NAS Performance Models. Michael Ball Yung Nguyen Ravi Sankararaman Paul Schonfeld Luo Ying University of Maryland

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1 NAS Performance Models Michael Ball Yung Nguyen Ravi Sankararaman Paul Schonfeld Luo Ying University of Maryland

2 FAA Strategy Simulator: analyze impact on NAS of major policy initiatives/changes significant infrastructure changes macro-economic shifts/demand shifts changes in industry structure Need to model airline and other user behavior as well as basic NAS behavior Challenge of performance modeling: predict NAS performance based on small number of key parameters

3 Performance Metrics Average Delay per Flight (more refined flight delay distribution info); % of flights on time. % of Flights Cancelled NAS-wide OAG Service level metric NAS-wide Actual Service level metric

4 Intuition: # Cancellations vs. # Flights Scheduled (capacity held constant) # Cancellations Z asymptotic slope = 1 # flights scheduled

5 Intuition: Delay vs. # of Flights Scheduled (capacity held constant) Avg. delay per flight # flights scheduled

6 ρ - Measure of congestion around a scheduled operation Assume an airport operation is either a flight departure or a flight arrival. Then for each operation, O, we compute ρ o as follows: Consider the time interval, I, starting h 1 hours before O is scheduled and h 2 hours after O is scheduled h 1 O h 2 time ρ o = # Operations scheduled during I at O s airport Capacity( in # operations) during I at O s airport ρ o is the queueing system utilization for an interval around O ; because of the way scheduling is done and also because of GDPs and other disruptions ρ o could sometimes be > 1

7 Cumulative Distribution of ρ Y = % of operations with ρ X Characterize distribution by a few parameters ρ 50 ρ 95 ρ 99 X= ρ

8 Distribution of ρ (or any of ρ 50, ρ 50, ρ 50 ) could be calculated for a single airport on a single day, the NAS on a single day, the NAS over a week, etc. For a given day, ρ is determined by the OAG schedule and the airport capacity profile for that day. Airport capacity on a given day depends on VMC/IMC status (VMC = visual meteorological conditions, IMC = instrument meteorological conditions), runway configuration, etc. ρ has potential to capture impact of weather and VMC/IMC capacity differences. Modeling challenge: Capacity + demand ρ average flight delay, flight cancellation probability.

9 Data Analysis For each day under consideration: Set up 24 1-hour buckets at each airport Determine number of scheduled operations (from OAG) Determine capacity (max number of ops) depends on IMC/VMC, runway config, etc Calculate ρ for each bucket assign this ρ value to each operation in bucket Create buckets based on ρ-values; create ρ distribution by combining data from all days and all airports under consideration.

10 Graph Avg Delay vs Rho50 Avg Del Rho50

11 Graph Avg Delay vs Rho95 Avg Del Rho95

12 Graphical Analysis Avg Del Rho99

13 Graph Pr Cancellation vs Rho50 Pr_Canc Rho50

14 Graph Pr Cancellation vs Rho95 Pr_Canc Rho95

15 Graph Pr Cancellation vs Rho99 Pr_Canc Rho99

16 Graphical Analysis Avg Del Rho95

17 Graphical Analysis Pr_Canc Rho95

18 Equations Average_Delay Avg_Del = < = Rho95 < 0.72 Avg_Del =0.178*EXP(4.3247*Rho95) 0.72 < = Rho95 < 1.09 Avg_Del = *(Rho95^2) *Rho < Rho95 < = 1.35 Avg_Del = LN(Rho95) 1.36 < = Rho95 < 1.49 R Square = 63.2% Probability Cancellation Pr_Cancel = <= Rho95 < 0.72 Pr_Cancel = *EXP(6.3406*Rho95) 0.72 <=Rho95<1.0 Pr_Cancel = 0.425*LN(Rho95) <= Rho95 < 1.49 R Square = 84.6%

19 NAS Performance scheduled demand for airport of type j non-scheduled demand for airport of type j VMC capacity of airport of type j IMC capacity of airport of type j rho for airport of type j RHO_AIRPORT % time w IMC for airport of type j % demand covered by airports of type j airport rho for NAS RHO50_NAS ave flight delay flight cancel probability FDELAY FCANCEL airline robustness factor Airspace rho for NAS airline creep factor P_EXTRA passenger performance metrics P_DELAY

20 Regression Analysis - Base Model Results of multiple regression for Ln(AvgDel_Flight_Min) Avg Delay (min) Delay Cancellation (90) Delay Cancellation (120) Delay Cancellation (150) Coeff p-value Coeff p-value Coeff p-value Coeff p-value Constant Rho Rho Rho R-Square 46.29% 50.09% 51.38% 52.21% Results of multiple regression for Ln(Pr_Canc) Coefficient p-value Constant Rho Rho Rho R-Square 45.38%

21 Regression Analysis - Improved Model Ln(AvgDel_Flight_Min) = Rho Rho Rho Month_Fall Month_Spring Pre 9/11_N Day_Mon Day_Tue Day_Wed Ln(Pr_Canc) = Rho Rho Rho Month_Fall Month_Spring Pre 9/11_N Day_Mon Day_Tue Day_Wed Predictor Constant Rho50 Rho95 Rho99 Month_Fall Month_Spring Pre 9/11 Day_Mon Day_Tue Day_Wed Coeff P-value Predictor Coeff p-value Constant Rho Rho Rho Month_Fall Month_Spring Pre 9/ Day_Mon Day_Tue Day_Wed R-Sq = 54.3% R-Sq = 54.9%

22 Regression Analysis - Best Model Based on Fridays from 2000, 2001, 2002 Results of multiple regression for Ln(AvgDel_Flight_Min) Results of multiple regression for Ln(Pr_Canc) Avg Delay (min) Pr_ Cancellation Coeff p-value Coeff p-value Constant Constant Rho Rho Rho Rho Rho Pre9/11_N Month_Fall Month_Fall Month_Spring Month_Spring R-Square 62.97% 56.25%

23 Conclusions of Analysis Basic concepts are sound Rho95 is best single predictor Some variation remains to be characterized Airline behavior changes based on: Load factor on that day, e.g. very high loads fewer cancellations Day-of-week

24 f1 canceled: P CAN Passenger Delay Metric DELAY U =DELAY DISRUPT direct trip: P dir f1 not canceled: 1 - P CAN DELAY U =D m f1 delay > thresh: P MISS DELAY U =DELAY DISRUPT 2-leg trip: 1 - P dir f1 not canceled: 1 - P CAN f1 delay thresh: 1 - P MISS f2 canceled: P CAN DELAY U =DELAY DISRUPT f1canceled: P CAN f2 not canceled: 1 - P CAN DELAY U = D m DELAY U = DELAY DISRUPT

25 Graph P_Delay vs Rho95 P_Delay Rho95

26 Model Features Track changes in NAS performance as a function of: Changes in airport infrastructure Changes in demand Changes in weather or ability of technology to adapt to weather, e.g. (VMC cap)/(imc cap) Technology improvements that imply capacity enhancements

27 On-Going Work Add independent variables, etc to achieve best model Create best model compatible with Vensim (focus this summer) Specific issues to address: Control variable that drives cancellation and delay models Daily yearly model Airspace effects Refined passenger model GA effect Airport-specific effects (delay airports; airports delay) Delay distribution information

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