1. The Relationship Between Traffic Stability and Capacity for Decentralized Airspace 7th International Conference for Research in Air Transportation
June 22, 2016
Emmanuel Sunil, Jerom Maas, Joost Ellerbroek, Jacco Hoekstra and Martijn Tra

2. Outline Introduction Previous Research on Stability and Capacity
Alternate Model Relating Stability and Capacity
Hypothesized Relationship between DEP and Density
Capacity Measurement for Decentralized Airspace
Conclusions
So, this presentation is organized into 6 parts. I will start by presenting an overview my phd project, and then focus on the concept of airspace stability and how it can be measured. After that, I will briefly go over a previous study that used traffic stability to measure capacity. Next, using the model in literature as starting point, I will go through the derivation of a more generalizable model that uses fewer assumptions to model traffic stability. In the fourth and fifth parts of this presentation, I will use this new model, and results from our previous work, to hypothesize the relationship between the Domino Effect Parameter, a measure of stability, and capacity, and I will also use this model to formulate a definition for the capacity of decentralized airspace. Finally, I will end with a summary of this talk, and our planned next steps.

3. 1.
Introduction
So let me start with the motivation behind my phd project

4. Decentralized Airspace
Decentralization: Transferring the traffic separation responsibility from the ground to each individual aircraft
Expected to increase en-route capacity
Significant research on airborne Conflict Detection and Resolution (CD&R) algorithms and interfaces
Not enough research on airspace design and capacity
My phd is centered around decentralized airspace, in which traffic separation ….
#[J.Hoekstra et al 2002]
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

5. Overview of PhD Research
Explicit Structure
Procedural mechanism for a priori separation of aircraft by imposing constraints on aircraft degrees of motion
Implicit Structure
Self organization as a result of Conflict Resolution (CR)
Capacity Models
Methods to measure and predict capacity of decentralized airspace
Decentralized Airspace Structure
This leads me to my phd project, which is about the influence of traffic structure on the capacity for decentralize airspace.
This diagram shows the three main parts of my phd; the first part deals with explicit structuring of traffic, and explicit structuring, as we have defined it, is the application of one or more constraints on aircraft degrees of motion to separate and organize traffic flows.
The second part is about implicit structuring, which is a self-organization of traffic as a result of conflict resolution algorithms.
The last part deals with capacity models for measuring and modeling capacity, for both explicit and implicit structuring.
This presentation mostly deals with this last part, capacity modelling.
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

6. Explicit Airspace Structure#
Layers
Four Airspace Concepts of Increasing Structure
Zones
Tubes
Full Mix
I started my phd roughly 2.5 years ago by looking at explicit structuring, and how the degree of structuring affects capacity. We did this by comparing four airspace concepts of increasing structure using fast-time simulations. But when we were doing this study, we quickly realized that there really isn’t a universally accepted definition of capacity for decentralized airspace.
Four concepts compared using fast-time simulations
#[E. Sunil et al 2016]
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

7. What is Capacity for Decentralized Airspace?
Air traffic controller workload not relevant for decentralization
Capacity is density at which airspace becomes saturated
Saturation => Variation of airspace performance metrics with density
Safety
Efficiency
Stability …
This is partly because exiting capacity measurement and modeling techniques, such as ATCo workload, are not relevant for decentralized airspace.
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

8. Conflicts vs. Intrusions
< dsep
Conflict
Intrusion
Conflicts are predicted intrusions within the look-ahead time
Intrusions occur when the minimum separation requirements are violated

9. Airspace Stability B 1 A C # Conflict 1 A-B
Ok, so lets go back to airspace stability. The best way to describe what stability means is to look at this very simple traffic scenario with three aircraft.
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

10. Airspace Stability B 1 A C # Conflict Type 1 A-B Primary 2 A-C
Secondary 2
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

11. Airspace Stability B 3 1 A C # Conflict Type 1 A-B Primary 2 A-C
Secondary 3
C-B 2
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

