[PPT] - Air Traffic Flow Management for the National Airspace System PowerPoint Presentation

SLIDE 1

Air Traffic Flow Management for the National Airspace System

Christopher Maes

MIT Operations Research Center

November 21, 2011

SLIDE 2

Outline

1 Model formulation 2 Estimating model parameters 3 Performance analysis and preliminary results 4 Conclusions and further work

SLIDE 3

Model formulation

SLIDE 4

Bertsimas, Lulli, and Odoni model

Planes fly between airports and through

sectors with defined capacity

Deterministic and discrete time model
Produces an optimal assignment of delays to flights
Flights may be dynamically rerouted to avoid congestion
Origin-destination routes represented as directed acyclic graph
rigf

i j destf Lf

i

Pf

j Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

SLIDE 5

Bertsimas, Lulli, and Odoni model

Planes fly between airports and through

sectors with defined capacity

Deterministic and discrete time model
Produces an optimal assignment of delays to flights
Flights may be dynamically rerouted to avoid congestion
Origin-destination routes represented as directed acyclic graph
rigf

i j destf Lf

i

Pf

j

Lf

i Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

SLIDE 6

Bertsimas, Lulli, and Odoni model

Planes fly between airports and through

sectors with defined capacity

Deterministic and discrete time model
Produces an optimal assignment of delays to flights
Flights may be dynamically rerouted to avoid congestion
Origin-destination routes represented as directed acyclic graph
rigf

i j destf Lf

i

Pf

j

Lf

i

Pf

j Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

SLIDE 7

Bertsimas, Lulli, and Odoni model

Planes fly between airports and through

sectors with defined capacity

Deterministic and discrete time model
Produces an optimal assignment of delays to flights
Flights may be dynamically rerouted to avoid congestion
Origin-destination routes represented as directed acyclic graph
rigf

i j destf Lf

i

Pf

j

[T f

i , T f i ] Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

SLIDE 8

Bertsimas, Lulli, and Odoni model

Planes fly between airports and through

sectors with defined capacity

Deterministic and discrete time model
Produces an optimal assignment of delays to flights
Flights may be dynamically rerouted to avoid congestion
Origin-destination routes represented as directed acyclic graph
rigf

i j destf Lf

i

Pf

j

u v liu liv

Christopher Maes Air Traffic Flow Management for the NAS 3 / 24

SLIDE 9

Decision variables

wf

j,t =

1

if flight f arrives at sector j by time t

therwise

wf

j,t only defined for those sectors j in f ’s graph, within the feasible

time interval [T f

j , T f j ]

t T f

j

T

f j

wf

j,t

wf

j,t−1

wf

j,t+1

Christopher Maes Air Traffic Flow Management for the NAS 4 / 24

SLIDE 10

Constraints

Capacity Constraints

1 # flights arriving at airport k at time t must not exceed Ak(t) 2 # flights departing airport k at time t must not exceed Dk(t) 3 # flights in sector j at time t must not exceed Sj(t)

Christopher Maes Air Traffic Flow Management for the NAS 5 / 24

SLIDE 11

Constraints

Capacity Constraints

1 # flights arriving at airport k at time t must not exceed Ak(t) 2 # flights departing airport k at time t must not exceed Dk(t) 3 # flights in sector j at time t must not exceed Sj(t)

Turnaround time for connecting flights

4 If (g, f ) are a pair of connecting flights,

flight f cannot depart until sf minutes after g has arrived g f

Christopher Maes Air Traffic Flow Management for the NAS 5 / 24

SLIDE 12

Constraints

Capacity Constraints

1 # flights arriving at airport k at time t must not exceed Ak(t) 2 # flights departing airport k at time t must not exceed Dk(t) 3 # flights in sector j at time t must not exceed Sj(t)

Turnaround time for connecting flights

4 If (g, f ) are a pair of connecting flights,

flight f cannot depart until sf minutes after g has arrived g f Definition of decision variables

5 If f has arrived at j by time t, it has arrived by time t + 1

Christopher Maes Air Traffic Flow Management for the NAS 5 / 24

SLIDE 13

Rerouting constraints

Sector traversal time

6 A flight cannot arrive at sector j by time t if it

has not arrived at a preceding sector j′ ∈ Pj by time t − lf

j′j

j

Christopher Maes Air Traffic Flow Management for the NAS 6 / 24

SLIDE 14

Rerouting constraints

Sector traversal time

6 A flight cannot arrive at sector j by time t if it

has not arrived at a preceding sector j′ ∈ Pj by time t − lf

j′j

j

Subsequent sector

7 If flight f has arrived in sector i by T f i , it must

arrive in at least one sector i′ ∈ Lf

i by T f i′ 8 Flight f can be in at most one sector

i′ ∈ Lf

i by T f i′

i

Christopher Maes Air Traffic Flow Management for the NAS 6 / 24

SLIDE 15

Rerouting constraints

Sector traversal time

6 A flight cannot arrive at sector j by time t if it

has not arrived at a preceding sector j′ ∈ Pj by time t − lf

j′j

j

Subsequent sector

7 If flight f has arrived in sector i by T f i , it must

arrive in at least one sector i′ ∈ Lf

i by T f i′ 8 Flight f can be in at most one sector

i′ ∈ Lf

i by T f i′

i

Total flight time

9 The total flight time must not exceed the maximum duration

f the flight

Christopher Maes Air Traffic Flow Management for the NAS 6 / 24

SLIDE 16

Model parameters

Airport capacities Ak(t), Dk(t) for all airports k, time t
Sector capacities Sj(t) for all sectors j, times t
The directed acyclic graphs that describe the flight routes
Time intervals: [T f

j , T f j ]

