# 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
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

• 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

### 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.