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Collective Human Mobility in Urban Area

Urban traffic flow in one area or between any pair of locations can be approximated by a linear combination of three steady basis flows corresponding to commuting, business, and other purposes, with random perturbations.​​​

 Motivation

  • ​Knowledge of the urban human mobility is essential in traffic modeling for simulation, forecasting and control

  • The mobility pattern and the consequential traffic flow can also interact with the land use

  • Better understanding of human mobility can help to more easily control the spreading of contagious diseases by limiting the contact among individuals

  • Previous statistical inferences of urban human mobility mostly focus on the individual level, while this work analyzes the collective dynamics

​​​Basis Traffic Flows: The Constancy

  • Data: 1.58 million taxi trips

 

 Hot locations: 1 Central Railway Station
                                  2 Municipal Square
                                  3 Finance & Trade Zone
                                  4 South Railway Station
                                  5 International Airport
  • Notation:  
                     Si,j : traffic flow time series at location (i,j)
                           B(k): basis time series
                           Pi,j : traffic power for basis series at location (i,j)
  • Method: Non-negative matrix factorization, Linear optimization
Non-negative matrix factorization
  • Result: find three purpose-based categories for the trips
                           B1: commuting between home and workplace
                           B2​: Business traveling between two workplaces
                           B3​: trips from or to other places
 

Daily Traffic Power: The Variation

  • Data: the traffic power P from trips data S and three basis series B​
                      $min\sum_{t-1}^h|\mathbf{S}_{i,j}^{(t)}-\mathbf{P}_{i,j}\times\mathbf{B}^{(t)}|$
  • Notation: 
​                          a : the relative deviation
                          v : a vector of average traffic flow
                          r, n : parameters of binomial functions satisfying vk=rn
                          $\sigma$ : weight for the distribution components
  • Model: based on a series of binomial distributions
                       $D_{\alpha,v_k}(a)=\sum_{k=0}^{|a\times v_k|}\left(\begin{array}{c}n\\ k\end{array}\right)r^k(1-r)^{n-
 
}$
                          $D_\alpha(a)=\sum_k\sigma_kD_{\alpha,v_k}(a)$
  • Results: our model can describe the daily traffic deviation correctly

 

Travel Purposes vs. Land Use Map

 

References

  1. M. Gonzalez, C. Hidalgo, and A. Barabasi, ``Understanding Individual Human Mobility Patterns", Nature, 453:779--782 (2008).

  2. C. Peng, X. Jin, K. Wong, M. Shi, and P. Lio', ``Collective Human Mobility Pattern from Taxi Trips in Urban Area", under review.

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