# Transport network

A transport network, or transportation network is a realisation of a spatial network, describing a structure which permits either vehicular movement or flow of some commodity.[1] Examples include but are not limited to road networks, railways, air routes, pipelines, aqueducts, and power lines.

## Methods

Transport network analysis is used to determine the flow of vehicles (or people) through a transport network, typically using mathematical graph theory. It may combine different modes of transport, for example, walking and car, to model multi-modal journeys. Transport network analysis falls within the field of transport engineering. Traffic has been studied extensively using statistical physics methods.[2][3][4] Recently a real transport network of Beijing was studied using a network approach and percolation theory. The research showed that one can characterize the quality of global traffic in a city at each time in the day using percolation threshold, see Fig. 1. In recent articles, percolation theory has been applied to study traffic congestion in a city. The quality of the global traffic in a city at a given time is by a single parameter, the percolation critical threshold. The critical threshold represents the velocity below which one can travel in a large fraction of city network. The method is able to identify repetitive traffic bottlenecks. [5] Critical exponents characterizing the cluster size distribution of good traffic are similar to those of percolation theory.[6]

An empirical study regarding the size distribution of traffic jams has been performed recently by Zhang et al. [7] They found an approximate universal power law for the jam sizes distribution.

Fig. 1: Percolation of traffic networks in a typical day in Beijing. A Shows the high speed clusters. In B one can see the clusters at the critical threshold, where the giant component breaks. C Shows the low speed case where one can reach the whole city. In D, one can see the percolation behavior of the largest (green) and second largest (orange) components as a function of relative speed. E Shows the critical threshold, ${\displaystyle qc}$, during the day for working days and weekends. High ${\displaystyle qc}$ means good global traffic while low ${\displaystyle qc}$ is bad traffic--during rush hour.