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I. Introductionhis paper is motivated by the need for improving departure scheduling advisories.A specific application is for Precision Departure Release Capability (PDRC) which has the goal of using surface trajectory based off-time predictions for Call for Release (CFR).Accurate wheels-off time estimation is important to PDRC both for 1) providing an initial estimate to the Traffic Management Advisor (TMA) for inserting a flight into a constrained overhead stream and for scheduling an inbound flight to a TMA-metered airport, and 2) determining when to release the aircraft from the gate so that its actual wheels-off time corresponds to the wheels-off time coordinated with the Air Route Traffic Control Center.Improved wheels-off time prediction would also benefit traffic flow management (TFM).TFM techniques first estimate traffic demand considering both airborne aircraft that are detected by the air traffic control radars and aircraft on the ground that are scheduled to depart within the forecasting interval, and then
II. Dallas-Fort Worth Airport Geometry and OperationsDallas-Fort Worth International Airport (DFW) is the third busiest airport in the United States.According to the March 2011 FAA Administrator's Factbook 7 , 652,000 operations were conducted at DFW in 2010 compared to 950,000 operations at Hartsfield-Jackson Atlanta International, the busiest US airport, and 883,000 operations at Chicago O'Hare International, the second busiest US airport.DFW is physically one of the largest airports in the United States and the world with an area spanning five nautical-miles east to west and three nautical-miles north to south.The airport has seven physical runways shown in Fig. A-1 in the Appendix.These runways are operated in the south-flow and north-flow configurations.The runways in south-flow configuration are designated as, 13L, 13R, 17L, 17C, 17R, 18L and 18R.The runways in the north-flow configuration are designated as, 31L, 31R, 35L, 35C, 35R, 36L and 36R.These designations also indicate the runway heading with respect to north; they are physically painted on the two ends of each runway.To get insight into DFW operations, hourly runway configurations (arrival and departure runways) for each day in 2011 were obtained by generating the "Daily Weather by Hour Report," from the ASPM database.These data were then processed to determine runways that are used for both arrivals and departures, runways that are used only for arrivals and runways that are used solely for departures.Table 1 lists the runways and the time duration of usage during 2011.This table shows that 10 of the 14 runways (considering the same physical runway to be two different runways based on the approach direction) are used both for arrivals and departures.Of these, 18R is used most often.Summing the runway utilization in both directions of the physical runways, it is seen that 17C/35C, 17R/35L, 18L/36R, 18R/36L, 17L/35R and 13R/31L usage is within 20% of each other.Runway 13L/31R usage is 27% of the usage of the most utilized runway, 18R/36L.Data in Table 1 show that runways 17C, 17R, 18L and 18R are utilized more often compared to the other runways; thus, south-flow is the dominant flow direction in DFW operations.Further analysis of ASPM runway configuration data revealed that 76 arrivaldeparture runway configurations out of 254 theoretically possible configurations were used in 2011.Number of theoretically possible combinations is obtained using,∑ ∑ ≤ ≤ ≤ ≤         +         = 7 1 7 1 7 7 k k k k n (1)where        k 7means the number of ways in which "k" runways can be chosen out of seven runways.The two summations are for the seven south-flow and seven north-flow runways.Table 2 lists the top ten configurations along with the percentage of time they were used with respect to 8,760 hours in the year.Observe that the ten configurations listed in Table 2 were used 95% of the time.Summing the percentage use of the 76 south-flow and north-flow configurations, it is seen that the south-flow configuration is used 70% of the time and the north-flow configuration is used 30% of the time.Reference 6 also cited the same numbers.Passenger and cargo traffic in and out of the 233 gates cross 59 spots to exit and enter a network of 96 taxiways to travel to and from the seven physical runways.The taxiways intersect at 215 locations.This includes intersection   of taxiways with runways.The taxiways consist of 360 segments partitioned by the intersections.These numbers were obtained by analyzing DFW geometry data derived from SODAA.The DFW airport design is also characterized by multiple runways, high-speed exit taxiways, non-intersecting runways, three towers, and perimeter taxiways near 35L and 35C that permit aircraft to taxi to and from the gates without crossing active runways.These features reduce congestion on the airport surface; delays are mostly weather related and independent of surface operations. 6This suggests that it might be possible to estimate taxi time with reasonable accuracy for different weather conditions at DFW.To estimate wheels-off time, estimates of gate departure time and taxi time are needed.Of these two estimates, gate departure time estimate is much more difficult to compute.In the absence of airline provided gate departure time, the choices are limited to the scheduled departure time from the Official Airline Guide (OAG) and the proposed departure time included in the filed flightplan.These times provide approximate estimates of gate-out time.Reference 1 proposes the use of pre-departure event times to improve estimate of gate-out time.The central idea employed in Ref. 1 is that gate-out time becomes more certain as completion of each step taken by airline and air traffic for preparing the flight for departure are reported via the Aircraft Communication Addressing and Reporting System (ACARS).Taxi time is a function of distance between the gate and the runway, taxi-speed and congestion of the surface.Since a taxi route is specified, distance along the route can be determined.Taxi-speed differences between flights are significant; taxi-speed is a function of pilot preference, stops