Time to fly from sector i to sector j: lf

ij

Maximum flight duration: maxf
Connecting flight pairs (g, f ) and turnaround time sf

Christopher Maes Air Traffic Flow Management for the NAS 7 / 24

SLIDE 17

Estimating model parameters

SLIDE 18

Data sources

Model requires large amounts of data from multiple sources Data from John Cho, Richard DeLaura, and Ngaire Underhill:

ETMS provides sector entrance/exit times for flight graphs
SDAT provides sector entrance/exit times for flights
ASPM provides arrival and departure times for flights
RITA provides delay information and tail numbers

(for tracking connecting flights)

APM provides airport arrival and departure capacities
Weather-impacted sector capacities from workload model of

Cho, Welch, Underhill

Christopher Maes Air Traffic Flow Management for the NAS 8 / 24

SLIDE 19

Airport capacities

Estimates from two months of historical APM data
Number of arrivals and departures in 15 min interval
Construct estimates for different runway configurations and

weather conditions (VMC or IMC)

Christopher Maes Air Traffic Flow Management for the NAS 9 / 24

SLIDE 20

Airport capacities

Estimates from two months of historical APM data
Number of arrivals and departures in 15 min interval
Construct estimates for different runway configurations and

weather conditions (VMC or IMC)

Christopher Maes Air Traffic Flow Management for the NAS 9 / 24

SLIDE 21

Weather-impacted sector capacities

Use impacted sector capacities from Cho, Welch, Underhill
Use SDAT data to compute fraction of time spent in sector for

each non-model flight

Lower sector capacities to account for non-model flights

10 20 30 40 50 60 2 4 6 8 10 12 model time ZHU 63 capacity and utilization 10 20 30 40 50 60 0.2 0.4 0.6 0.8 1 model time wx Blockage Fraction

Christopher Maes Air Traffic Flow Management for the NAS 10 / 24

SLIDE 22

Time spent in sector

Model uses 15 minute time intervals
Necessary to obtain airport and sector capacities
Flights often spend much less than 15 min in a sector
Drop sectors occupied for less than 8 minutes
Maintains total flight time (through [T f

j , T f j ], lf j′j)

But ignores effect on sector capacity

5 10 15 20 25 30 35 40 2 4 6 8 10 12 14 x 10

4

minutes Distribution of sector crossing times

Mean: 9.6 minutes

Christopher Maes Air Traffic Flow Management for the NAS 11 / 24

SLIDE 23

Constructing flight graphs

Use 25 days of ETMS data to construct a graph of sectors traversed by flights (e.g. flights from JFK to LAX):

Christopher Maes Air Traffic Flow Management for the NAS 12 / 24

SLIDE 24

Constructing flight graphs

Use 25 days of ETMS data to construct a graph of sectors traversed by flights (e.g. flights from JFK to LAX):

