Air Transportation System
Architecture Analysis
Project Final Presentation
Advanced System Architecture
Spring 2006
May 9th, 2006
Presentation by:
Philippe Bonnefoy
Roland Weibel
Instructors: Chris Magee, Joel Moses and Daniel Whitney
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
1
Motivation
• Future demand is expected to increase significantly due
to the introduction of new classes of aircraft, such as
Very Light Jets and Unmanned Aerial Vehicles
• There are several constraints on system evolution driven
by infrastructure, economics, safety, and technology
• The air transportation system is facing and will continue
to face significant challenges in terms of meeting
demand for mobility
• Current multi-agency effort to establish a roadmap for
the “Next Generation of Air Transportation System”
• Future (evolved) architecture of the system require
understanding of the structure of the current system
• Lack of integrated quantitative analysis of structure of
the current system
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
2
Objective of the project
• Better understand the architecture of the current system
through network analyzes
• Understand
– the network characteristics of individual system layers
– Influence of constraints, desired properties (i.e. safety, capacity,
etc.) in explanation of network characteristics
– comparison of network characteristics across different layers,
through coupling of infrastructure or comparison of different
network characteristics across layers
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
3
Overview of the System
DEMAND
System layer
Demand layer
Population, income,
location of businesses
Transport layer
Unscheduled
Scheduled
Image removed for
copyright reasons.
Airplane.
Intra-layer
comparison
Unscheduled
Image removed for
copyright reasons.
Airplane.
Scheduled
SUPPLY
Cross-layer
comparison
Airspace
Ground
Infrastructure
layer
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
Image removed for
copyright reasons.
Chart of jet routes.
4
Transport Layer Analysis
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
5
Analysis of the Wide-Body/Narrow Body
&Regional Jet Flight Network
Narrow Body Jets
Wide Body Jets
(Images removed for
copyright reasons.)
Regional Jets
Degree Distribution
Cumulative Probability p(>k)
1
0.1
Wide/Narrow Body &
Regional Jets
0.01
WB/NB/RJ + with primary &
secondary airports
aggregated
0.001
1
10
100
1000
10000
Degree
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
6
Analysis of the Wide-Body/Narrow Body &
Regional Jet Route Network
Degree Distribution Analysis
10
Cumulative Probability p(>k)
WB/NB/RJ + w ith primary &
secondary airports aggregated
Beyond Pow er Law
Pow er (WB/NB/RJ + w ith primary &
secondary airports aggregated)
1
Coefficient of the degree distribution
power law function: γ = 1.49
Hypotheses for the exponential cut-off:
- Nodal capacity constraints
0.1
y = 1.85x
- Connectivity limitations between core
and secondary airports
-0.49
0.01
1
10
100
1000
10000
Degree
Network Characteristics
Network
Scheduled
transportation
network
n
m
Density
Clustering
coeff.
r
Centrality vs.
connectivity
13/20
249
3389
0.052
0.64
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
-0.39
most central also part
of the top 20 most
connected
7
Analysis of the Light Jet Route Network
Image removed for copyright reasons.
Light Jets
Degree Distribution
Cumulative Frequency (n(>k))
1
0.1
0.01
0.001
0.0001
1
10
100
1000
10000
Degree
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
8
Analysis of the Light Jet Route Network
Degree Distribution Analysis
1
Degree distribution identified as
resulting from sub-linear preferential
attachment.
Cumulative Frequency (n(>k))
Power law network
degree signature
0.1
0.01
nk = a.k
Light Jet
Network
−γ
0.001
with:
0.0001
1
10
100
1000
10000
Degree
⎡ ⎛ k 1−γ − 21−γ
exp ⎢− µ ⎜⎜
⎣ ⎝ 1− γ
⎞⎤
⎟⎟⎥
⎠⎦
γ = 0.57
µ = 0.16
a = 0.13
Network Characteristics
Network
Light Jet Network
(Unscheduled)
n
m
Density
Clustering
coefficient
r
900
5384
0.005
0.12
0.0045
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
9
Underlying Processes and Attributes Influencing
the Sub linear Attachment Dynamics
Hypotheses:
• Spatial Constraints
– Aircraft range (number of airports reachable given aircraft range
compatibilities)
•
Nodal Capacity
– Airport capacity
•
Underlying demand drivers
– Population distribution
•
Investigated
in Report
Modal competition
– Focusing on the nodes
• Scheduled transportation with the transition from on-demand traffic to
scheduled traffic
– Focusing on the arcs
• Economics, passenger mode choice
– Demand for long range on-demand flights (modal competition)
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
10
Overview of the System
DEMAND
System layer
Demand layer
Population, income,
location of businesses
Transport layer
Unscheduled
Scheduled
Image removed for
copyright reasons.
Airplane.
Intra-layer
comparison
Unscheduled
Image removed for
copyright reasons.
Airplane.
Scheduled
SUPPLY
Cross-layer
comparison
Airspace
Ground
Infrastructure
layer
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
Image removed for
copyright reasons.
Chart of jet routes.
11
Airport-Level Interactions between
Transport Layers
On-Demand
Scheduled
Transport layer
90
TEB
80
Unscehduled Traffic LJ
(weighted degree)
70
CMH
60
50
40
CLT
ATL
30
20
ORD
10
0
0
200
400
SEA
DFW
600
800
1000
Scheduled Traffic WB/NB/RJ
(weighted degree)
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
1200
1400
12
Overview of the System
DEMAND
System layer
Demand layer
Population, income,
location of businesses
Transport layer
Unscheduled
Scheduled
Image removed for
copyright reasons.
