Aircraft Arrival Sequencing Group members: Sponsor and mentor: - - PowerPoint PPT Presentation

• May 11, 2007

Group members: Vivek Kumar David Teale Jianfeng Wang Seth Wenchel (Team Lead) Sponsor and mentor:

• Dr. Lance Sherry, Associate Professor
• Dr. John Shortle, Associate Professor

SEOR Dept. George Mason University

Aircraft Arrival Sequencing

2

• Outline

Motivation Problem Statement and Approach

• Strategies (FCFS, WCG, Optimization Strategies)
• Constraints and assumptions
• Performance metrics

Methods

• FCFS
• Optimization Strategies

– Optimization using MPL – Sequential optimization using C++ to call MPL

• WCG

Results

• LaGuardia Case Study

Conclusions and Future Work Questions

3

• Situation

Stakeholders:

Air Traffic Control Airlines Passengers (PAX)

Concerns:

Vehicle Throughput Vehicle Delay Airline Fairness PAX Delay

4

• Motivation
• Air Traffic Control uses first come, first

served (FCFS) queueing discipline to sequence arrival aircraft.

• This is not always the best for every

stakeholder.

• What strategies might be better?

5

• Problem Statement

runway 5 miles 2 min

Given multiple competing interests, how can arrivals be sequenced fairly and efficiently?

6

• Approach Overview

Strategies Different constraints, assumptions Flight schedule

• Scheduled arrival time
• Aircraft type/seats
• Airline

Actual reshuffled sequence Performance metrics

• Passenger transportation
• Vehicle transportation
• Service

7

• Strategies for Resequencing

Heuristic Resequencing

• 1. First come, first served {FCFS}
• 2. Weight Class Grouping {WCG}

Optimization Strategies for Resequencing

• 1. Vehicle throughput maximization {V_thrpt}
• 2. Vehicle delay minimization {V_delay}
• 3. Passenger delay minimization {P_delay}
• 4. Airline fairness maximization {A_fair}

8

• Constraints And Assumptions
• Treating data as deterministic
• All aircraft show up on time before final approach
• No early arrivals allowed
• Aircraft cannot be delayed more than 30 minutes
• All flights seats are full
• Arrival slot size differs by aircraft type because of

wake-vortex categories

9

• Wake-Vortex Categories

Separation standard Larger aircraft generate stronger turbulence than smaller aircraft. Larger aircraft can also withstand more turbulence than smaller

• nes.

Hence, a smaller plane following a larger plane will always require more separation than a larger plane following a smaller plane.

120 83 77 72 Small 182 83 77 72 Large 271 121 103 96 B757 280 157 137 96 Heavy Leading aircraft Small Large B757 Heavy Trailing aircraft Time Separation (sec) If all planes are Large, then 43 arrivals per hour (in theory)

10

• System Metrics
• Throughput = Entities / Unit Time
• Capacity = Upper limit of throughput
• Utilization = Throughput / Capacity

Delay Throughput capacity

Tradeoff between delay and utilization

11

• System Metrics

Flight delay: delayi = arrival_timei – sched_timei Ave Veh Delay = Ave PAX Delay = Ave PAX Delay per airline (k) =

(for flights in contention with others)

Sk is the set of flights of airline k in contention

*

i i i i i

PAX delay PAX      

∑ ∑

i i

delay N

∑

i is the flight index i = 0 to N N is the number of flights to be sequenced PAXi = Total number of Passengers on flight i

∑ ∑

∈ ∈ Sk i PAX Sk i delay PAX

i i i *

12

• Optimization Strategies: Objective Functions
• Vehicle throughput

MIN timelastplane

V_thrpt

• Vehicle delay

MIN

V_delay

• PAX delay

MIN

P_delay

• Airline fairness

MIN A_fair

(spread the penalty)

                            ∈ ∈

∑ ∑

Sk i PAX Sk i delay PAX k Max

i i i *

∑

i i i delay

PAX *

∑

i i

delay

13

• MIP (Mixed Integer Program)

Decision variables in Blue:

ti is assigned landing time

Data:

M is a large constant tseparation(i,j) is known based on plane sizes

MIN Z = OBJECTIVE FUNCTION SUBJECT TO:

ti – tj ≥ tseparation(j,i) – M yij

for j>i

tj – ti ≥ tseparation(i,j) – M (1-yij)

for j>i

Every pair of planes (independent of relative order) is separated by at least the minimum safety requirement