needed at intersections and congestion along the route to the runway threshold.To determine gate to runway distances and taxi-out times to the runways at DFW, one week-spanning 7 August 2011 through 13 August 2011 of surface traffic data were obtained by processing SMS logs.The chosen seven days had good weather, and consisted of 6,284 departures.After discarding flights with more than 60 minutes of gate departure delay and 30 minutes of gate to runway entry time, 5,822 departures were considered for further analysis.It was determined that 393 unique gate-runway combinations were used by these aircraft.Figure 1 shows the gate to runway distance distribution and Fig. 2 shows the average taxi speed distribution of 5,822 departures.Average taxi speed is obtained as the ratio of gate to runway distance to taxi-out time.Average, standard deviation and maximum gate to runway distance were found to be 1.6, 0.6 and 4.0 nautical-miles, respectively.The average, standard deviation and maximum of the average taxi-out speed were found to be 13, 3.6 and 34.5 knots, respectively.Average and standard deviation of the taxi-out time were determined to be 7.8 and 3.6 minutes, respectively.
III. Correlation Between Metrics and Gate to Wheels-off Time and Gate Departure DelayCorrelation coefficients between gate to wheels-off time (SMS Log Data Item 4 in the Appendix) and variables selected from the two sets discussed in the SMS Log Data and ASPM Data sections in the Appendix were computed to make an assessment of their suitability as predictors of gate to wheels-off time in a neural network and a linear model framework.The procedure was repeated for correlations with respect to gate departure delay (SMS Log Data Item 15 in the Appendix) to ascertain the ability of these variables to predict gate departure delay.Prior to computing the correlation coefficients, data were conditioned as follows.SMS Log data for flights with absolute value of the gate departure delay greater than the specified threshold of 60 minutes were discarded.The data were found to contain large negative gate departure delays.Another check was performed for gate to runway taxi time with a threshold value of 30 minutes.Only flights with gate to runway entry time of less than 30 minutes were considered.Total number of samples prior to pruning is 6,284.After pruning 5,822 remain.462 samples removed represent a 7.4% loss with respect to 6,284 samples.Table 3 shows the correlation (with 100% being perfect correlation) and p-value of the selected variables with gate to wheels-off time.Here, correlation means the cross-correlation coefficient derived from the covariance matrix of the two variables being compared and the p-value is the probability of obtaining a correlation as large as the observed value by random chance, when the true correlation between the variables is zero.p-value of less than 0.05 is considered to be significant.The gate to runway distance has the highest correlation followed by average taxi-out delay and number of departures on the surface.Wind angle, visibility and temperature were found to be negatively correlated.Weak negative correlation with visibility and temperature is reasonable in that as visibility and temperature decrease, one would expect taxi-time to increase a bit.Wind angle correlation is difficult to interpret without examining wind velocity components relative to the surface trajectory.Few variables that are independent of each other (contain different type of information) with high correlation can be used to develop a linear model or a neural network model for predicting gate to wheels-off time.Such models could be adequate for CFR at DFW because in current operations, CFR is initiated after pushback from the gate.This means that the gate departure time is known.At some other airports, for example at San Jose International airport, airlines are asked to inform air traffic control (ATC) some time (for example, 15 minutes) prior to ready for departure when the flight is impacted by CFR.Gate departure time uncertainty can be expected to be small in this scenario therefore wheels-off time could be predicted with these models.For predicting gate departure time, the only available information about when an aircraft might leave the gate is the scheduled gate departure time.Improvement beyond the scheduled gate departure time is possible if metrics derived from observed or estimated airport state are found to be good predictors of gate departure delay.This is examined next.Table 4 shows the correlation of the selected metrics with gate departure delay.The table shows that time of day at the scheduled gate departure time has the highest correlation followed by average gate departure delay in the previous 15-minutes.Average taxi-in delay in previous 15-minutes is similarly correlated with gate departure delay.While unexpected, temperature was found to be mathematically correlated to gate departure delay.It turns out that temperature increase from morning to afternoon and then decrease in the evening is somewhat correlated to the schedule of the departure pushes.The degree of correlation can be expected to change with different weather conditions.Comparing Tables 3 and4, it is seen that the degree of correlation of the selected metrics with gate departure delay is much lower compared to with gate to wheels-off time.This suggests that constructing a model for reliable prediction of gate departure delay based on these metrics might be difficult.Furthermore, wheels-off time prediction at the scheduled gate departure time requires that the metrics computed based on airport state data at scheduled departure time be correlated to gate to wheels-off time at actual gate departure time.These correlations are likely to be worse compared to the correlations in Table 3 which are based on airport state data at or close to the actual gate departure time and not at an earlier time.These issues have not been examined further in this paper.The rest of the paper assumes that gate departure time is known and a prediction of gate to wheels-off time is needed for wheels-off time estimate.
