1. A traffic complexity approach through cluster analysis
Géraud Granger - Nicolas Durand
STERIA/Eurocontrol - CENA
LOG (Laboratoire d ’Optimisation Globale)
CENA/ENAC Toulouse

2. Outlines Cluster definition Goals of cluster analysis
Theoretical study
Experimental results
The influence of uncertainty on clusters
The feedback effect
Conclusion and future work
How to order aircraft inside clusters ?

3. Cluster definition: transitive closing of conflicting aircraft

4. Goals of cluster analysis
Conflict solvers generally fail in dense areas whatever the resolution strategy (global or sequential resolution)
Even ASAS solvers are sensitive to neighbouring aircraft
 A robust solver must be able to deal with large clusters.
 Clusters must be limited in size.

5. What characterizes a cluster ?
The number of aircraft involved
The number of conflicts
The geometry (aircraft attitude)
The number of maneouvres necessary to solve it
The cluster diameter
A cluster can be represented by a connected graph: (the aircraft are the nodes and the conflicts are the edges)

6. A connected graph can be represented by a graphic sequence
A graphic sequence (d1,d2,…,dn) is a sequence of numbers which can be the degrees of some graph.

7. 3 aircraft clusters
3 aircraft / 2 conflicts
3 aircraft/ 3 conflicts

8. 4 aircraft clusters
3 conflicts
4 conflicts
5 conflicts
6 conflicts

9. 4 conflicts
5 aircraft clusters
10 conflicts

11. Experimental results A french loaded traffic day (21 may 1999)
5% / 15% of uncertainty on H / V speed
8 minutes time window detection
detection is updated every 2 minutes
CATS/OPAS simuator
Standard and Direct routes

12. Standard routes (no resolution)

13. Direct routes (no resolution)

14. The cluster diameter
The distance between two nodes of a graph is the minimum number of edges connecting these two nodes
The diameter of a graph is the maximum distance among every nodes pair
Example:

15. Experimental results

16. The influence of uncertainty on cluster sizes (with resolution)

17. The feedback effect

19. Conclusions
The number of cluster types and their complexity grow exponentially with the number of aircraft  large clusters are too complex for human analysis
Solving large clusters is difficult  the key point for future control systems is to limit the maximum cluster size
Cluster sizes are very sensitive to speed uncertainties  An efficient and robust solver requires a good trajectory forecast.
The phenomenon is increased by the feedback effect.
Direct routes are better than standard routes as they limit cluster sizes and increase cluster diameters.

20. NEXT STEPS
Take into account the aircraft attitude (climbing, levelled, descending) in the cluster analysis
Complexity is increased: with 3 different attitudes (climbing, descending, levelled aircraft), for 3 aircraft, 16 cluster types instead of 2.
Cluster complexity depends on the resolution method: most of the ASAS projects or Conflict solvers are based on sequential resolution  what is the best priority order to solve conflicts ?
Extended Flight Rules ?
Arbitrary order ? ….

21. What is the best priority order ? An open question ?
Experiment on aircraft clusters (levelled aircraft, toy problems)
Solved conflicts:
Random order: 738
Most conflicting aircraft first: 787
Less conflicting aircraft first: 702
Earliest conflict first: 884
Earliest conflict last: 677 …
No Free Lunch : Some of the unsolved conflicts with the earliest conflict first rule are solved with other rules.

22. What is the best priority order ? An open question ?
Experimental results on real traffic
best order:
1. earliest conflict first
2. already manoeuvred first
3. max number of conflicts first
No Free Lunch:
sometimes with other priority orders there are less remaining conflicts
some unsolved conflicts could have been solved with other priority orders