1 flight j follows flight i

• therwise

ij

y   =    

14

• Approaches: Optimization Using C++

Problem : Computation time for MIP increases rapidly with number of flights considered Workaround

• Exploit problem structure
• Optimize small windows. Things to consider:
• Window size
• Windows should overlap

Arrive for sequencing

• ptimize and slide window

15

• Sequential Optimization - Flow chart

MPL Optimization code

Start Central Application ( C++) OPTIMAX Library 2 1 a 1 b 3 All flights Sequenced? Stop No Yes trigger

Consolidated Input Data

• Arrival time, size, # PAX..

Current EXCEL sheet for Input DATA FINAL OUTPUT EXCEL sheet

4 Return winning flight index

16

• Window Size: Speed vs Efficiency Trade-Off

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Minutes

Ave PAX Delay Ave Veh Delay Processing time Vs Window Size

1000 2000 3000 4000 5000 6000 7000 5 6 7 8 9 10

Window Size

Processing time(seconds)

V_thrpt V_delay

Window Size 5 7 10

Speed Efficiency Conclusion: Without compromising too much on Efficiency we make

considerable gain in Processing Speed. Hence, windowing works!!

17

• Same Weight Class Grouping
• Objective is to provide a strategy that gives
• better performance than FCFS
• faster implementation than optimization strategies
• Heuristics to sequence aircraft landing

1. Similar to knapsack heuristics 2. If there is a gap between adjacent flights, use FCFS 3. If there is not a gap between adjacent flights

• choose same weight class aircraft if available
• choose next weight class aircraft if same weight class unavailable

Small Small Large Large B757 B757 Heavy

18

• Same Weight Class Grouping
• Reasoning behind the heuristic
• Arbitrary sequence of different weight class

aircraft requires long separation overall

• Grouping same weight class requires shorter

time to land all aircraft

• RESULTS

Case Study: New York’s LaGuardia Airport June 1st, 2006

20

• Example Resequencings

For the given sequence: S←L←B←S

(assuming they have same scheduled arrival time)

Strategy Resultant Sequence: FCFS: S←L←B←S V_thrpt: S←S←L←B V_delay: S←S←L←B P_delay: B←L←S←S WCG: S←S←L←B

S: Small L: Large B: B757

21

• LGA Case Study: Input Data

FAACARRIER FLTNO ETMS_EQPT DEP_LOCID ARR_LOCID SCHINTM TCF 6453 E170 DFW LGA 00:04 CHQ 3028 E145 PHL LGA 00:16 FFT 514 A319 DEN LGA 06:15 DAL 1905 MD88 BOS LGA 06:59 COM 618 CRJ1 DCA LGA 06:59 USA 2158 A319 DCA LGA 06:59 PDT 4110 DH8B MHT LGA 07:00 USA 2115 A319 BOS LGA 07:07 CHQ 3108 E145 BWI LGA 07:12 AWI 3716 CRJ2 PHL LGA 07:12 EGF 867 E135 BGR LGA 07:15 CJC 4880 SF34 ITH LGA 07:15 CHQ 3276 E145 RIC LGA 07:17 EGF 863 E135 CMH LGA 07:18 … … … … … …

ETMS_NAME TYPICAL_SEATS EDMS_AIRFRAME A124 8 B747-200 A300 250 A300-600 A30062 266 A300-B4-622R A306 266 A300-B4-605R A30B 250 A300B A310 220 A310 A318 107 A318 A319 124 A319 A32 164 A320 A320 164 A320 A32023 150 A320-200 A321 199 A321 A32123 199 A321 A330 295 A330 A33034 295 A330-300 … … … Aircraft type Weight catogory A319 L A320 L A321 L B190 S B712 L B732 L B733 L B734 L B735 L B737 L B738 L B752 B757 B763 L … …

ASPM data, June, 1, 2006 Separation standard Aircraft weight category Number of seats

120 83 77 72 Small 182 83 77 72 Large 271 121 103 96 B757 280 157 137 96 Heavy Leading aircraft Small Large B757 Heavy Trailing aircraft Time Separation (sec)