IV. Neural Network Model and ResultsA three-layer neural network with seven nodes in the input layer, 20 nodes in the hidden layer and one node in the output layer was designed to predict gate to wheels-off time.Such a neural network is shown in Fig. 3.The seven selected inputs are, 1) gate to runway distance, 2) average taxi-out delay in previous 15-minutes, 3) number of departures on surface at actual gate departure time, 4) average taxi-out delay of departures on same runway in previous 15-minutes, 5) average taxi-out delay of departures to same fix in previous 15-minutes, 6) wind angle and 7) ATC set airport arrival rate.Gate departure count in previous 15 minutes (#6 in Table 3) and number of departures to same fix in previous 15 minutes (#7 in Table 3) were not considered as inputs for the neural network because they were found to be significantly correlated to the other inputs.For example, correlation between metric #6 and #3 is 53.5% and between #7 and #5 is 43.5%.The single output is the gate to wheels-off time.Maximum absolute value of each input was determined for the entire seven day  dataset.Inputs were then normalized with these values.The gate to wheels-off time data used for training the neural network were also normalized by the maximum absolute value obtained from seven days of gate to wheels-off time data.Figure 3 shows that the inputs are multiplied by weights and summed together with a bias at each hidden layer node and input to the sigmoid function, which is real-valued and differentiable.This means that the neural network had 140 weights and 20 biases for seven inputs and 20 nodes in the hidden layer.The output of the sigmoid functions in the hidden layer are multiplied with another set of weights and summed together with a bias and input to sigmoid functions in the output layer.Since this neural network has 20 nodes in the hidden layer and one node in the output layer, there are 20 weights and one bias between the hidden and output layers.The 160 neural network weights and 21 biases were initialized with values between -1 and 1 using a uniform random number generator.These weights were then adjusted using the standard gradientbased back-propagation algorithm in the neural network training step.Four-hundred iterations resulted in reduced error between the gate to wheels-off time predicted by the neural network and the gate to wheels-off time used for training the network as shown in Fig.     runway distance correlation with gate to wheels-off time of 66.3%.Average and standard deviation of the error with respect to the gate to wheels-off time training data turned out to be 23 seconds and 2.6 minutes, respectively.The average and standard deviation of gate to wheels-off time in the six day training set is 8.9 and 3.8 minutes, respectively.A histogram of the training error is shown in Fig. 5.Reference 8 notes that while the compliance window for CFR varies by facility and that a nationwide standard does not exist, information from traffic managers and inter-facility agreements ask for flights to depart within a three-minute window, two-minutes early to one-minute late, with respect to the coordinated departure time.The reason for allowing departures to be two-minutes early compared to one-minute late is because it is easier to slow down the flight compared to accelerating it for merging into the constrained flow.Considering the neural network predicted gate to wheels-off time to be the coordinated departure time and the difference of the actual gate to wheels-off time with respect to this predicted time to be delay, 53.5% of the flights were found to be in compliance with the CFR window based on the error distribution in Fig. 5.This increased to 61.2% when the window was expanded to allow two-minute early to two-minute late departures.For the 13 August gate to wheels-off time test data, the correlation with the neural network generated gate to wheels-off time estimate is 74%.Average and standard deviation of the error with respect to the test data are 35 seconds and 2.3 minutes.These values can be compared to the average and standard deviation of gate to wheels-off time of 8.7 minutes and 3.4 minutes.Gate to wheels-off time test data are shown in Fig. 6 and the departure distribution of the flights whose gate to wheels-off time are in Fig. 6 are shown in Fig. 7 in 15-minute bins.The error distribution is given in Fig. 8. Actual gate to wheels-off times for 59.2% of the flights in the test set were found to be within the two-minute early and one-minute late CFR window with respect to the neural network predicted gate to wheels-off times.This result compares favorably with the observation in Ref. 8, which is based on onemonth of data, that 69.2% of aircraft subject to CFRs in which TMA automation was utilized were compliant with the CFR window.Compliance of the test set improved to 66.5% when the window was expanded to allow twominute early to two-minute late departures.These results confirm that the neural network performance on the test data is as good as it is on the training data.Results discussed in this section show that the selected metrics can be used as inputs to a neural network for generating gate to wheels-off time predictions for CFR after gate pushback.The performance of the neural network can be improved further by removing outliers from the training and test sets.This would require flights with unusual delay to be identified and removed from the training and test sets based on detailed analysis of surface trajectory of each flight.To compare the results obtained with the neural network with the earlier study reported in Ref. 5, a linear model was set up as follows:∑ ≤ ≤ = 7 1 k k k x c y (2)with 1x through 7x representing the seven non-normalized neural network inputs, 1 c through 7 c representing the corresponding coefficients and y representing the non-normalized gate to wheels-off time.These seven coefficients were computed using the leastsquares method with the left and the right hand sides of Eq. ( 2) derived from six days of data that had been used earlier to train the neural network.The numerical values of the coefficients are given in Table 5. Inputs derived from one day of data used for testing the neural network were then multiplied with these coefficients