efficiency and equity tradeoffs in rationing airport arrival slots preliminary results

Efficiency and Equity Tradeoffs in Rationing Airport Arrival Slots

Preliminary Results

Taryn [email protected]

Robert Hoffman, [email protected]

Metron Aviation, Inc.Herndon,Virginia

mailto:[email protected]

mailto:[email protected]

04/20/23 2

Single Airport GDP

• A Ground Delay Program (GDP) is a traffic management initiative used to control the arrival flow into a single airport– The arrival flow is controlled by reducing the airport

acceptance rate (AAR), therefore reducing the number of flights the airport can handle

– Arrival slots are allocated using the Ration-by-Schedule (RBS) algorithm + compression

04/20/23 3

RBS Algorithm in a Nutshell

• RBS is a greedy algorithm• Algorithm:

1. AAR is established by traffic flow management (TFM) for specific hours

2. Arrival slots are determined by dividing each hour into the number of slots determined by the AAR• E.g. If AAR=30 flights/hour, then the hour is divided into 30

arrival slots: 1 slot every 2 minutes

3. Flights are assigned to slots based on their scheduled and earliest arrival times, and such that the AAR is not exceeded (essentially, first-scheduled first-served)

04/20/23 4

Multi-fix GDP

• A Multi-fix GDP expands the control of arrivals out to the arrival fixes for a single airport– The AAR may be reduced at the airport and at any of

the arrival fixes

– Multiple flow constraints instead of one

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Why a Multi-fix GDP?

• More precise airport flow is needed for– Fix load balancing (juggle flights between fixes)

– Lowered capacity may occur at some (but not all) of the fixes

– Demand surges can occur at some fixes but not others

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Multi-fix GDP Complications

• A flight’s arrival fix is not always predictable• Fix capacities are difficult to estimate because

they are mutually dependent– Wx not very predictable hours in advance

• TFM might over-control the airport

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How would Multi-fix RBS work?

1. AAR and fix arrival rates (FARs) are established2. Arrival slots are determined for the airport3. Establish arrival bins for each fix

• Divided the FAR equally among the bins• E.g. If FAR=40 and 15-min bins are established, then no more

than 10 flights may arrive every 15 minutes

4. Assign flights to arrival slots based on scheduled and earliest arrival times such that the AAR and the FAR are not exceeded

5. If the flight can not be assigned to a slot without exceeding the FAR, skip that flight and move to the next flight

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Comparison

AirportSW

NE

NW

SE Airport arrival flow

Fix arrival flows

Multi-fix GDP

Airport and fix arrival flows are controlled

Single Airport GDP

Airport

Only airport arrival flow is controlled

Airport arrival flow

04/20/23 9

Counter-example

A

B

Flights Fixes Airport

g

Period 1

f

11

1

A

B

Period 2

01

1

A

B

Period 3

11

1

2 delay units

A

B

Flights Fixes Airport

g

Period 1

f

11

1

A

B

Period 2

01

1

A

B

Period 3

11

1

1 delay unit

Suboptimal solution from greedy algorithm. One of two flights must be delayed to a later time period, due to airport capacity constraint in period 1. If flight g is delayed, then it must be delayed two time periods due to constraints at fix B (left). However, if flight f is delayed, then only one time period of delay will result (right).

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Purpose

• The purpose of this study is to examine efficiency versus equity tradeoffs in allocating NAS resources– The resources are the arrival slots at an airport or at an

arrival fix– The optimization model used in this study seeks to

allocate resources efficiently (disregards equity)– The prototype software used allocates resources

“equitably” (in a manner similar to what is done now)

• A comparison is also made between the two solutions

04/20/23 11

Optimization Model

• Integer program model, similar to an assignment problem

• For this analysis, delay is defined as the difference between an assigned arrival time/slot and the earliest scheduled arrival time/slot that the flight could use – The delay coefficient in the objective function is the difference between

the earliest available slot for a flight and all possible slots for the same flight

• Variables:

• The objective is to assign flights as early as possible, therefore minimizing delay

fetaearliesttslottft_eta – earliest slot fDelay _

GDP n thehour withiquarter every for slot hour quarter theis _

, __

11 ttafix

SlotsAirporttFixesArrivalislotafixacid ti

04/20/23 12

Optimization Model

• The following is a mathematical description of the model objective and constraints:

1

21211

_

__

:Integer

4

, 1__

:Bounds

1__:c3

bin,slot fix theis ),( where),( 0_ ) __(:c2

1__:c1

:subject to

)__(*Minimize

tafix

slotafixacid

fixesarrivalfFAR

afix

slotstflightsislotafixacid

slotstslotafixacid

fixesarrivalfttttttafixslotafixacid

flightsislotafixacid

slotafixaciddelay

ti

f

ti

flightsiti

afixafixflightsi slotst

ti

slotstti

i tti

i

04/20/23 13

Prototype Software

• A prototype resource allocation tool was used to execute the greedy algorithm– RBS++ algorithm adapted to multiple fix constraints

• The tool was developed by Metron Aviation, Inc.