12. Domino Effect Parameter#
Airspace Stability B 3 1 A C #
Conflict
Type 1
A-B
Primary 2
A-C
Secondary 3
C-B 2
Conflict Chain Reactions
Domino Effect Parameter#
#[K. Bilimoria et al 2000]
[J. Krozel et al 2000]
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

13. Domino Effect Parameter (DEP)
The Domino Effect Parameter or DEP can be explained by using this simple venn-diagram
𝐷𝐸𝑃= 𝑅3−𝑅1 𝑆1 = 𝑆2 𝑆1 −1
CR = Conflict Resolution
#[K. Bilimoria et al 2000]
[J. Krozel et al 2000]

14. Airspace Stability B 3 1 A C # Conflict Type 1 A-B Primary 2 A-C
Secondary 3
C-B 2
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

15. DEP Examples S1 = 1 𝐷𝐸𝑃= 3 1 −1=2 S2 = 3 S1 S2
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

16. DEP Examples S1 = 1 𝐷𝐸𝑃= 3 1 −1=2 S2 = 3 S1 = 3 𝐷𝐸𝑃= 6 3 −1=1 S2 = 6
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

17. Domino Effect Parameter (DEP)
Number of secondary conflicts per primary conflict
Higher DEP Lower stability
Uses
Compare performance of different CR methods
Measure capacity of decentralized airspace
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

18. Domino Effect Parameter
Airspace Capacity
Domino Effect Parameter
Stability
Safety
Efficiency
In fact, by the end of this presentation, I will show that the DEP relates the capacity of the airspace via the safety, efficiency and stability performance of the airspace.
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

19. 2. Previous Research on Stability and Capacity
A lot of the ideas in this work was inspired by a paper written by Matt Jardin in 2004

20. Previous Research Relating Stability and Capacity
𝐷𝐸𝑃 = 𝜌 𝐴𝐶 −1/𝐴 𝜌 𝑚𝑎𝑥 − 𝜌 𝐴𝐶 −1/𝐴 #
Where: 𝑑 𝑠𝑒𝑝 = separation minima 𝑡 𝑙 = look-ahead time
𝜌 𝑚𝑎𝑥 = 2 𝑡 𝑙 𝑑 𝑠𝑒𝑝 𝑘 #
If 𝜌 𝐴𝐶 ≡ 𝜌 𝑚𝑎𝑥 and 𝜌 𝐴𝐶 ≫1/𝐴 then 𝐷𝐸𝑃 → ∞
#[M. Jardin et al. 2004]
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

21. Conflict Rate With and Without Conflict Resolution Experimental Evidence for a Decentralized Direct Routing Concept
Density
Conflict rate with and without CR is not always same
Assumption 2 is not valid for all densities
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

22. Effect of Conflict Rate on DEP
Low Density Simulations#
High Density Simulations %
Density
Same CR algorithm (MVP) in both studies:
DEP negative for a range of low densities
DEP positive for higher densities
#[J. Maas et al 2016]
%[E. Sunil et al 2016]
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

23. How can DEP be Negative? S2 = 3 𝐷𝐸𝑃= 3 4 −1=− 1 4 S1 = 4
Conflict Resolution can reduce the total number of conflicts for some densities and some CR methods
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

24. Previous Research Relating Stability and Capacity
𝐷𝐸𝑃 = 𝜌 𝐴𝐶 −1/𝐴 𝜌 𝑚𝑎𝑥 − 𝜌 𝐴𝐶 −1/𝐴
Does not account for negative DEP at any density
𝜌 𝑚𝑎𝑥 = 2 𝑡 𝑙 𝑑 𝑠𝑒𝑝 𝑘
2 Assumptions:
Conflict resolution maneuvers increase the amount of airspace searched for conflicts
The conflict rate (per unit time/distance) is the same with and without conflict resolution
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

