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.^{[3]}^{[4]}^{[5]}
Recently a real transport network of Beijing was studied using network approach and percolation theory.
The research showed that one can characterize the quality of 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 represent the velocity below which one can travel in a large fraction of city network. The method is able to identify repetitive traffic bottlenecks.
^{[6]}
Critical exponents characterizing the cluster size distribution of good traffic are similar to those of percolation theory.^{[7]}
An empirical study regarding the size distribution of traffic jams has been performed recently by Zhang et al. ^{[8]} They found an approximate universal power law for the jam sizes distribution.
Fig. 1: Percolation of traffic networks in a typical day in Beijing.
^S., Kerner, Boris (2004). The Physics of Traffic : Empirical Freeway Pattern Features, Engineering Applications, and Theory. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN9783540409861. OCLC840291446.
^Wolf, D E; Schreckenberg, M; Bachem, A (June 1996). Traffic and Granular Flow. Traffic and Granular Flow. WORLD SCIENTIFIC. p. 1. doi:10.1142/9789814531276. ISBN9789810226350.
^Switch between critical percolation modes in city traffic dynamics
G Zeng, D Li, S Guo, L Gao, Z Gao, HE Stanley, S Havlin
Proceedings of the National Academy of Sciences 116 (1), 23-28 (2019)
Scale-free resilience of real traffic jams
^Scale-free resilience of real traffic jams
Limiao Zhang, Guanwen Zeng, Daqing Li, Hai-Jun Huang, H Eugene Stanley, Shlomo Havlin
Proceedings of the National Academy of Sciences 116(18), 8673-8678 (2019)