![Page 1: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/1.jpg)
Towards a scientific basis for determining En Route capacity
Alex BayenCharles Roblin Dengfeng Sun Guoyuan Wu
University of California, BerkeleyDepartment of Civil Engineering
Systems Engineering
March16th, 2006, Pacific Grove, CA
Work funded by NASA Ames under Task Order TO.048.0.BS.AF
![Page 2: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/2.jpg)
Motivation for this work
Importance of en-route capacity (analysis) Safety, quality of service, delays, efficiency, performance metrics,…
Establishing a scientific base for the envelope of operationsQuestion 1: reachability in terms of delays
Question 2: reachability in terms of counts or similar metrics
Provide input data for estimating storage capacity Question 1: how much aircraft / delay can one portion of airspace absorb
Question 2: what is the relation to WITI?
Question 2: space / time definition of capacity
![Page 3: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/3.jpg)
Outline
Building blocks towards scientific capacity analysis
1. Systematic identification of the topological features of the National Airspace System (graph theoretic)
2. Automated model building (aggregation procedure)
3. Parameter identification (travel time)
4. Model Analysis (storage)
5. Model validation
6. Capacity assessment (in progress)1. Delays that can be absorbed
2. Aircraft that can be stored
3. Stability of the storage (backpropagation)
![Page 4: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/4.jpg)
The National Airspace System (NAS)
![Page 5: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/5.jpg)
Air Route Traffic Control Centers in the US
[Menon, Sweriduk, Bilimoria 2004]
[Sridhar, Soni, Sheth, Chatterji 2004]
[Roy, Sridhar, Verghese 2003], [Devasia, Meyer 2002]
![Page 6: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/6.jpg)
Air Route Traffic Control Center (Oakland)
![Page 7: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/7.jpg)
Flight trajectories
![Page 8: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/8.jpg)
Conceptual goal: graph building
[Histon, Hansman, 2000]
![Page 9: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/9.jpg)
A state of the art clustering algorithm
![Page 10: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/10.jpg)
A state of the art clustering algorithm
![Page 11: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/11.jpg)
Outline
Building blocks towards scientific capacity analysis
1. Systematic identification of the topological features of the National Airspace System (graph theoretic)
2. Automated model building (aggregation procedure)
3. Parameter identification (travel time)
4. Model Analysis (storage)
5. Model validation
6. Capacity assessment (in progress)1. Delays that can be absorbed
2. Aircraft that can be stored
3. Stability of the storage (backpropagation)
![Page 12: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/12.jpg)
Data analysis procedure
1. Airspace segmentation using sector boundaries
2. Link building using clustering techniques
3. Data aggregation using ASDI/ETMS information (flight plan information)
4. Filtering using LOAs, and observed flow patterns
5. Computation of the aggregate flow pattern features
Sequential (automated) algorithm
Output: topology of the flows
![Page 13: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/13.jpg)
Data analysis procedure
![Page 14: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/14.jpg)
Data analysis procedure
![Page 15: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/15.jpg)
Data analysis procedure
![Page 16: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/16.jpg)
Data analysis procedure
![Page 17: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/17.jpg)
Main question: what is the aggregate dynamics?
How to relate inflow to outflow (MIMO)?
What is the internal dynamics?
How to use these models to assess capacity?