and summed to generate gate to wheelsoff time predictions for comparison with the actual gate to wheels-off time.Results obtained with the linear model matched the distributions shown in Fig. 5 and 8 based on the Mahalanobis distance metric, which is the ratio of the Euclidean Norm of the error (data in Figs. 5 and8) and the standard deviation of the gate to wheels-off time distributions used for training and testing.Mahalanobis distance metric values were determined to be 49.55 and 49.02 with neural network and linear model outputs with respect to training data, respectively.With respect to test data, the values were found to be 19.42 and 19.29 with neural network and linear model outputs, respectively.Actual gate to wheels-off times of 62.1% of the flights in the test set were found to be within the two-minute early and one-minute late CFR window with the linear model.CFR compliance is a bit better than 59.2% obtained with the neural network.These results do not show a benefit of using the neural network over a simple linear model for DFW traffic.It remains to be seen if the neural network would perform better on surface data from other airports.Results obtained with both the neural network and linear model validate the suitability of the chosen metrics for predicting gate to wheels-off time.For follow on work, these metrics will be computed using data from airports where SMS will not be available and used with the neural network and linear model to assess the accuracy of gate to wheels-off time predictions.
V. ConclusionsCorrelation of airport state metrics derived from the Aviation System Performance Metrics database and Surface Management System logs with gate to wheels-off time and gate departure delay were examined to identify metrics with significant correlation as inputs for a neural network.Gate to runway distance was found to have the highest correlation of 66.3% with gate to wheels-off time.Scheduled departure time of day was found to have the highest correlation of 13.8% with gate departure delay.Given low correlation with gate departure delay, this study did not attempt to develop a model for predicting gate departure time.Instead, gate departure time was assumed to be known.The neural network was trained with six days of data to predict gate to wheels-off time.After training, the correlation with gate to wheels-off time predicted by the neural network and that used for training increased by 6% to 72.4% compared to 66.3% correlation with gate to runway distance.Average and standard deviation of the error with respect to the gate to wheels-off time training data were found to be 23 seconds and 2.6 minutes.One day of data were used for testing the neural network.A 74% correlation was found between these test set data and the neural network generated gate to wheels-off time estimate.Average and standard deviation of the error with respect to the test data were determined to be 35 seconds and 2.3 minutes.These results show that the neural network performance on the test data is comparable to its performance on the training data.Actual wheels-off times for 59% of the departures in the test set were found to be within the two-minute early to one-minute late Call for Release window with respect to the trained neural network predicted wheels-off times.This result is comparable to 69% compliance within the Call for Release window reported in an earlier study.Results based on analysis of Dallas-Fort Worth data show that it is feasible to use the selected metrics as inputs to a neural network for generating gate to wheels-off time predictions for Call for Release after gate pushback.Results obtained with a linear model, with coefficients obtained using the least-squares method, were found to be as good as those obtained with the neural network based on the Mahalanobis distance metric.While a clear benefit of using a neural network over the simple linear model was not found for Dallas-Fort Worth traffic, it remains to be seen if it would perform better on surface data from other airports.Both the approaches suggest that the selected metrics can be used for predicting gate to wheels off time.These metrics will be computed using data from airports where the Surface Management System will be unavailable and used with the neural network and the linear model to determine the accuracy with which gate to wheels-off time can be predicted.
Parameters for Modeling Gate to Wheels-off Time and Gate Departure DelayThe variables chosen for predicting gate to wheels-off time and gate departure delay are discussed in this section.These input variables were obtained by processing seven days, 7 August 2011 through 13 August 2011, of SMS logs and ASPM data.
SMS Log DataSurface trajectory data, consisting of a sequence of latitudes and longitudes as a function of time, of every flight departing DFW were analyzed to determine the following:1. Actual gate-out time in hours, minutes and seconds.2. Time of day in 15-minute interval.For example, 02:45 means 2 hours and 45 minutes past 00:00 local time.Actual gate-out time is within this 15-minute bin. 3. Actual wheels-off time in hours, minutes and seconds.4. Actual wheels-off time minus actual gate-out time.This is the sum of time spent in the ramp area, time taken to taxi to the runway and time spent on runway till the wheels are off the ground.5. Flight ID. 6. Departure gate ID. 7. Departure runway ID. 8. Name of the departure fix.9. Name of the destination airport.10.Actual gate to runway distance in nautical-miles based on surface trajectory.11.Actual taxi-out time of the flight in seconds.This is the gate to runway entrance time; sum of time spent in ramp area and taxi time to the runway entry.12. Aircraft type.For example, Boeing 747-400.13.Airline name.14.Scheduled gate departure time in hours, minutes and seconds.15.Gate departure delay.This is the difference between the actual gate departure time and the scheduled departure time.16.Number of departures on the surface at the actual gate departure time.These flights are out of the gate and moving towards departure runways.17.Number of arrivals on the surface at the actual gate departure time.These flights have landed and are moving