A universal model for mobility and migration patterns

Transcription

1 A universal model for mobility and migration patterns US migrations image by Mauro Martino Filippo Simini 1,2,3, Marta C. González 4, Amos Maritan 2, and Albert-László Barabási 1 1 Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA. 2 Dipartimento di Fisica G. Galilei, Università di Padova, CNISM and INFN, Padova, Italy. 3 Institute of Physics, Budapest University of Technology and Economics Budafoki út 8, Budapest, H-1111, Hungary 4 MIT - Department of Civil and Environmental Engineering, Cambridge, MA.

2 Question: Is it possible to predict the number of commuters between two locations? Boston New York City

3 History 1940 George K. Zipf Human Behaviour and the Principle of Least Effort "It is human nature to want the greatest outcome for the least amount of work." friction of distance

4 History 1950 Gravity Models Large cities: more opportunities & services. The closer the cities, the greater the attraction. Analogy with Gravitation mass population

5 History It turns out that the law of gravitation for masses doesn t work so well with people... How this was fixed adding parameters this is the Gravity Model changing the function

6 GM Unsatisfactory aspects of the. 1) Lack of rigorous derivation 2) Does not have a universal form 3) Requires previous data to fit the parameters 4) Analytical inconsistencies

7 Can we do better? Idea The commuting fluxes reflect human behavior in the choice of the employment. commuting fluxes job selection

8 the Radiation model! An individual looks for a better job outside his home county.! The individual accepts the job in the closest county in which benefits are higher than in his home county.! ? ! We capture the benefits of a potential employment opportunity with a single number that represents a combination of income, working hours, conditions...! The fluxes are generated by repeating this process for each commuter, assigning new benefits in each case.!

9 the Radiation model: analytical results m population in the origin. n m n population in the destination. s s population in all locations closer than the destination P(1 m, n, s ) Pm($) probability of one trip given m, n and s. probability that the maximum benefit offered by m companies is $. P(1 m, n, s ) = $ Pm($) Ps(< $) Pn(> $)

10 the Radiation model: analytical results m population in the origin. n m n population in the destination. s s population in all locations closer than the destination P(1 m, n, s ) Pm($) probability of one trip given m, n and s. probability that the maximum benefit offered by m companies is $. P(1 m, n, s ) = mn (m + s) (m + n + s)

11 the Radiation model: analytical results! T ij m i P (1 m i,n j,s ij ) m 2 i n j (m i + s ij )(m i + n j + s ij )

12 the Radiation model: performances Census data commuting fluxes from New York County 10 >10,000 INCREASING NUMBER OF TRAVELERS

13 commuting fluxes from New York County Census Gravity Radiation

14 commuting fluxes from New York County Census Gravity Radiation

15 commuting fluxes with more than 600 travelers in New York Sate Census Gravity Radiation

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17 the Radiation model: performances fraction of trips between two locations at distance r. fraction of trips toward a location with population n. pairwise comparison, Radiation vs. Data Commuting

18 the Radiation model: performances Hourly Trips

19 the Radiation model: performances Migrations

20 the Radiation model: performances Freight

21 the Radiation model: performances Phone calls

22 Conclusions Population is the key factor in determining mobility fluxes, and not distance.

23 Conclusions! The radiation model predicts a hidden self-similarity in the mobility data.! Probability to observe a trip from a location with population m to a destination in the region beyond a population s from the origin.! p s (>s m) = m m + s

24 Conclusions! The radiation model can easily adsorb improvements.! Home-field advantage in job searching:! Equivalent to add! / n jobs employment opportunities in the home county! p s (>s m, ) = (m + ) (m + )+s (m + ) λ(m + ) s λs

25 Conclusions The radiation model can easily adsorb improvements.

26 thank you!