25. 3.
Alternate Model Relating Stability and Capacity

26. Overview of Derivation
𝐷𝐸𝑃= 𝑆2 𝑆1 −1= 𝑃 2 𝑊𝑅 𝑃 2 𝑁𝑅 ∙ 𝑁 𝑊𝑅 𝑁 𝑁𝑅 𝑡 𝑓 𝑊𝑅 𝑡 𝑓 𝑁𝑅 ∙ 1 1− 𝐸 𝐶 𝑅𝑀 −1
Main Difference: Conflict rate with and without resolution are not required to be equal
Expected number of conflicts per aircraft:
Without conflict resolution
During one resolution maneuver
With conflict resolution
Note: Derivation not complete, but current form provides insights on capacity
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

27. Number of Conflicts Without Conflict Resolution Per Flight
2 𝑑 𝑠𝑒𝑝
𝑉 𝑡 𝑙 𝐴
Proportion of area searched for conflicts
𝐸 𝐶 𝑁𝑅 = 𝑟 𝐶 𝑁𝑅 𝑡 𝑓 𝑁𝑅
𝑟 𝐶 𝑁𝑅 = 2𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝐴 𝑃 2 𝑁𝑅 𝑇
𝐸 𝐶 𝑁𝑅 = 2 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝑃 2 𝑁𝑅 𝑡 𝑓 𝑁𝑅 𝐴𝑇
tfnr is the time spent searching for conflicts. For the no resolution case, this is equivalnet to
Where:
𝐸 𝐶 𝑁𝑅 = Number of conflicts per flight with no resolution
𝑟 𝐶 𝑁𝑅 = Conflict rate with no resolution
𝑑 𝑠𝑒𝑝 = Separation minima
𝑉 = Average speed of all aircraft
𝑃 2 𝑁𝑅 = Conflict probability no resolution
𝑡 𝑙 = Look-ahead time
𝑡 𝑓 𝑁𝑅 = Average flight time with no resolution
𝑇 = Observation time
𝐴 = Observation area
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

28. Number of Conflicts During One Resolution Per Flight
2 𝑑 𝑠𝑒𝑝
𝐸 𝐶 𝑅𝑀 = 𝑟 𝐶 𝑊𝑅 𝑡 𝑙
𝑉 𝑡 𝑙
𝑟 𝐶 𝑊𝑅 = 2𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝐴 𝑃 2 𝑊𝑅 𝑇
𝐸 𝐶 𝑅𝑀 = 2 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 2 𝑃 2 𝑊𝑅 𝐴𝑇
During a resolution, the time spent searching for conflicts is equal to the look-ahead time
During one resolution, the time spent searching for conflicts is equal to the look-ahead time
Where:
𝐸 𝐶 𝑅𝑀 = Number of conflicts per flight during 1 resolution
𝑟 𝐶 𝑊𝑅 = Conflict rate with resolution
𝑑 𝑠𝑒𝑝 = Separation minima
𝑉 = Average speed of all aircraft
𝑃 2 𝑊𝑅 = Conflict probability with resolution
𝑡 𝑙 = Look-ahead time
𝑇 = Observation time
𝐴 = Observation area
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

29. Number of Conflicts With Conflict Resolution Per Flight
𝐸 𝐶 𝑊𝑅 = 𝑟 𝐶 𝑊𝑅 𝑡 𝑓 𝑊𝑅 + 𝑡 𝑙 𝐸 𝐶 𝑊𝑅
With conflict resolution, each conflict causes as an extra area to be searched for conflicts, but not flown threw.
𝑉 𝑡 𝑙
𝑟 𝐶 𝑊𝑅 = 2𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝐴 𝑃 2 𝑊𝑅 𝑇
𝐸 𝐶 𝑊𝑅 = 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝑃 2 𝑊𝑅 𝑡 𝑓 𝑊𝑅 𝐴𝑇 + 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 2 𝑃 2 𝑊𝑅 𝐴𝑇 𝐸 𝐶 𝑊𝑅
𝐸 𝐶 𝑅𝑀
𝐸 𝐶 𝑊𝑅 = 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝑃 2 𝑊𝑅 𝑡 𝑓 𝑊𝑅 𝐴𝑇 1− 𝐸 𝐶 𝑅𝑀
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

