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.