towards arrival gates.18. Number of takeoffs from the same runway as this flight in the previous 15-minute interval with respect to the time of day.19.Average taxi-out delay of departures in seconds using the same runway as this flight in the previous 15minute interval with respect to the time of day.Taxi-out delay of each departure is computed as the difference of the actual taxi-out time and the unimpeded taxi-out time, where the unimpeded taxi-out time is computed as the ratio of the actual taxi-out distance to the average speed of 13 knots.20.Number of takeoffs that used the same departure fix as this flight in the previous 15-minute interval with respect to the time of day.21.Average taxi-out delay of departures in seconds using the same fix in the previous 15-minute interval with respect to the time of day.Taxi-out delay is computed in the same manner as in Item 19.22. Number of departures to the same destination airport in the previous 15-minute interval with respect to time of day.23.Average taxi-out delay of departures in seconds to the same destination airport in the previous 15-minute interval with respect to time of day.Taxi-out delay is computed in the same way as in Item 19.24.Number of departures from all gates in the previous15-minute interval with respect to the time of day.25.Number of takeoffs from all runways in the previous15-minute interval with respect to the time of day.26.Number of arrivals at all gates in the previous15-minute interval with respect to the time of day.27.Number of landings on all runways in the previous15-minute interval with respect to the time of day.28.Time of day in 15-minute interval such that the scheduled gate-out time is within this time interval.31.Average taxi-out delay of departures from the same runway as this flight in the previous 15-minute interval with respect to time of day.Taxi-out delay is computed in the same way as in Item 19.32.Average taxi-out delay of departures through the same departure fix in the previous 15-minute interval with respect to time of day.Taxi-out delay is computed in the same way as in Item 19.33.Average taxi-out delay of departures to the same destination airport in the previous 15-minute interval with respect to time of day.Taxi-out delay is computed in the same way as in Item 19.Note that the variables 29 through 33 are with reference to time of day related to the scheduled gate departure time.The other variables are with respect to the actual gate departure time.While some variables, such as 16 and 17, are with respect to the actual gate departure time, most variables are with respect to a broader interval of the time of day.Many variables, such as 1 and 3-15 are flight specific.Other variables like 16-23 and 29-33 are aggregate metrics based on other flights.Additionally, variables like 18-27 and 31-33 are based on aggregate metrics in the 15-minute time interval just prior to either the actual gate departure time or the scheduled gate departure time.It is assumed that these variables can be computed with flight plan data and Out-Off-On-In (OOOI) data provided by airlines available in the current air traffic system.Aggregate metrics 24-27 consider traffic to and from all gates and runways.Thus, they represent general state of airport operations.Time of day variables 2 and 28 are used for relating variables derived from the SMS logs and ASPM data.Variables based on ASPM data are discussed next.
ASPM DataFederal Aviation Administration's (FAA) Aviation System Performance Metrics (ASPM) database, which is accessible on the web for authorized users, provides detailed data on flights to and from the 77 major U. S. airports (ASPM 77 airports) and flights operated by 29 major carriers (ASPM 29 carriers).Flights operated by ASPM carriers to international and domestic non-ASPM airports are also included.ASPM database also contains information on airport weather, runway configuration, and arrival and departure rates.Data in ASPM provide insight into air traffic and air carrier activity.FAA uses these data for monitoring airport efficiency, aspects of system performance, and retrospective trend analysis studies.Two different reports were extracted from the ASPM database for Dallas-Fort Worth airport operations spanning the period of 7 August 2011 through 13 August 2011.The first report, "Daily Weather by Quarter Hour Report," provided weather (visual meteorological condition or instrument meteorological condition), ceiling in feet, visibility in statute miles, temperature in degrees Fahrenheit, wind angle in degrees, wind speed in knots, arrival/departure runway configuration, airport departure rate and airport arrival rate in fifteen minute intervals as a function of local time.The second report, "Analysis By Airport By Quarter Hour Report (compared to flight plan)," includes numbers of scheduled departures/arrivals and departures/arrivals used for metric computation, percentages of on-time gate departures, airport departures and gate arrivals, average gate departure delay, average taxi-out time, average taxi-out delay, average airport departure delay, average taxi-in delay, and average gate arrival delay.Times and delays are in minutes.Numbers of scheduled arrivals and departures are based on carrier published schedules.Numbers of arrivals and departures for metric computation are based on itinerant flights to/from the ASPM 77 airports or operated by one of the ASPM 29 carriers.General aviation and military flights are excluded.Percent on-time gate departures is computed as the ratio of the number of flights that departed within 15-minutes past the flight plan gateout time to the number of departures for metric computation.Percent on-time airport departures is given as the ratio of the number of flights that departed within 15-minutes past the flight plan wheels-off time to the number of departures for metric computation.Percent on-time gate arrivals is determined as the ratio of the number of flights that arrive at the gate less than 15-minutes late compared to the flight plan gate-out time plus the scheduled block time to the total number of arrivals for metric computation.Taxi-out/taxi-in delay is the difference between taxiout/taxi-in time and unimpeded taxi-out/taxi-in time.Airport departure delay is computed as the difference between the actual wheels-off time and the sum of flight plan gate-out time and unimpeded taxi-out time.Average gate arrival delay is determined by adding minutes of gate arrival delay of one-minute or more, and dividing it by number of arrivals for metric computation.Gate arrival delay is defined as the difference between the actual gate-in time and the flight plan gate-in time.ASPM data from the two reports were processed to determine the following:1. Time of day in 15-minute intervals in hours and minutes format with respect to 00:00 local time.Figure 1 .1Figure 1.Gate to runway distance distribution.Figure 2. Average taxi speed distribution.