JFK ZBW 09 ZBW 38 ZDC 04 ZDC 42 ZID 79 ZID 97 ZNY 07 ZNY 08 ZNY 09 ZNY 10 ZNY 34 ZNY 42 ZNY 49 ZNY 56 ZNY 72 ZNY 73 ZOB 57 ZOB 59 ZOB 67 ZOB 68 ZOB 69 ZOB 79 ZMP 12 ZDC 03 ZDC 07 ZDC 37 ZDC 52 ZDC 72 ZID 96 ZID 95 ZLA 39 ZID 70 ZID 92 ZID 93 ZID 94 ZME 63 ZAU 47 ZAU 83 ZID 76 ZID 78 ZID 98 ZID 99 ZKC 98 ZOB 64 ZOB 36 ZOB 37 ZOB 38 ZOB 39 ZOB 77 ZOB 45 ZAU 52 ZOB 48 ZOB 49 ZAU 33 ZID 87 ZOB 66 ZID 77 ZOB 47 ZOB 26 ZAU 60 ZAU 61 ZMP 13 ZTL 15 ZTL 42 LAX ZID 91 ZME 61 ZME 33 ZKC 14 ZME 25 ZID 82 ZME 62 ZME 35 ZME 26 ZME 27 ZAU 91 ZAU 95 ZAU 41 ZKC 92 ZKC 94 ZAU 45 ZKC 12 ZKC 32 ZKC 84 ZAU 76 ZAU 75 ZAU 90 ZAU 94 ZAU 92 ZID 80 ZID 89 ZAU 36 ZID 75 ZKC 21 ZLA 37 ZKC 33 ZKC 90 ZKC 31 ZID 88 ZOB 18 ZOB 27 ZOB 19 ZAU 23 ZOB 29 ZOB 07 ZAU 46 ZAU 84 ZID 66 ZAU 34 ZAU 25 ZAB 39 ZAB 92 ZLA 36 ZLA 53 ZAB 50 ZAB 58 ZAB 67 ZAB 68 ZAB 93 ZAB 70 ZDV 37 ZDV 38 ZDV 23 ZDV 24 ZLA 32 ZLA 35 ZAB 71 ZAB 72 ZAB 95 ZDV 30 ZAB 96 ZDV 46 ZAB 79 ZAB 94 ZDV 25 ZDV 65 ZDV 64 ZDV 04 ZAB 87 ZAB 97 ZAB 98 ZMP 15 ZMP 17 ZAU 71 ZMP 28 ZMP 30 ZMP 42 ZMP 43 ZMP 38 ZMP 19 ZMP 18 ZDV 09 ZDV 35 ZMP 29 ZMP 39 ZDV 08 ZDV 18 ZDV 67 ZKC 24 ZKC 41 ZDV 47 ZKC 26 ZAU 24 ZKC 47 ZKC 30 ZKC 03 ZKC 07 ZKC 06 ZKC 28 ZKC 02 ZKC 97 ZKC 29 ZDV 16 ZMP 20 ZDV 33 ZDV 17 ZDV 61 ZDV 39 ZKC 20 ZAU 85 ZAU 88 ZAU 89 ZDV 05 ZDV 14 ZKC 22 ZDV 29 ZMP 11 ZMP 22 ZMP 25 ZTL 40 ZTL 39 ZME 34 ZTL 02 ZTL 36 ZME 32 ZTL 37 ZDV 03 ZLC 34 ZLC 46 ZLA 33 ZLA 34 ZDV 28 ZLC 04 ZDV 34 ZLC 33 ZLC 44 ZDV 32 ZLC 16 ZLC 05 ZLC 18 ZLC 03 ZFW 26 ZFW 43 ZFW 51 ZFW 98 ZFW 49 ZKC 23 ZFW 47 ZFW 93 ZFW 48 ZFW 50 ZFW 90 ZKC 27 ZME 19 ZME 22 ZID 81 ZME 28 ZME 20 ZME 21 ZME 44 ZME 31 ZOB 28

Christopher Maes Air Traffic Flow Management for the NAS 12 / 24

SLIDE 25

Constructing simple flight graphs

Need a way to simplify flight graphs
Consider two different paths from JFK to LAX

JFK ZNY 09 ZDC 04 ZLA 39 LAX JFK ZDC 04 ZID 72 ZLA 39 LAX

Define a metric on paths:

d(p1, p2) = max(|p1|, |p2|) − |p1 ∩ p2|

Select K unique paths that share many edges with
ther paths by solving:

minimize

{˜ pk}K

k=1

K

k=1
pj=˜

pk

d(˜ pk, pj) subject to ˜ pr = ˜ ps, ∀r, s

Christopher Maes Air Traffic Flow Management for the NAS 13 / 24

SLIDE 26

Constructing simple flight graphs

Graph is union of K unique paths (e.g. JFK to LAX with K = 10)

JFK ZNY 08 ZNY 10 ZOB 68 ZID 97 ZOB 64 ZOB 69 ZAU 47 ZID 98 ZID 99 ZID 87 ZAB 58 ZAB 67 ZAB 92 ZLA 39 LAX ZKC 94 ZKC 98 ZKC 33 ZKC 92 ZKC 03 ZKC 26 ZDV 24 ZLA 36 ZLA 37 ZDV 30 ZDV 38 ZDV 39 ZDV 46 ZID 78 ZKC 12 ZKC 84 ZKC 07 ZKC 21 ZKC 20 ZKC 24

Christopher Maes Air Traffic Flow Management for the NAS 14 / 24

SLIDE 27

Constructing simple flight graphs

Graph is union of K unique paths (e.g. JFK to LAX with K = 10)

These paths may lie in a cluster
Tactical rather than strategic rerouting
Might prefer graphs with more diverse routes

Christopher Maes Air Traffic Flow Management for the NAS 14 / 24

SLIDE 28

Performance analysis and preliminary results

SLIDE 29

Model information

Model includes:

All (302) high-altitude sectors within continental US
130 super-high-altitude sectors (missing ZOA and ZSE)
OEP 35 largest airports (excluding Honolulu)
Time frame: 9AM - midnight GMT
15 minute time intervals

Model used to analyze July 16th, 2010

Flight DAGs for 985/1122 airport pairs
3590 flights included in the model
1123 pairs of connecting flights
Adjust time intervals [T f

j , T f j ] by scheduled departure time df

Christopher Maes Air Traffic Flow Management for the NAS 15 / 24

SLIDE 30