Scaling in transportation networks

Transcription

1 Scaling in transportation networks

2 Acknowledgments Marc Barthelemy Camille Roth RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014)

3 Motivation What we understand about transportation networks Topological properties Geometrical properties Evolution in time RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014)

4 Motivation What we understand about transportation networks Topological properties Geometrical properties Evolution in time Issue Networks do not grown in empty space Mutual influence between substrate and network RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014)

5 Motivation What we understand about transportation networks Issue Topological properties Geometrical properties Evolution in time Questions Networks do not grown in empty space Mutual influence between substrate and network (1) Link between network properties and the underlying country/city? (2) Are subways scaled down railways? RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014)

6 RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014) Theoretical Framework Cost-benefit analysis

7 RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014) Theoretical Framework Cost-benefit analysis Benefits

8 RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014) Theoretical Framework Cost-benefit analysis Benefits Costs (maintenance)

9 RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e (2014) Theoretical Framework Cost-benefit analysis Steady state Benefits Costs (maintenance)

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11 Subway Framework Fare Passengers

12 Subway Framework Fare Maintenance costs Passengers Network length

13 Subway Framework Fare Maintenance costs Maintenance costs Passengers Network length Number of stations

14 Subway Estimate the ridership People using the subway population density coverage

15 Subway Estimate the ridership People using the subway population density coverage (Human constraints)

16 Subway Estimate the ridership People using the subway population density coverage (Human constraints)

17 Subway Estimate the ridership Linear Fit

18 Subway Interstation distance

19 Subway Interstation distance

20 Subway Interstation distance For a reasonably designed network

21 Subway Interstation distance For a reasonably designed network

22 Subway Length and number of stations 10 3 Linear fit

23 Subway Interstation distance Using the previous equations and we find

24 Subway Interstation distance Using the previous equations and we find increases with

25 Subway Interstation distance Using the previous equations and we find increases with decreases with

26 Subway Interstation distance Using the previous equations and we find increases with decreases with Interstation length can be adjusted through the ticket fare subsidies

27 Subway Size of the system What determines the size of the subway?

28 Subway Size of the system What determines the size of the subway? fraction of wealth for public transports wealth (GDP) COST PER STATION (and 1 portion of line)

29 Subway Size of the system 10 3 Linear Fit

30 Railway Networks

31 Railway networks Framework kilometers travelled fare/km

32 Railway networks Framework kilometers travelled network length fare/km maintenance costs

33 Railway networks Length and number of stations If we assume the network links closest neighbouring cities surface area of the country interstation distance

34 Railway networks Length and number of stations If we assume the network links closest neighbouring cities surface area of the country interstation distance And thus

35 10 2 powerlaw fit Railway networks Length and number of stations

36 Railway networks Ridership In steady state

37 Railway networks Ridership In steady state Assuming that the typical trip length is

38 Railway networks Ridership Linear Fit

39 Railway networks Size What determines the size of a railway at a given time?

40 Railway networks Size What determines the size of a railway at a given time?

41 Railway networks Size 10 6 Linear Fit

42 Railway networks Size 10 6 Linear Fit United Arab emirates

43 Conclusion Results and perspective Better understanding of how the systems interact with the region they serve Common mechanisms seem to be at play during networks's evolution

44 Conclusion Results and perspective Better understanding of how the systems interact with the region they serve Common mechanisms seem to be at play during networks's evolution Subway and Railway behave differently, at different scales

45 Conclusion Results and perspective Better understanding of how the systems interact with the region they serve Common mechanisms seem to be at play during networks's evolution Subway and Railway behave differently, at different scales Could help building more realistic models with less exogeneous parameters

46 Conclusion Results and perspective Better understanding of how the systems interact with the region they serve Common mechanisms seem to be at play during networks's evolution Subway and Railway behave differently, at different scales Could help building more realistic models with less exogeneous parameters General notes All the relations have to be understood as average trends Good starting point for the study of particular cases

47 Conclusion Results and perspective Better understanding of how the systems interact with the region they serve Common mechanisms seem to be at play during networks's evolution Subway and Railway behave differently, at different scales Could help building more realistic models with less exogeneous parameters General notes All the relations have to be understood as average trends Good starting point for the study of particular cases Necessity of a model, data analysis is not enough

48 Quanturb: Marc Barthelemy Giulia Carra Riccardo Gallotti Thomas Louail Rémi