Figure 2 .2Figure 1.Gate to runway distance distribution.Figure 2. Average taxi speed distribution.
Figure 3 .3Figure 3. Neural network.
Figure 4 .4Figure 4. Neural network convergence.
Figure 7 .7Figure 7. Test set departure distribution.
Figure 6 .6Figure 6.Test set data.Figure 5. Training error distribution.
Figure 5 .5Figure 6.Test set data.Figure 5. Training error distribution.
Figure 8 .8Figure 8. Test error distribution.
Figure A- 1 .1Figure A-1.Dallas-Fort Worth airport layout.
2 .2Meteorological condition-Visual Meteorological condition (VMC) or Instrument Meteorological Condition (IMC).3. Visibility in statute miles.4. Temperature in degrees Fahrenheit. 5. Wind angle in degrees.6. Wind speed in knots.7. Runway configuration indicating runways used for arrivals and runways used for departures.
Table 1 .12011 runway usage summary.RunwaysRunwaysRunwaysUsed for bothUsageUsedUsageUsed onlyUsageArrivals and(hours)only for(hours)for(hours)DeparturesArrivalsDepartures18R6,96017L5,84435L2,55617R6,14213R5,62413L33517C6,11918L5,16736R2,56935C2,54731L2,53736L2,52635R2,31831R2,208Downloaded by NASA AMES RESEARCH CENTRE on April 17, 2013 | http://arc.aiaa.org| DOI: 10.2514/6.2012-5699
Table 2 .22011top-ten runway configurations.ArrivalDepartureUsage (%)Flow13R,17C,17L,18R17R,18L45.4South31R,35C,35R,36L 31L,35L,36R22.7North13R,17C,17L,18R17R,18R9.7South17C,17L,18R17R,18L4.7South13R,17C,17L,18R 13L,17R,18L3.1South13R,17C,18R17R,18L2.9South35C,35R,36L31L,35L,36R2.9North31R,35C,36L31L,35L,36R1.5North13R,17C,17L17R,18R1.2South13R,17C,17L17R,18L0.8South
Table 3 .3Gate to wheels-off correlations.#MetricCorrelation (%)p-value1 Gate to runway distance66.30.002 Average taxi-out delay in previous 15-minutes36.70.003 Number of departures on surface at actual gate departure time36.20.004 Average taxi-out delay of departures on same runway in previous 15-minutes23.50.005 Average taxi-out delay of departures to same fix in previous 15-minutes22.90.006 Gate departure count previous 15-minutes13.20.007 Number of departures to same fix in previous 15-minutes12.60.008 Wind angle-12.00.009 ATC set airport arrival rate9.70.00Number of departures on same runway in previous 15-minutes9.40.00Average taxi-in delay in previous 15-minutes8.30.00Wind speed on surface7.50.00Average taxi-out delay of departures to same destination in previous 15-minutes6.90.00ATC set airport departure rate6.00.00Number of departures to same destination in previous 15-minutes5.50.00Number of arrivals on surface at actual gate departure time5.30.00Visibility-4.40.00Average gate departure delay in previous 15-minutes3.80.00Takeoff count previous 15-minutes3.60.00Time of day at gate departure3.00.02Landing count previous 15-minutes2.50.05Temperature-2.20.09Gate arrival count previous 15-minutes2.00.13Average gate arrival delay in previous 15-minutes1.60.23Meteorological condition (VMC or IMC)1.30.33
Table 4 .44. Note that the error is dimensionless because the training and neural network outputs are normalized.Six days, 7 August 2011 through 12 August 2011, of data were used for training the neural network and one day, 13 August 2011, of data were used for evaluating the gate to wheels-off time estimation ability of the neural network.Correlation between the gate to wheels-off time used for training and that generated by the neural network after training on the same set of neural network input data was found to be 72.4%.This is an improvement over gate to Gate departure delay correlations.#MetricCorrelation (%)p-value1Time of day at scheduled gate departure13.80.002Average gate departure delay in previous 15-minutes11.00.003Temperature10.10.004Average taxi-in delay in previous 15-minutes9.60.005Landing count previous 15-minutes8.90.006Gate arrival count previous 15-minutes7.70.007Number of arrivals on surface at scheduled gate departure time6.50.008Wind angle-5.30.009Average gate arrival delay in previous 15-minutes5.10.0010 Average taxi-out delay of departures to same destination in previous 15-minutes4.90.0011 Takeoff count previous 15-minutes4.80.0012 ATC set airport departure rate4.20.0013 Average taxi-out delay in previous 15-minutes3.50.0114 Number of departures on surface at scheduled gate departure time3.10.0315 Gate departure count previous 15-minutes3.00.0416 Wind speed on surface-1.20.4017 Visibility1.10.4318 Average taxi-out delay of departures on same runway in previous 15-minutes0.60.6619 ATC set airport arrival rate0.60.6920 Gate to runway distance0.50.7321 Average taxi-out delay of departures to same fix in previous 15-minutes-0.40.8022 Meteorological condition (VMC or IMC)-0.10.93
Table 5 .5Linear model coefficients.Downloaded by NASA AMES RESEARCH CENTRE on April 17, 2013 | http://arc.aiaa.org| DOI: 10.2514/6.2012-5699CoefficientValue1 c241.18282 c10.00573 c10.15214 c0.10495 c0.03696 c-0.24917 c2.4563
Time is given in the same format as Item 2 of this list.Observe that Item 2 is with reference to actual gate-out time while Item 28 is with respect to scheduled gate-out time.29.Number of departures on the surface at the scheduled gate departure time.Similar to Item 16 except at scheduled, not actual, gate departure time.30.Number of arrivals on the surface at the scheduled gate departure time.Similar to Item 17. by NASA AMES RESEARCH CENTRE on April 17, 2013 | http://arc.aiaa.org| DOI: 10.2514/6.2012-5699Downloaded
			Downloaded by NASA AMES RESEARCH CENTRE on April 17, 2013 | http://arc.aiaa.org| DOI: 10.2514/6.2012-5699
		
