IntroductionThe continued growth of air traffic within the United States, combined with the use of Òhub and spokeÓ operations by air carriers, has led t o increased congestion and delays in the terminal airspace surrounding the nationÕs busier airports.The problem of congestion is exacerbated at hub airports, where air carriers schedule large numbers of flights to arrive and depart within a short time period.These arriving and departing groups of aircraft are commonly referred to as banks, and the simultaneous arrival of several banks of aircraft can easily strain the capacity of an airport.In order to ensure that the safe capacity of the terminal area is not exceeded, ATM often places restrictions on arriving flights transitioning from en route airspace to terminal airspace.The constraint of arrival traffic is commonly referred to as arrival flow management, and includes techniques such as metering, vectoring, and the imposition of miles-in-trail restrictions.These constraints are enacted without regard for the relative priority which airlines may be placing on individual flights, based on factors such as crew criticality, passenger connectivity, critical turnaround times, gate availability, on-time performance, fuel status, or runway preference [1].To air carriers, ÒhubbingÓ makes good economic and competitive sense [2].At the same time, however, hubbing operations often lead to overcapacity periods and precipitate delays which can directly impact the economic efficiency of an air carrierÕs flight operations.Air traffic control automation tools are used in arrival flow management to assist controllers in efficiently matching traffic demand and airport capacity while minimizing delays.These tools use sequencing and scheduling algorithms t o automatically plan the most efficient landing order and landing times for arriving aircraft [3].NASA and the Federal Aviation Administration (FAA) have designed and developed a suite of software decision support tools (DSTs) to improve the efficiency of high-density airspace [4].Collectively known as the Center-TRACON Automation System (CTAS), operational evaluation of these DSTs has shown them to be effective in improving airport throughput and reducing delays while maintaining controller workload at a reasonable level [4].One of these tools, the Traffic Management Advisor (TMA), is currently being used at the Fort Worth Air Route Traffic Control Center (Center) to perform arrival flow management of traffic into the Dallas/Fort Worth airport (DFW).The TMA is a time-based planning tool that assists Traffic Management Coordinators (TMCs) and Center controllers in efficiently balancing arrival demand with airport capacity [5].The primary algorithm in the TMA is a real-time scheduler which generates efficient landing sequences and landing times for arrivals within about 200 n.mi.from touchdown [6].Aircraft are scheduled so that they arrive in a firstcome-first-served (FCFS) order based on an estimated time of arrival (ETA) at the runway.While FCFS scheduling establishes a fair order based on estimated times of arrival, it does not take into account individual airline priorities among incoming flights.The development of new arrival flow management techniques which consider priorities expressed by air carriers will likely reduce the economic impact of ATM restrictions on the airlines.This will in the future lead to increased airline economic efficiency by allowing airlines to have greater control over their individual arrival banks of aircraft.As part of its Collaborative Arrival Planning (CAP) research and development program, NASA-Ames is exploring the possibility of allowing airlines to express relative arrival priorities to ATM through the development of new CTAS sequencing and scheduling algorithms which take into account airline arrival preferences.An earlier study focused on the feasibility of scheduling Òdelay exchangesÓ among pairs of individual arrival aircraft as a means of accommodating an airline request for an earlier arrival [7]. Priority SchedulingSuccessful airline operations today require increasingly complex airline schedules.The interconnection of the schedules of major airlines with their subsidiary carriers and code-sharing partners adds to this complexity.As a result of increasing scheduling complexities and interdependencies, achieving a specific order within a bank of arrival aircraft has become of greater importance to the smooth and efficient operation of many airlines.Even a small group of aircraft belonging to a single airline may be interconnected in a fairly complex manner, with passengers and cargo from multiple flights feeding one large connecting flight or vice-versa.For example, an arriving bank of aircraft may include a large jet which is primarily delivering passengers to a number of smaller turboprop aircraft arriving in the same bank.This same large jet in turn, may be taking on passengers from other jet aircraft in the bank to deliver passengers/cargo to their final destinations.Passenger connectivity is only one of many factors which influence an airlineÕs schedule.Consideration must also be given to factors such as the availability of gates, and ground equipment and personnel to service aircraft and transfer passengers and cargo between flights.Even in the simple example just cited, the efficient operation of these flights will depend strongly on maintaining the integrity of the airline schedule by meeting the planned times of arrival and hence the desired order of arrival.For most airlines, the schedule which is determined internally by the airline to satisfy its business and economic objectives is an ÒidealÓ schedule.This schedule is ideal in the sense that the everyday realities of operating an airline and interacting with the various elements of the National Airspace System (NAS) largely preclude this ideal schedule from ever being achieved.Because of the uncertainties throughout both the airline (equipment breakdowns, maintenance problems, personnel shortages) and the NAS (weather, ground delays, ATM restrictions), aircraft often arrive in the terminal airspace in an order which does not match the ideal order of the airline schedule.Current arrival flow management using FCFS sequencing and scheduling algorithms will likely result in aircraft arriving at the runways in an order which does not match the preferred arrival order.The ability to specify the preferred arrival order within the userÕs own arrival bank is useful for maximizing bank integrity and minimizing bank time (i.e., exchange of passengers/cargo, and aircraft servicing) [8].Earlier studies have shown that scheduling aircraft according to an FCFS sequence based on estimated time of arrival at the runway produces a schedule which