class 16: individual mobility and transportation networks prof. albert-lászló barabási prof....
TRANSCRIPT
Class 16: Individual Mobility and Transportation Networks
Prof. Albert-László BarabásiProf. Marta Gonzalez
Network Science: Nobility 2015
Prof. Boleslaw Szymanski
600 million passenger cars worldwide (roughly one car per eleven people). 250 million passenger registered cars in the US. 806 million cars and light trucks on the road in 2007.
Worldwide Flights 4.8 billion passengers 2014 Average trip length per passenger 1,393 km
Worldwide Ground Trips
~588 billion trips per year~Average trip distance 25km
Image: D. Brockmann (NWU)
(c) Nonhub connectors (green), provincial hubs (yellow), and connector hubs (brown) in the worldwide air transportation network
What can we learn from roads?
6
Different Centrality Measures of Streets in Venice
1. Closeness,2. Betweenness centrality,3. Straightness, 4. Information
Closeness.Closeness measures to what extent a certain node is near all the other nodes in a system along the shortest path, more formally the inverse of cumulative distance required to reach from that node to all other nodes.
Betweenness centrality Betweenness centrality is equal to the number of shortest paths from all vertices to all others that pass through that node
Straightness.Straightness centrality measures the efficiency in the communication between two nodes in a system that increases when there is less deviation of their shortest path from the virtual straight line.
P. Crucitti et al.Centrality measuresin spatial networks of urban streets. Phys. Rev.E, 73:036125, 2006.
Finding and evaluating community structure in networks, M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004).
Betweenness centrality is an indicator of a node's centrality in a network. It is equal to the number of shortest paths from all vertices to all others that pass through that node.
1. Calculate betweenness scores for all edges in thenetwork.2. Find the edge with the highest score and remove itfrom the network.3. Recalculate betweenness for all remaining edges.4. Repeat from step 2.
eii, the fraction of all edges in the network that link vertices in community i to vertices in this community
which represent the fraction of edges that connect vertices incommunity i to vertices in community j.
(in random structures )
Famous Newman Modularity metric Q compares the number ofin-community edges to the edges in a random graph with the samenumber of nodes.
9
Betweeness Centrality of road in the City of Dresden
S. Lammer, B. Gehlsen, and D. Helbing. Scaling laws in the spatial structure of urban road networks. Physica A, 363:89, 2006.
10(a) Location of commercial and service activities (red dots); (b) Kernel density estima-tion (KDE) (c) Street global betweenness (d) KDE of (bC)
Street vs. Betweenness and commercial activity
E. Strano at alEnv. And Plann. B: Planning and Design, 36:450 { 465, 2009.
• Quantify?• Validate?• Applications?
90% of US population own mobile phones (2014)
Mobile Phone Data (Basic Info)
Regularity of the most common location by time of the day (average overmobile phone users)
Number of different locations visitedby time of the day (average overmobile phone users)
Mobile Phone Data (Basic Info)
Song, Qu, Blumm, Barabasi, Science 327,108(2010)
Data in Two Metropolitan Areas
360,000 Mobile Phone Users892 Towers 680,000 Mobile Phone Users
700 Census Tracts
Understanding Road Usage Patterns in Urban AreasWith Records of Mobile Calls
P. Wang
From phone Data to t-OD
GPS Probes
A. Zoomed Neighborhood
B. GPS reads(7.5 per sq.meter)
C. GPS connections
D. Estimated Travel Time: Mon 8am
Validation of Travel times with GPS probe vehicles
α = 0.15, β =4
BPR function (Bureau of Public Roads function measures congestion on the link
VOC = Volatile Organic Compounds
PCC = Pesrson’s Correlation Coefficient
P(V)~ e^(-V/ν)
ν = 414
ν =259
[veh/hour]
Distribution of Traffic Flow (Quantify)
Traffic Flow V
Pollution as Volatile Organic Compounds
1.6% of sources produce 60% of volume in a road
Fraction of Flow vs. Rank
Road Usage Patterns based on Rank of Sources of Flow
Gini distribution
Road Usage Patterns Using Gini Distribution
Definition
Number of Major Driver Sources
90% of roads have less than 80 NMDS (Major Driver Sources)
Road Usage Patterns Using Major Driver Sources
Comparison with other metrics
Gini is a new property of the streets
Mitigation of Congestion
We can target few affected neighborhoods.
Mitigation of Congestion
We find that when m=1%:Bay Area: δT reaches 26,210 minutes, corresponding to a 14% reduction of one hour morning commute (triangles in Fig. E).
Boston Area: δT reaches 11,762 corresponding to 18% reduction of additional travel time during a one hour morning commute (diamonds in Fig. E)
Mitigation of Congestion
The reason….
1% in car usage reduction
16% reduction in travel time(vs. 3% obtained traditionally)
Why they are travelling?
S. Jang & J. Ferreira (DUSP)
S. Jang, J. Ferreira and M.C. Gonzalez"Clustering Temporal Patterns of Human Activities in the City", Data Mining and Knowledge Discovery 25.3 (2012): 478-510.
- City 2,695,598 - Rank 3rd US - Density 4,447.4/km2
Highly Populated US City:
Chicago!
Chicago 1% representative sample by activity survey
Time of Day
Sam
ple
ID
4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:00 2:00
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
x 104
Home
Work
Schl.
Trans.
Shopping
Personal
Rec.
Civic
Other
Weekday: Temporal Activity Patterns
Weekday: Eigenactivities 1-3H
ome No. 1 Eigenactivity
4 6 8 10 12 14 16 18 20 22 24 2
Wor
k
4 6 8 10 12 14 16 18 20 22 24 2
Sch
l.
4 6 8 10 12 14 16 18 20 22 24 2
Tra
ns.
4 6 8 10 12 14 16 18 20 22 24 2
Sho
p.
4 6 8 10 12 14 16 18 20 22 24 2
Per
s.
4 6 8 10 12 14 16 18 20 22 24 2
Rec
.
4 6 8 10 12 14 16 18 20 22 24 2
Civ
ic
4 6 8 10 12 14 16 18 20 22 24 2
Oth
er
4 6 8 10 12 14 16 18 20 22 24 2
No. 2 Eigenactivity
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
No. 3 Eigenactivity
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2
4 6 8 10 12 14 16 18 20 22 24 2-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
37
Low probability of staying at home from 7:00 am till 5:00 pm
High probability of working from 7:00 am till 5:00 pm
Most components of each eigenactivity are close to the sample mean
Weekday: Clusters (K=8)
Spatio-temporal Patterns of Urban Human MobilityMeasured from Subway Smart Cards
Aereal Image of London
Source: google image
Smartcards from London
Structure of flows
C. Schneider (Postdoc)
Motifs in Daily Mobility
Percentage of trips in daily routine (from Survey)
40,000 active users with calls during the day at at least 8 time windows (time step 30min)
Perturbation based model
SummarySpatial Networks properties have several applications: Communities of airports, roadcharacteristics.
There is a hierarchical network in the way neighborhoods connect to different streets: “Street popularity index”. Individuals can be clustered by their daily travel activities.
A preferential attachment model can describe that heterogeneity of fluxes.
A perturbation based model can describe the Burts and motifs of daily trips.