		
			
			
			

				


	
		Improved Prediction of Gate Departure Times Using Pre-Departure Events
		
			LaraCook
		
		
			StephenAtkins
		
		
			YoonJung
		
		10.2514/6.2008-8919
	
	
		The 26th Congress of ICAS and 8th AIAA ATIO
		Anchorage, Alaska
		
			American Institute of Aeronautics and Astronautics
			September 14-19, 2008
		
	
	AIAA 2008-8919
	Cook, L. S., Atkins, S., and Jung, Y., "Improved Prediction of Gate Departure Times Using Pre-Departure Events," AIAA 2008-8919, Proc. 26 th Congress of International Council of the Aeronautical Sciences (ICAS), Anchorage, Alaska, September 14-19, 2008.



	
		Aircraft Taxi Times at U.S. Domestic Airports
		
			DerekRobinson
		
		
			DanielMurphy
		
		10.2514/6.2010-9147
	
	
		10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference
		Fort Worth, TX
		
			American Institute of Aeronautics and Astronautics
			September 13-15, 2010
		
	
	Aircraft Taxi Times at U. S. Domestic Airports
	Robinson, D. P., and Murphy, D. J., "Aircraft Taxi Times at U. S. Domestic Airports," AIAA 2010-9147, Proc. 10th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Fort Worth, TX, September 13-15, 2010.



	
		An Analytical Queuing Model of Airport Departure Processes for Taxi Out Time Prediction
		
			IoannisSimaiakis
		
		
			NikolasPyrgiotis
		
		10.2514/6.2010-9148
	
	
		10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference
		Fort Worth, TX
		
			American Institute of Aeronautics and Astronautics
			September 13-15, 2010
		
	
	Simaiakis, I., and Pyrgiotis, N., "An Analytical Queuing Model of Airport Departure Process for Taxi Out Time Prediction," AIAA 2010-9148, Proc. 10th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Fort Worth, TX, September 13-15, 2010.