![Page 18: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/18.jpg)
Outline
Building blocks towards scientific capacity analysis
1. Systematic identification of the topological features of the National Airspace System (graph theoretic)
2. Automated model building (aggregation procedure)
3. Parameter identification (travel time)
4. Model Analysis (storage)
5. Model validation
6. Capacity assessment (in progress)1. Delays that can be absorbed
2. Aircraft that can be stored
3. Stability of the storage (backpropagation)
![Page 19: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/19.jpg)
System identification (example: one link)
![Page 20: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/20.jpg)
System identification (example: one link)
![Page 21: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/21.jpg)
System identification (example: one link)
![Page 22: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/22.jpg)
Outline
Building blocks towards systematic capacity analysis
1. Systematic identification of the topological features of the National Airspace System (graph theoretic)
2. Automated model building (aggregation procedure)
3. Parameter identification (travel time)
4. Model Analysis (storage)
5. Model validation
6. Capacity assessment (in progress)1. Delays that can be absorbed
2. Aircraft that can be stored
3. Stability of the storage (backpropagation)
![Page 23: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/23.jpg)
Delay system: Link level
Link level model
Cell
![Page 24: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/24.jpg)
Illustration of the model: state vector
delay system at the link leveltime step
1
state: cell counts
![Page 25: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/25.jpg)
Illustration of the model: states transition
time step
2delay system at the link level
state: cell counts
![Page 26: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/26.jpg)
Illustration of the model: states transition
time step
3delay system at the link level
![Page 27: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/27.jpg)
Illustration of the model: states transition
time step
4delay system at the link level
![Page 28: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/28.jpg)
Illustration of the model: entry input
time step
5delay system at the link level
input to the link (forcing)
![Page 29: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/29.jpg)
Illustration of the model: entry input
time step
6delay system at the link level
![Page 30: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/30.jpg)
Illustration of the model: delay control
time step
7delay system at the link level
one aircraft about to be held
![Page 31: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/31.jpg)
Illustration of the model: delay control
time step
8delay system at the link level
control input
![Page 32: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/32.jpg)
Illustration of the model: delay control
time step
9delay system at the link level
two aircraft about to be held
![Page 33: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/33.jpg)
Illustration of the model: delay control
time step
10delay system at the link level
![Page 34: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/34.jpg)
Sector level
Delay system: Sector level
[Robelin, Sun, Wu, Bayen 2006]
![Page 35: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/35.jpg)
Center level:
A Bu Bf
Delay system: Center (ARTCC) level
[Robelin, Sun, Wu, Bayen 2006]
![Page 36: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/36.jpg)
Outline
Building blocks towards systematic capacity analysis
1. Systematic identification of the topological features of the National Airspace System (graph theoretic)
2. Automated model building (aggregation procedure)
3. Parameter identification (travel time)
4. Model Analysis (storage)
5. Model validation
6. Capacity assessment (in progress)1. Delays that can be absorbed
2. Aircraft that can be stored
3. Stability of the storage (backpropagation)
![Page 37: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/37.jpg)
Aggregate model validation
![Page 38: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/38.jpg)
Outline
Building blocks towards systematic capacity analysis
1. Systematic identification of the topological features of the National Airspace System (graph theoretic)
2. Automated model building (aggregation procedure)
3. Parameter identification (travel time)
4. Model Analysis (storage)
5. Model validation
6. Capacity assessment and control (in progress)1. Delays that can be absorbed
2. Aircraft that can be stored
3. Stability of the storage (backpropagation)
![Page 39: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/39.jpg)
IP: Formulation
Challenges >1M variables, >1M constrains.
CPLEX: <6 minute running time (LP)
[Borelli 2003, Feron 2000, Bertsimas 1997] [Robelin, Sun, Wu, Bayen 2006]
![Page 40: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/40.jpg)
Overload control
![Page 41: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/41.jpg)
Eulerian models
1. Eulerian models scale well: complexity is independent of number of aircraft
2. Control volume based: appropriate for capacity analysis
3. Linear features make them suitable for analysis
4. Can rely on control theory for controllability, observability
5. Combinatorial optimization algorithms can be applied
Generic features of Eulerian models
Features of the current model
1. Can take any set of ETMS/ASDI data as input
2. Eulerian model, validated against ETMS/ASDI data
3. Compared to 2 other existing models (AIAA GNC 2006)
4. Interface with FACET
![Page 42: Towards a scientific basis for determining En Route capacity Alex Bayen Charles Roblin Dengfeng Sun Guoyuan Wu University of California, Berkeley Department](https://reader038.vdocument.in/reader038/viewer/2022103022/56649cc55503460f9498e1c6/html5/thumbnails/42.jpg)
Acknowledgments
UC Berkeley: Mark HansenNASA Ames: Banavar Sridhar, Kapil Sheth, Shon Grabbe, George MeyerFAA: Dave Knorr CNA: Doug Williamson