Scaling in transportation networks
Acknowledgments Marc Barthelemy Camille Roth RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e102007 (2014)
Motivation What we understand about transportation networks Topological properties Geometrical properties Evolution in time RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e102007 (2014)
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): e102007 (2014)
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): e102007 (2014)
RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e102007 (2014) Theoretical Framework Cost-benefit analysis
RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e102007 (2014) Theoretical Framework Cost-benefit analysis Benefits
RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e102007 (2014) Theoretical Framework Cost-benefit analysis Benefits Costs (maintenance)
RL, C. Roth & M. Barthelemy, PLOS ONE 9(7): e102007 (2014) Theoretical Framework Cost-benefit analysis Steady state Benefits Costs (maintenance)
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Subway Framework Fare Passengers
Subway Framework Fare Maintenance costs Passengers Network length
Subway Framework Fare Maintenance costs Maintenance costs Passengers Network length Number of stations
Subway Estimate the ridership People using the subway population density coverage
Subway Estimate the ridership People using the subway population density coverage (Human constraints)
Subway Estimate the ridership People using the subway population density coverage (Human constraints)
Subway Estimate the ridership 10 10 Linear Fit 10 9 10 8 10 7 10 6 10 5 10 4 10 5 10 6
Subway Interstation distance
Subway Interstation distance
Subway Interstation distance For a reasonably designed network
Subway Interstation distance For a reasonably designed network
Subway Length and number of stations 10 3 Linear fit 10 2 10 1 10 0 10 1 10 2
Subway Interstation distance Using the previous equations and we find
Subway Interstation distance Using the previous equations and we find increases with
Subway Interstation distance Using the previous equations and we find increases with decreases with
Subway Interstation distance Using the previous equations and we find increases with decreases with Interstation length can be adjusted through the ticket fare subsidies
Subway Size of the system What determines the size of the subway?
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)
Subway Size of the system 10 3 Linear Fit 10 2 10 1 10 0 10 10 10 11 10 12 10 13
Railway Networks
Railway networks Framework kilometers travelled fare/km
Railway networks Framework kilometers travelled network length fare/km maintenance costs
Railway networks Length and number of stations If we assume the network links closest neighbouring cities surface area of the country interstation distance
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
10 2 powerlaw fit Railway networks Length and number of stations 10 1 10 0 10 1 10 2 10 3 10 4
Railway networks Ridership In steady state
Railway networks Ridership In steady state Assuming that the typical trip length is
Railway networks Ridership Linear Fit 10 11 10 10 10 9 10 3 10 4
Railway networks Size What determines the size of a railway at a given time?
Railway networks Size What determines the size of a railway at a given time?
Railway networks Size 10 6 Linear Fit 10 5 10 4 10 3 10 2 10 1 10 3 10 4 10 5 10 6 10 7 10 8
Railway networks Size 10 6 Linear Fit 10 5 10 4 10 3 10 2 United Arab emirates 10 1 10 3 10 4 10 5 10 6 10 7 10 8
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
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
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
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
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
Quanturb: Marc Barthelemy Giulia Carra Riccardo Gallotti Thomas Louail Rémi Louf @remilouf remi.louf@cea.fr www.notonebitsimpler.com www.quanturb.com