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
Hot locations: 1 Central Railway Station
2 Municipal Square
3 Finance & Trade Zone
4 South Railway Station
5 International Airport
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

- 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
$min\sum_{t-1}^h|\mathbf{S}_{i,j}^{(t)}-\mathbf{P}_{i,j}\times\mathbf{B}^{(t)}|$
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
M. Gonzalez, C. Hidalgo, and A. Barabasi, ``Understanding Individual Human Mobility Patterns", Nature, 453:779--782 (2008).
C. Peng, X. Jin, K. Wong, M. Shi, and P. Lio', ``Collective Human Mobility Pattern from Taxi Trips in Urban Area", under review.