04/20/23 14

Test Sets

• The prototype program was used to output flight information for the following airports, dates, times (Zulu):

AIRPORT DATE GDP BEGIN GDP END # FLIGHTS

ATL 11/13/2002 1800 0200 585

DFW 11/13/2002 1600 2300 477

JFK 11/13/2002 2100 0100 134

ORD 11/13/2002 1900 0100 547

SFO 11/14/2002 1700 0100 208

04/20/23 15

Experiments

• There were two cases explored for each experiment:– Case 1

• The airport is constrained during the GDP and then returns to the maximum capacity after the GDP

• The fixes are not constrained• Analogous to a single airport GDP• This case is used to determine if the CPLEX model

and greedy algorithm agree on the single airport, single constraint case

– Case 2• The airport is constrained during the GDP and then

returns to the maximum capacity after the GDP• The arrival fixes are constrained during the GDP

and then return to the maximum capacity after the GDP

• Analogous to a multi-fix GDP

Reduced airport capacity

Consistent fix capacity

Case 1

Reduced airport capacity

Reduced fix capacity

Case 2

04/20/23 16

ATL Results

• Case 1– % difference = 0.270

– Run time = 1113.89 sec

• Case 2– % difference = 0.268


Solutions are essentially the same

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DFW Results

• Case 1– % difference = 0.012%


• Case 2– % difference = -5.521%


Greedy algorithm is slightly suboptimal

04/20/23 18

JFK Results





Greedy algorithm is slightly suboptimal

04/20/23 19

ORD Results




– Run time = 853.16

Greedy algorithm is substantially suboptimal

04/20/23 20

SFO Results





Greedy algorithm is highly suboptimal

04/20/23 21

Additional SFO Experiments

• Additional experiments were conducted for SFO to further investigate the large percent difference in Case 2

• The following are the parameters used:

AIRPORT DATE GDP BEGIN GDP END # FLIGHTS

SFO 11/14/2002 1700 0100 208

SFO 11/19/2002 1700 0100 211

04/20/23 22

SFO Experiment 2






04/20/23 23

SFO Experiment 3



• Case 2– % difference = -19.335



04/20/23 24

All Results

Airport Case 1 Case 2

ATL 0.270% 0.268%

DFW 0.012% -5.521%

JFK 0.156% -9.525%

ORD 1.131% -13.199%

SFO 1 1.759% -24.563%

SFO 2 -0.359% -31.031%

SFO 3 1.561% -19.335

04/20/23 25

Conclusions

• The greedy algorithm assigned slightly less delay in all but one Case 1 experiment– Assume greedy algorithm is optimal

– Optimization model is a good match

– Little, if any, tradeoff between equity and efficiency in the single-constraint case

• The model performed better than the greedy algorithm in all but one Case 2 experiment– Greedy algorithm is suboptimal

– Sizeable tradeoff between equity and efficiency in the multi-constraint case

04/20/23 26

Conclusions

• RBS approach greedy algorithm is not an optimization model and is quite complicated

• There are some differences in the way the model and the prototype software create available slots at the airport, which may account for the large differences in Case 2– The CPLEX model does RBS and Compression in one step but the

greedy algorithm does these in two separate steps• RBS throws away slots that flights do not get assigned to and

therefore, when Compression looks to move flights to earlier slots, those earlier slots are no longer there

• The CPLEX model does not throw away any slots and can therefore move flights to slots as early as the earliest_eta for the flight

• RBS does not use the earliest_eta, but Compression does– Cancelled flights are handled a little differently in the greedy algorithm

04/20/23 27

Conclusions

• A flight-by-flight analysis and an in-depth analysis of the greedy algorithm is necessary to determine why certain flights were assigned to certain slots

• Greedy Algorithm– Multi-queue problem may not make optimal use of the

airport slots

– Single queue problem is almost always optimal

efficiency and equity tradeoffs in rationing airport arrival slots preliminary results

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