30. DEP Model 𝐸 𝐶 𝑊𝑅 = 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝑃 2 𝑊𝑅 𝑡 𝑓 𝑊𝑅 𝐴𝑇 1− 𝐸 𝐶 𝑅𝑀
𝐸 𝐶 𝑊𝑅 = 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝑃 2 𝑊𝑅 𝑡 𝑓 𝑊𝑅 𝐴𝑇 1− 𝐸 𝐶 𝑅𝑀
𝐸 𝐶 𝑁𝑅 = 2 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 𝑃 2 𝑁𝑅 𝑡 𝑓 𝑁𝑅 𝐴𝑇
𝐷𝐸𝑃= 𝑃 2 𝑊𝑅 𝑃 2 𝑁𝑅 ∙ 𝑁 𝑊𝑅 𝑁 𝑁𝑅 𝑡 𝑓 𝑊𝑅 𝑡 𝑓 𝑁𝑅 ∙ 1 1− 𝐸 𝐶 𝑅𝑀 −1
𝐸 𝐶 𝑅𝑀 = 2 𝑑 𝑠𝑒𝑝 𝑉 𝑡 𝑙 2 𝑃 2 𝑊𝑅 𝐴𝑇
Airspace parameters through ECRM equation
𝐷𝐸𝑃= 𝑆2 𝑆1 −1= 𝑁 𝑊𝑅 𝐸 𝐶 𝑊𝑅 𝑁 𝑁𝑅 𝐸 𝐶 𝑁𝑅 −1
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

31. 4.
Hypothesized Relationship between DEP and Density

32. The Three Components of the DEP
𝐷𝐸𝑃= 𝑃 2 𝑊𝑅 𝑃 2 𝑁𝑅 Safety ∙ 𝑁 𝑊𝑅 𝑁 𝑁𝑅 𝑡 𝑓 𝑊𝑅 𝑡 𝑓 𝑁𝑅 Efficiency ∙ − 𝐸 𝐶 𝑅𝑀 Domino −1
Where:
𝑃 2 𝑊𝑅 = Conflict probability with resolution
𝑃 2 𝑁𝑅 = Conflict probability without resolution
𝑁 𝑊𝑅 = Total number of aircraft during observation time with resolution
𝑁 𝑁𝑅 = Total number of aircraft during observation time without resolution
𝑡 𝑓 𝑊𝑅 = Average flight time with resolution
𝑡 𝑓 𝑁𝑅 = Average flight time without resolution
𝐸 𝐶 𝑅𝑀 = Number of conflicts per flight during 1 resolution
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

33. Hypothesis: Domino vs. Density
𝐷𝑜𝑚𝑖𝑛𝑜= 1 1− 𝐸 𝐶 𝑅𝑀
If 𝐸 𝐶 𝑅𝑀 =1, − 𝐸 𝐶 𝑅𝑀 →∞
If 𝐸 𝐶 𝑅𝑀 = 1, every conflict resolution will cause a new conflict, and all aircraft will perpetually be in conflict
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

34. Hypothesis: Efficiency vs. Density
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦= 𝑁 𝑊𝑅 𝑁 𝑁𝑅 𝑡 𝑓 𝑊𝑅 𝑡 𝑓 𝑁𝑅
Flight time with conflict resolution increases nonlinearly as the number of conflicts increases with density
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

35. Modified Voltage Potential (MVP)
No Resolution
MVP
MVP#
Reduces relative velocities
Increases distances between aircraft
#[J.Hoekstra 2001]
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

