Topological Properties of the Air Navigation Route System using - - PowerPoint PPT Presentation

Topological Properties of the Air Navigation Route System using Complex Network Theory

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Xiaoqian Sun1, Sebastian Wandelt2, and Florian Linke1

1Institute of Air Transportation Systems, German Aerospace Center 2Department of Computer Science, Humboldt-University Berlin

27 May 2014

Outline

• Motivation
• Complex air transportation systems
• Background
• Complex network theory
• Network analysis of the air navigation route systems
• Conclusions

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Motivation: ATS as complex systems

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Air Transportation Systems (ATS) Challenging Tasks

• Large number of system components

with different characteristics.

• Multiple stakeholders involved to

meet ambitious goals for future ATS.

• Regulate the flow of air traffic and use of airspace in a

safe, cost-efficient, and environmental-friendly way. One solution: Complex Network Theory

Background: Complex network theory

• A network: is a collection of nodes joined together in pairs by edges.
• Network examples:

Social network: People (nodes) linked by social interaction (edges). Airport/Airline flight network: Airports (nodes) are linked by flights (edges).

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A B C D E F H G

Two perspectives of Complex ATS:

• One perspective - Airport network
• Nodes: Airports
• Edges: Flight connections between two airports
• Weights: Number of available seats, number of flights, etc.
• Another perspective - Air navigation route network
• Nodes: Significant points
• Edges: Route segments between two significant points.
• Weights: Great circle distance, number of flights, etc.

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Air navigation route network

• an example (Germany)

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Database- EAD European Aeronautical Information Service Database

• EAD is a centralized reference database of aeronautical information using

XML.

• We build the air navigation route network based on the EAD, effective on

18 October 2012.

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Air navigation route networks for 15 countries

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Topological properties of air navigation route networks

1) Degree 2) Distance strength 3) Weighted betweenness centrality 4) Weighted closeness centrality 5) Edge length distribution

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Topological property 1: Degree

• Degree: the number of edges connected to a node.
• Node A (4) > Node C (3) > Node B (2)
• In a social network, higher degree indicates more influence, more

access to information, or more prestige.

• Degree distribution: The cumulative degree distribution P(k) is the

probability that a randomly chosen node has a degree at least k.

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A B C D E F H G

Poisson distribution

Topological property 1: Degree Log-log scale

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Power law with cutoff

Topological property 2: Distance strength

• Distance strength (weighted degree): the cumulative distances of all the

connections from (or to) the considered node [Barrat, 2005].

• In the airport network
• A linear behavior indicates uncorrelated random connections
• A power law behavior reveals important correlation between

topology and geography

• Larger airports also have farther-reaching connections
• Hub airports have large connectivity, large traffic, and long-

distance connections.

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A B C D E F H G

Topological property 2: Distance strength Log-log scale

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Power law

Topological property 3: Betweenness centrality

• Betweenness: How often a node lies on shortest paths between all pairs
• f other nodes in the network [Freeman, 1977].
• In this example, there are in total (7*6/2=21) pairs of nodes.
• Betweeness: A (15) > B (12) > C(11)
• Nodes with high betweenness have considerable influence within a

network via their control over information passing between others.

• Removal of the nodes with high betweenness from the network will most

disrupt the flow of information between other nodes.

• Betweenness is not a measure of how well-connected a node is (degree),

instead it measures how much a node falls “between” others [Newman,

2010] .

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A B C D E F H G

Topological property 3: Betweenness centrality Semi-log scale

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Exponential

Topological property 4: Closeness centrality

• Closeness: average distance from a node to all other nodes.
• A : (4*1+2+2*3)/7=1.71 (for unweighted)
• B : (1+1+5*2)/7=1.71 (for unweighted)
• C : (3*1+2+3*3)/7=1.875 (for unweighted)
• Nodes with lower values have better access to information at other

nodes or more direct influence on other nodes.

• More central nodes have lower values; while less central nodes have

higher values. Thus, we take the inverse of the average distance.

• We use the great circle distance as the edge weight.

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A B C D E F H G

Topological property 4: Closeness centrality Semi-log scale

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Topological property 5: Edge length distributions Semi-log scale

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Exponential

Summary of regressions on five metrics in the 15 air navigation route networks

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Hierarchical clustering for the 15 countries

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Conclusions

• Air navigation route networks for all fifteen countries are rather

heterogeneous: most nodes have only a few connections with other nodes and a few hub nodes have a large number of connections.

• Our analysis for weighted betweenness centrality shows that some

countries (e.g. USA) are more robust against node failures than other countries (e.g. South Africa).

• The hierarchical clustering based on the regression coefficients shows

that the countries with similar network features are clustered together.

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Future work

• Network analysis of the air navigation route system can be used to

identify potential bottlenecks of air traffic in the future. For example, an air navigation node with high degree or betweenness centrality is most likely to be congested.

Thank you for your attention!

Contact: Xiaoqian Sun Institute of Air Transportation Systems, German Aerospace Center (DLR) xiaoqian.sun@dlr.de

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