A traffic complexity approach through cluster analysis Géraud Granger - Nicolas Durand STERIA/Eurocontrol - CENA LOG (Laboratoire d ’Optimisation Globale) CENA/ENAC Toulouse granger,durand@recherche.enac.fr

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 ?

Cluster definition: transitive closing of conflicting aircraft

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.

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)

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.

3 aircraft clusters 3 aircraft / 2 conflicts 3 aircraft/ 3 conflicts

4 aircraft clusters 3 conflicts 4 conflicts 5 conflicts 6 conflicts

4 conflicts 5 aircraft clusters 10 conflicts

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

Standard routes (no resolution)

Direct routes (no resolution)

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:

Experimental results

The influence of uncertainty on cluster sizes (with resolution)

The feedback effect

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.

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 ? ….

What is the best priority order ? An open question ? Experiment on 1000 6-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.

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