Efficiency and Equity Tradeoffs in Rationing Airport Arrival Slots Preliminary Results

1. Efficiency and Equity Tradeoffs in Rationing Airport Arrival SlotsPreliminary Results Taryn Butler butler@metronaviation.com Robert Hoffman, Ph.D. hoffman@metronaviation.com Metron Aviation, Inc. Herndon,Virginia

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

3. RBS Algorithm in a Nutshell • RBS is a greedy algorithm • Algorithm: • AAR is established by traffic flow management (TFM) for specific hours • 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 • 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)

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

5. 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

6. 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

7. How would Multi-fix RBS work? • AAR and fix arrival rates (FARs) are established • Arrival slots are determined for the airport • 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 • Assign flights to arrival slots based on scheduled and earliest arrival times such that the AAR and the FAR are not exceeded • If the flight can not be assigned to a slot without exceeding the FAR, skip that flight and move to the next flight

8. Multi-fix GDP Single Airport GDP Fix arrival flows NW NE Airport Airport Airport arrival flow SE Airport arrival flow SW Airport and fix arrival flows are controlled Only airport arrival flow is controlled Comparison

9. Counter-example 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).

10. 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

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

12. Optimization Model • The following is a mathematical description of the model objective and constraints:

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.

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

15. Case 1 Reduced airport capacity Consistent fix capacity Case 2 Reduced airport capacity Reduced fix capacity 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

16. ATL Results • Case 1 • % difference = 0.270 • Run time = 1113.89 sec • Case 2 • % difference = 0.268 • Run time = 1141.81 sec Solutions are essentially the same

17. DFW Results • Case 1 • % difference = 0.012% • Run time = 409.93 sec • Case 2 • % difference = -5.521% • Run time = 494.14 sec Greedy algorithm is slightly suboptimal

18. JFK Results • Case 1 • % difference = 0.156% • Run time = 5.93 sec • Case 2 • % difference = -9.525% • Run time = 6.29 sec Greedy algorithm is slightly suboptimal

19. ORD Results • Case 1 • % difference = 1.131% • Run time = 1229.76 sec • Case 2 • % difference = -13.199% • Run time = 853.16 Greedy algorithm is substantially suboptimal

20. SFO Results • Case 1 • % difference = 1.759% • Run time = 34.68 sec • Case 2 • % difference = -24.563% • Run time = 26.86 sec Greedy algorithm is highly suboptimal

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:

22. SFO Experiment 2 • Case 1 • % difference = -0.359% • Run time = 16.05 sec • Case 2 • % difference = -31.031% • Run time = 15.40 sec Greedy algorithm is highly suboptimal

23. SFO Experiment 3 • Case 1 • % difference = 1.561% • Run time = 40.32 sec • Case 2 • % difference = -19.335 • Run time = 26.42 sec Greedy algorithm is highly suboptimal

24. All Results

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

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

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