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] It is also found that during rush hours the traffic network can have several metastable states of different network sizes and the alternate between these states.[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.

A method to identify functional clusters of spatial-temporal streets that represent fluent traffic flow in a city has been developed by Serok et al.[9] G. Li et al.[10] developed a method to design an optimal two layer transportation network in a city.

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, q
  
    
      
        c
      
    
    {\displaystyle c}
  
,  during the day for working days and weekends. High q
  
    
      
        c
      
    
    {\displaystyle c}
  
 means good global traffic while low q
  
    
      
        c
      
    
    {\displaystyle c}
  
 is bad traffic—during rush hour.
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, q, during the day for working days and weekends. High q means good global traffic while low q is bad traffic—during rush hour.

Flow patterns of traffic

River-like patterns of traffic flow in urban areas in large cities during rush hours and non rush hours have been studied by Yohei Shida et al.[11]

See also

References

  1. ^ Barthelemy, Marc (2010). "Spatial Networks". Physics Reports. 499 (1–3): 1–101. arXiv:1010.0302. Bibcode:2011PhR...499....1B. doi:10.1016/j.physrep.2010.11.002. S2CID 4627021.
  2. ^ Helbing, D (2001). "Traffic and related self-driven many-particle systems". Reviews of Modern Physics. 73 (4): 1067–1141. arXiv:cond-mat/0012229. Bibcode:2001RvMP...73.1067H. doi:10.1103/RevModPhys.73.1067. S2CID 119330488.
  3. ^ S., Kerner, Boris (2004). The Physics of Traffic : Empirical Freeway Pattern Features, Engineering Applications, and Theory. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN 9783540409861. OCLC 840291446.
  4. ^ Wolf, D E; Schreckenberg, M; Bachem, A (June 1996). Traffic and Granular Flow. Traffic and Granular Flow. WORLD SCIENTIFIC. pp. 1–394. doi:10.1142/9789814531276. ISBN 9789810226350.
  5. ^ Li, Daqing; Fu, Bowen; Wang, Yunpeng; Lu, Guangquan; Berezin, Yehiel; Stanley, H. Eugene; Havlin, Shlomo (2015-01-20). "Percolation transition in dynamical traffic network with evolving critical bottlenecks". Proceedings of the National Academy of Sciences. 112 (3): 669–672. Bibcode:2015PNAS..112..669L. doi:10.1073/pnas.1419185112. ISSN 0027-8424. PMC 4311803. PMID 25552558.
  6. ^ 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)
  7. ^ G. Zeng, J. Gao, L. Shekhtman, S. Guo, W. Lv, J. Wu, H. Liu, O. Levy, D. Li, ... (2020). "Multiple metastable network states in urban traffic". Proceedings of the National Academy of Sciences. 117 (30): 17528–17534. doi:10.1073/pnas.1907493117. PMC 7395445. PMID 32661171.CS1 maint: multiple names: authors list (link)
  8. ^ 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)
  9. ^ Nimrod Serok, Orr Levy, Shlomo Havlin, Efrat Blumenfeld-Lieberthal (2019). "Unveiling the inter-relations between the urban streets network and its dynamic traffic flows: Planning implication". SAGE Publications. 46 (7): 1362.CS1 maint: multiple names: authors list (link)
  10. ^ G. Li, S.D.S. Reis, A.A. Moreira, S. Havlin, H.E. Stanley, J.S. Andrade Jr. (2010). "Towards Design Principles for Optimal Transport Networks". Phys. Rev. Lett. 104 (1): 018701. arXiv:0908.3869. Bibcode:2010PhRvL.104a8701L. doi:10.1103/PhysRevLett.104.018701. PMID 20366398. S2CID 119177807.CS1 maint: multiple names: authors list (link)
  11. ^ Y. Shida, H. Takayasu, S. Havlin, M. Takayasu (2020). "Universal scaling laws of collective human flow patterns in urban regions". Scientific Reports. 10 (1): 21405. doi:10.1038/s41598-020-77163-2. PMC 7722863. PMID 33293581.CS1 maint: multiple names: authors list (link)