22

• FAACARRIER FLTNO ETMS_EQPT DEP_LOCID ARR_LOCID SCHINTM

TCF 6453 E170 DFW LGA 00:04 CHQ 3028 E145 PHL LGA 00:16 FFT 514 A319 DEN LGA 06:15 DAL 1905 MD88 BOS LGA 06:59 COM 618 CRJ1 DCA LGA 06:59 USA 2158 A319 DCA LGA 06:59 PDT 4110 DH8B MHT LGA 07:00 USA 2115 A319 BOS LGA 07:07 CHQ 3108 E145 BWI LGA 07:12 AWI 3716 CRJ2 PHL LGA 07:12 EGF 867 E135 BGR LGA 07:15 CJC 4880 SF34 ITH LGA 07:15 CHQ 3276 E145 RIC LGA 07:17 EGF 863 E135 CMH LGA 07:18 … … … … … …

ASPM data, June, 1, 2006

Input: Flight Schedule

23

• Input: Aircraft Separation Standard

120 83 77 72 Small 182 83 77 72 Large 271 121 103 96 B757 280 157 137 96 Heavy Leading aircraft Small Large B757 Heavy Trailing aircraft Time Separation (sec)

24

• Aircraft weight category

Input: Aircraft Weight Category

Aircraft type Weight category B738 Large B752 B757 B763 Large C560 Small C750 Large CL60 Small CRJ1 Large … …

25

• ETMS_NAME TYPICAL_SEATS

EDMS_AIRFRAME A124 8 B747-200 A300 250 A300-600 A30062 266 A300-B4-622R A306 266 A300-B4-605R A30B 250 A300B

Number of seats

Input: Aircraft Seat Information

26

• Pre-Scheduled LGA Arrival Rate

5 10 15 20 25 30 35 40 45 2 4 6 8 1 1 2 1 4 1 6 1 8 2 2 2

Hour of Day Number of Flights

Fleet mix: 90% Large 7% B757 3% Small

27

• Benchmark: LGA Results (FCFS)

Ave flight delay: 4.9 min Ave pax delay: 4.7 min 85% of flights delayed and 39% have delay >5 min

2 4 6 8 10 12 14 16 18 20 0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00 Time of Day D elay, m in

28

• LGA Results: Vehicle (Flight) Delay

4.9 4.7 5.0 4.3 5.2 4.5

1 2 3 4 5 6 FCFS V_Thrpt P_Delay V_Delay A_Fair WCG

Model Minutes

29

• LGA Results: PAX Delay

4.7 5.2 2.7 4.6 5.1 4.2

1 2 3 4 5 6 FCFS V_Thrpt P_Delay V_Delay A_Fair WCG

Model Minutes

30

• LGA Hourly PAX Delay
• 2

4 6 8 10 12 14 2 4 6 8 1 1 2 1 4 1 6 1 8 2 2 2 Hour of Day Average Pax Delay, min

FCFS V_thrpt V_delay P_delay A_fair WCG

31

• Pax Delay: P_delay Results

100 200 300 400 500 100 200 300 400 500 Presorted Position Sorted Position

Amount of Re-Sequencing Where does P_delay assign the most delay?

1 5 22

5 10 15 20 25

B757 Large Small Ave Veh Del, min

32

• PAX Delay And Vehicle Delay

2 3 4 5 6 2 3 4 5 6 Ave Pax Delay, min A v e V e h D e la y , m in

FCFS V_thrpt P_delay V_delay A_fair WCG Ave Veh Del * Ave PAX Delay

5 10 15 20 25 30 P_delay WCG V_delay FCFS V_thrpt A_fair Delay Product, min^2

33

• LGA: Airline Fairness

Comparison of FCFS and A_fair

1 2 3 4 5 6 7 8 9 10 A m e r i c a n A i r l i n e s A i r C a n a d a A m e r i c a n T r a n s A i r C h a u t a u q u a A i r l i n e s C

• l

g a n A i r C

• n

t i n e n t a l A i r l i n e s C

• m

a i r D e l t a A i r l i n e s A m e r i c a n E a g l e J e t B l u e M i d w e s t E x p S p i r i t A i r l i n e s N

• r

t h w e s t A i r l i n e s U s a i r E x p A i r t r a n A i r l i n e s U n i t e d A i r l i n e s U s a i r Airline Average delay per PAX FCFS A_fair

6.5 7.4 Range 5.9 5.0 Ave A_fair FCFS PAX Delay

34

• Conclusions
• Little to no gains seen over FCFS for V_trpt,

V_delay, A_fair, and WCG

• Input data is very homogenous
• LGA is operating at or near capacity for most of the day
• Airline fairness maximization gives worst

performance in terms of vehicle delay and passenger delay

• Constraints are imposed without considering delay metrics
• PAX_delay model shows gains at the cost of smaller

flights

• Delaying small aircraft (3% of the fleet mix) reduces

average passenger delay significantly.