Airplane.
Intra-layer
comparison
Unscheduled
Image removed for
copyright reasons.
Airplane.
Scheduled
SUPPLY
Cross-layer
comparison
Airspace
Ground
Infrastructure
layer
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
Image removed for
copyright reasons.
Chart of jet routes.
13
Analysis of the Demand Layer
•
Single Layer Analysis
Notations:
Pct: population of census track ct
Population/Airport Gravity Model
bi =
∑ pct
ct ∈C i
bi: size of population basin around
airport i
⎫
⎧
s.t. Ci = ⎨ct d ct ,i = min d ct , j ⎬
j
⎭
⎩
ct: census track
di,j: Euclidean distance
1
0.0
Distribution of
population around
airports does not
follow a power law
Cumulative Density Function p(>b)
based on 66,000 Census Track data
0.1
1.0
10.0
0.1
Power law network
degree signature
0.01
Population distribution
(based on the gravity model)
0.001
0.0001
0.00001
Sizeofof
population
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute
Technology
basin (b) [in millions]
14
Infrastructure Layer Analysis
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
15
Infrastructure layer analysis
• Problem
– Airspace is a shared resource between various type of traffic
(e.g. scheduled commercial, unscheduled commercial, general
aviation, etc.)
– What is the level of interaction between types of traffic at key
points in the airspace
• Network analysis
– Betweenness centrality
– Connectivity
• Methodology
– Shortest-path search through fully-connected airport network
along ground-based Navigational Aids
– For scheduled & unscheduled traffic data
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
16
Unweighted Betweenness Centrality Unscheduled
Legend
Percentage of geodesics
through each Navaid
5-9%
4-5%
3-4%
2-3%
1-2%
0-1%
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
17
Unweighted Betweenness Centrality Scheduled
Legend
Percentage of geodesics
through each Navaid
5-9%
4-5%
3-4%
2-3%
1-2%
0-1%
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
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Degree vs. Betweenness for Navaid/Airport
Networks
Betweenness Centrality
9%
8%
Unscheduled
7%
6%
5%
4%
3%
2%
1%
0%
0
5
10
15
20
Degree
Betweenness Centrality
9%
8%
Scheduled
7%
6%
5%
4%
3%
2%
1%
0%
0
5
10
15
20
Degree
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
19
Conclusions
• Distribution of Scheduled & Unscheduled Nodes
– Scheduled: power law with exponential cut-off
– Unscheduled: product of exponential and power law
– Air transportation system is not scale free
• Several System Attributes That Impose Scale on System
– Apparent in degree sequences investigated
– Apparent in utilization of airports and navigational aids
– Influences such as capacity, economics, and policy are acting to
limit nodal connections and edge flows
• Several Implications for future growth of the Air
Transportation System
– Constraints important in future system evolution
– Analysis forms basis for further understanding of constraints and
growth dynamics
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
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Questions & Comments
Thank you
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
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Infrastructure Layer Analysis
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
22
Navigation Infrastructure Analysis
Nodes & Link Highlighted
Image removed for copyright reasons.
Chart of jet routes.
• Nodes: FAA-Defined
Navigational Aids of Different
Types
– VORs, Reporting Points, etc
• Links: Air Routes Between
Nodes
– Victor (low alt) & Jet Routes (high alt)
• Network Metrics
– Clustering Coefficient (Watts method) – Proxy for robustness of
network
– Correlation Coefficient
• Architecture Analyses
– Shortest-Path Navigational vs. Direct Distance between
Airports
– Nodal Betweenness/Centrality
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
23
Degree Sequence
Frequency
2000
Other Points
Victor Airways
-All Points (left)
-VOR/VORTAC (below)
VOR/VORTAC
1500
1000
500
120
100
1
2
3
4
5
Frequency
0
6
80
7 8 9 10 11 12 13 14 15
60
Degree
40
20
0
1
600
500
3
4
5
6
7 8 9 10 11 12 13 14 15
Degree
VOR/VORTAC
400
300
200
35
100
30
25
Frequency
Frequency
2
Other Points
0
1
2
3
4
5
6
7
8
20
9 10 11 12 13 14 1515
Degree
Jet Routes
-All Points (left), VOR/VORTAC (right)
10
5
0
1
2
3
4
5
6
7 8 9
Degree
10 11 12 13 14 15
NavAid Network
n
m
C (Watts)
r
Jet Routes
1787
4444
0.1928
-0.0166
Victor Airways
2669
7635
0.2761
-0.0728
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
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Navigation Architecture Analysis
• End Nodes: Navaids corresponding to published
airports
• Geodesic (shortest path by navigational distance)
computed between top 1,000 airport pairs
– Airports ranked based on 2004 FAA traffic data
– A-Star search algorithm implemented to find shortest distance along
network
• Results – Dynamics Along Network
– Navigational Distance Compared to Shortest Path Distance by
Airport Ranking – Maximum “direct-to” efficiency
– Betweenness centrality to be calculated for navigation nodes as
measure of their utilization
• Number of shortest-paths through nodes as a proportion to total
shortest paths
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
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Navigation Distance Results
) n airports n airports
d = ∑ ∑ d ij
% Distance Reduction
i
% reduction = 1 −
j, j>i
d̂
d
9.0%
8.5%
8.0%
7.5%
7.0%
6.5%
6.0%
0
200
400
600
800
1000
1200
Number of Airport Pairs
© 2006 Philippe A. Bonnefoy, Roland E. Weibel, Engineering Systems Division, Massachusetts Institute of Technology
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