	
		Quantitative Analysis of Uncertainty in Airport Surface Operations
		
			DavidRappaport
		
		
			PeterYu
		
		
			KatyGriffin
		
		
			ChrisDaviau
		
		10.2514/6.2009-6987
	
	
		9th AIAA Aviation Technology, Integration, and Operations Conference (ATIO)
		Hilton Head, SC
		
			American Institute of Aeronautics and Astronautics
			September 21-23, 2009
		
	
	Rappaport, D. B., Yu, P., Griffin, K., and Daviau, C., "Quantitative Analysis of Uncertainty in Airport Surface Operations," AIAA 2009-6987, Proc. 9th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Hilton Head, SC, September 21-23, 2009.



	
		Relationship Between Airport Efficiency and Surface Traffic
		
			MatthewKistler
		
		
			GautamGupta
		
		10.2514/6.2009-7078
	
	
		9th AIAA Aviation Technology, Integration, and Operations Conference (ATIO)
		Hilton Head, SC
		
			American Institute of Aeronautics and Astronautics
			September 21-23, 2009
		
	
	Kistler, M. S., and Gupta, G., "Relationship between Airport Efficiency and Surface Traffic," AIAA 2009-7078, Proc. 9th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Hilton Head, SC, September 21-23, 2009.



	
		Air Traffic Management System Development and Integration (ATMSDI) Acquisition CTO-05--Surface Management System CTOD-2--Airport Site Surveys
		
			AtmsdiRaytheon
		
		
			Team
		
		NAS2-00015
	
	
		Contract Number
		Moffett Field, CA
		
			June 5, 2001
			
		
		
			NASA Ames Research Center
		
	
	Raytheon ATMSDI Team, "Air Traffic Management System Development and Integration (ATMSDI) Acquisition CTO-05- -Surface Management System CTOD-2--Airport Site Surveys," Contract Number NAS2-00015, NASA Ames Research Center, Moffett Field, CA 94035-1000, June 5, 2001.



	
		Foreword from Acting Administrator of the Health Resources and Services Administration (HRSA) and Associate Administrator of the Federal Office of Rural Health Policy (FORHP), U.S. Department of Health and Human Services
		
			JimMacrae
		
		
			TomMorris
		
		10.1353/hpu.2016.0195
		
	
	
		Journal of Health Care for the Poor and Underserved
		Journal of Health Care for the Poor and Underserved
		1548-6869
		
			27
			4A
			
			March 2011
			Project MUSE
		
	
	Administrator's Fact Book. cited: 4/24/2012
	Assistant Administrator for Financial Services, "Administrator's Fact Book," Federal Aviation Administration, U. S. Department of Transportation, March 2011, URL: http://www.faa.gov/about/office_org/headquarters_offices/aba/admin_factbook/media/201103.pdf [cited: 4/24/2012].



	
		Characterization of Tactical Departure Scheduling in the National Airspace System
		
			RichardCapps
		
		
			ShawnEngelland
		
		10.2514/6.2011-6835
	
	
		11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference
		Virginia Beach, VA
		
			American Institute of Aeronautics and Astronautics
			September 20-22, 2011
		
	
	AIAA 2011-6835
	Capps, A., and Engelland, S. A., "Characterization of Tactical Departure Scheduling in the National Airspace System," AIAA 2011-6835, Proc. 11th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Virginia Beach, VA, September 20-22, 2011.



	
		Observations of Departure Processes at Logan Airport to Support the Development of Departure Planning Tools
		
			HusniRIdris
		
		
			IoannisAnagnostakis
		
		
			BertrandDelcaire
		
		
			RJohnHansman
		
		
			John-PaulClarke
		
		
			EricFeron
		
		
			AmedeoROdoni
		
		10.2514/atcq.7.4.229
	
	
		Air Traffic Control Quarterly
		Air Traffic Control Quarterly
		1064-3818
		2472-5757
		
			7
			4
			
			
			American Institute of Aeronautics and Astronautics (AIAA)
		
	
	15-minute airport departure rate set by air traffic control.



	
		Estimating One-Parameter Airport Arrival Capacity Distributions for Air Traffic Flow Management
		
			TashaRInniss
		
		
			MichaelOBall
		
		10.2514/atcq.12.3.223
	
	
		Air Traffic Control Quarterly
		Air Traffic Control Quarterly
		1064-3818
		2472-5757
		
			12
			3
			
			
			American Institute of Aeronautics and Astronautics (AIAA)
		
	
	15-minute airport arrival rate set by air traffic control.



	
		Supplementary file 1.
		10.7554/elife.04535.023
		
			null
			eLife Sciences Publications, Ltd
			11
		
	
	Average gate departure delay in the previous 15-minute interval with respect to the time of day
	Average gate departure delay in the previous 15-minute interval with respect to the time of day. 11. Average taxi-out delay in the previous 15-minute interval with respect to the time of day. 12. Average taxi-in delay in the previous 15-minute interval with respect to the time of day. 13. Average gate arrival delay in the previous 15-minute interval with respect to the time of day. The first 9 items are measured and directly available at the tower. The remaining four items can be calculated based on flight plan and OOOI data.