35

• Improvements and Future Work
• Optimize multiple weighted objectives at once
• Allow flights to arrive early by a small amount
• Weight A_Fair by number of flights scheduled
• Look for a more heterogeneous data set
• Only process slots where there are collisions
• Increase number of flights that get fixed at each

iteration

36

• Acknowledgements

Thanks to our sponsors, Dr. Shortle and Dr. Sherry from GMU’s Center for Air Transportation Systems Research for their continued guidance and encouragement through the semester and to Dr. Laskey for helping us improve our presentation and keeping us on track.

• Questions

• Back up

39

• Multi Objective Optimization

Airline Fairness Vehicle throughput PAX delay Vehicle delay Different Strategies A B D C E F

A strategy represents a different approach to solving the problem such as FCFS.

40

• LGA Schedule, Delay

0.0 1.0 2.0 3.0 4.0 5.0 6.0 F C F S T

• 5

T

• 7

T

• 1

D

• 5

D

• 7

D

• 1

V

• 5

V

• 7

V

• 1

A i r l i n e

Model (code - window) Minutes

Ave PAX Delay Ave Veh Delay T = throughput, D = Pax delay, V = Veh delay

41

• LGA Case Study: Complexity

FT = FCFS with throughput opt FD = FCFS with delay opt FTD = FCFS with delay and throughput opt T = throughput opt D = delay opt TD = delay and throughput opt Run statistics: [for non-FCFS: number of integer variables ~ O(N2) ] MODEL FLIGHTS SOLN TIME, SEC FT 50 30 FD 40 30 FTD 40 30 T 20 10 D 15 1 TD 15 1

42

• Research

Analysis of Sequencing and Scheduling Methods for Arrival Traffic, 1990 Polynomial Time Feasibility Condition for Multi-Class Aircraft Sequencing on a Single Runway Airport, 2004 Air Transportation: A Tale of Prisoners, Sheep and Autocrats, 2007 Equitable Allocation of Limited Resources, 2003 Potential Benefits of a Time-based Separation Procedure to maintain the Arrival Capacity of an Airport in strong head-wind conditions

43

• LGA results: passenger delay in a year

50000 100000 150000 200000 250000 300000 FCFS V_thrpt P_delay V_delay A_fair WCG Total Pax Delay, psn minutes

44

• Inter-arrival landing time constraint

Constraint based on specified number of nautical miles We consider it based on time (varies with wind speed and direction HLHL inter-arrival delay is ~5½ min Single shift to HHLL delay becomes ~5 min

Large Heavy Large 3 3 Heavy 5 4 First to land Second to Land Separation in nm Large Heavy Large 78 78 Heavy 125 104 First to land No wind Separation in sec Second to Land Large Heavy Large 91 91 Heavy 145 122 20 Knot head wind Separation in sec Second to Land First to land

45

• LGA: Vehicle Utilization

Overall utilization = 0.511 for all models Hourly throughput varies by 1-2 flights

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 2 4 6 8 10 12 14 16 18 20 22 Hour of Day Utilization FCFS V_thrpt P_delay V_delay A_fair WCG

Assumes: Veh capacity = 40 /hr (all Large)

46

• LGA: Pax Utilization

Overall utilization = 0.483 for all models

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 4 6 8 10 12 14 16 18 20 22 Hour of Day Utilization FCFS V_thrpt P_delay V_delay A_fair WCG Assumes: Veh capacity = 40 /hr (all Large) and 100 pax/veh

47

• LGA Results: Delay

4.7 5.2 2.7 4.6 5.1 4.2 4.9 4.7 5.0 4.3 5.2 4.5

1 2 3 4 5 6 FCFS V_Thrpt P_Delay V_Delay A_Fair WCG

Model

Minutes

Ave PAX Delay Ave Veh Delay

48

• LGA: Airline Fairness

1 2 3 4 5 6 7 8 9 10 500 1000 1500 2000 2500 Total Pax In Contention From Airline k Ave Pax Delay For Airline k, m in . A_fair FCFS