ shortest path length, $r\sim \ell_{\rm O}^{-\beta}$. Similarly, the fraction of one-way streets in a shortest route also decays as $\ell_{\rm O}^{-\alpha}$. Based on semi-analytic arguments, we show that $\beta=(1+\alpha)/2$. Thus, the value of the exponent $\beta$ is related to correlations in the structure of the underlying street network.