36. Hypothesis: Safety vs. Density For MVP
𝑆𝑎𝑓𝑒𝑡𝑦= 𝑃 2 𝑊𝑅 𝑃 2 𝑁𝑅
MVP is hypothesized to reduce conflict probabilities for some densities by dispersing the over the available airspace
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

37. Hypothesis: DEP vs. Densityx x
− 1 =
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

38. Hypothesis: DEP vs. Densityx x
− 1 = ?
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

39. 5.
Capacity Measurement for Decentralized Airspace

40. The Three Components of the DEP
𝐷𝐸𝑃= 𝑃 2 𝑊𝑅 𝑃 2 𝑁𝑅 Safety ∙ 𝑁 𝑊𝑅 𝑁 𝑁𝑅 𝑡 𝑓 𝑊𝑅 𝑡 𝑓 𝑁𝑅 Efficiency ∙ − 𝐸 𝐶 𝑅𝑀 Domino −1
𝜌 𝑠𝑎𝑓𝑒𝑡𝑦
𝜌 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦
𝜌 𝑠𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

41. Definition of Capacity for Decentralized Airspace
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

42. Definition of Capacity for Decentralized Airspace
Capacity is defined as the lowest density at which the rate of change of safety/efficiency/stability metrics tend to infinity
Capacity is limited by the safety or efficiency or stability performance of the airspace
𝜌 𝑐𝑎𝑝𝑐𝑖𝑡𝑦 = min 𝜌 𝑆𝑎𝑓𝑒𝑡𝑦 , 𝜌 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 , 𝜌 𝑆𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 lim 𝜌→ 𝜌 𝑆𝑎𝑓𝑒𝑡𝑦 𝜕𝑆𝑎𝑓𝑒𝑡𝑦 𝜕𝜌 =∞ , lim 𝜌→ 𝜌 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝜕𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝜕𝜌 =∞ , lim 𝜌→ 𝜌 𝑆𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝜕𝑆𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝜕𝜌 =∞
Theoretical Definition
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

43. Theory vs. Reality
In practice capacity is also determined by airline economics => efficiency driven
Public will not accept asymptotic behavior of safety as a capacity limit
Practical capacity hard to quantify
Workload varies from ATCo to ATCo
But, the theoretical capacity definition is a useful and unbiased benchmark:
Capacity limits for different methods of organizing traffic
Effect for different CR methods on capacity
We could the theoretial definition to determine the capacity limits of different ways of structuring traffic
or how different CR methods affect capacity for decentralization
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

44. 6.
Conclusions

45. Summary
The Domino Effect Parameter (DEP) measures the number of secondary conflicts per primary conflict
A model of the DEP has been derived that does not require the conflict rate to be the same with and without conflict resolution:
DEP relates safety, stability and efficiency to capacity for decentralized airspace
Capacity is defined as the lowest density at which the rate of change of safety/efficiency/stability metrics tend to infinity
𝐷𝐸𝑃= 𝑃 2 𝑊𝑅 𝑃 2 𝑁𝑅 Safety ∙ 𝑁 𝑊𝑅 𝑁 𝑁𝑅 𝑡 𝑓 𝑊𝑅 𝑡 𝑓 𝑁𝑅 Efficiency ∙ − 𝐸 𝐶 𝑅𝑀 Domino −1
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

46. Next Steps in PhD Research…
Validate the hypothesized relationships between DEP components and density
Using fast-time simulations
Wide range of densities
Complete the derivation of DEP model
Link to density
Implicit structuring of airspace
Extend DEP model to take into account effect of (explicit) airspace structure
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

47. Explicit Airspace Structure#
Layers
Four Airspace Concepts of Increasing Structure
Zones
Tubes
Full Mix
23 June Hall 1 13:40
#[E. Sunil et al 2016]
Introduction - Previous Research - Alternate DEP Model - Hypothesis - Capacity Measurement - Conclusions

48. Thankyou For Your Attention! [