is considered to be both fair to air carriers and efficient in terms of minimizing delays which must be absorbed [3].These studies also have shown that the resulting scheduled arrival sequence at the runway will, for the most part, match the FCFS sequence which is input to the scheduling algorithm.Because the scheduling algorithm attempts to preserve the input sequence, specifying a preferred sequence will result in a schedule which closely approximates the preferred arrival order.The concept of Òpriority schedulingÓ is then defined as the scheduling of a bank of arrival traffic according to a preferred order of arrival.The focus of the present study is t o determine the feasibility of scheduling a bank of arrival aircraft using a preferred sequence instead of an FCFS sequence based on ETA at the runway. It is importantto distinguish between ÒschedulingÓ or ÒscheduleÓ in the context of airline operations, and ÒschedulingÓ or ÒscheduleÓ in the context of air traffic control automation.The former refers to the daily scheduled times of departure and arrival which an airline determines for all of its flights, while the latter refers to the process of automatically choosing (a) the order or sequence in which the aircraft should land or cross a particular fix, and (b) the time that each aircraft in the sequence should pass over a specified fix [6]. Fast-time SimulationA fast-time simulation originally developed for statistical evaluation of CTAS sequencing and scheduling algorithms has been modified for use in this investigation [9].In contrast to real-time simulation or field tests, which would require on the order of ninety minutes to examine a single traffic rush period, the fast-time simulation allows examination of large numbers of statistically similar rush periods in a matter of minutes.For each simulated traffic situation, the deviation of a designated bankÕs scheduled arrival order from the preferred arrival order can be determined.The impact of priority scheduling on delays is also determined by comparing delays for priority scheduling and FCFS scheduling.Because this simulation does not provide any information about the controller workload required to meet the calculated schedule, the output of the simulation is used only to determine the effectiveness of priority scheduling and its impact on scheduled delays.The fast-time simulation is comprised of three major components: an airport model, a statistical model of the arrival traffic flow, and the scheduler. Airport ModelThe arrival airspace at DFW is divided into Center and Terminal Radar Approach Control (TRACON) regions, with the TRACON encompassing the airspace within approximately 40 n.mi. of the airport.Arrival traffic is merged at four waypoints on the Center-TRACON boundary which correspond to the four primary arrival directions.These waypoints are referred to as feeder gates because during heavy traffic periods traffic is funnelled through these gates as a means of controlling or metering the flow rate into the terminal area [6].Traffic flowing to each gate is separated into two independent streams which are vertically separated by 2,000 feet at the feeder gate.This allows jet and turboprop aircraft, which have significantly different airspeed ranges, t o cross the feeder gates independently and avoid conflicts due to overtakes near the gates.The airport is modeled according to the landing practices at DFW with four feeder gates and three runways available for landing.The runways are considered to be independent so that no stagger requirements are necessary for scheduling.The airport model is comprised of the minimum flight times from each feeder gate to all landing runways for each independent stream.These TRACON transition times were obtained from an analysis using the minimum flight times measured for several traffic samples [10].The TRACON transition times vary with feeder gate, aircraft type, runway assignment, and airport configuration.The airport model contains transition times for both airport configurations at DFW: Ònorth flowÓ with arrival traffic arriving/departing in a northerly direction, and Òsouth flowÓ with traffic arriving/departing in a southerly direction.It should be noted that since the data used in this simulation were collected, a fourth arrival runway has been added at DFW.However, the three-runway model and traffic data are sufficient for purposes of this investigation. Traffic ModelThe traffic model is based on actual traffic data recorded during six rush periods at DFW.Although the traffic data were recorded over a span of several months, the mix of aircraft type remained nearly constant for each traffic sample.The data were recorded during the Ònoon balloon,Ó a daily arrival rush lasting approximately ninety minutes.The noon balloon was chosen as the basis for the traffic model because during this arrival rush demand exceeds airport capacity and air traffic managers impose time-based metering restrictions through CTAS sequencing and scheduling algorithms.Data recorded during the six rush periods include the aircraft type, aircraft identification, arrival stream, and the estimated time of arrival at the feeder gate (ETA FG ).The average of these estimated times of arrival for the six rushes is taken as the nominal ETA FG .Errors in aircraft time of arrival in Center airspace are modeled by adding an approximately Gaussian distribution to the nominal estimated time of arrival at the feeder gate.The maximum range of the variation in the ETA FG is specified as an input to the simulation and is referred to as the Center arrival error. Bank DefinitionAlthough an actual arrival bank of aircraft for an airline may consist of between 30 and 50 aircraft, in this study it is assumed that a bank is comprised of a single group of up to 20 aircraft belonging t o one airline and its subsidiary carrier.With a majority of the flights in the traffic model belonging to American Airlines (AAL) and American Eagle (EGF), these flights are used t o form arrival banks.The bank is not a contiguous set of aircraft because aircraft belonging to other airlines are interspersed among the bank aircraft, as would be the case in a real traffic situation.The bank of aircraft is defined by specifying the first member of the bank, and the number of aircraft belonging to the bank.For the purposes of this simulation, we assume that the preferred order of arrival at the runway equals the order of arrival based on the minimum ETA at the runway with no Center arrival error.Each of the bank aircraft is assigned a priority ranking which is simply equal t o the preferred order of arrival for the aircraft within the bank.The minimum estimated time of arrival at the runway (ETA RWY ) is calculated by adding the TRACON transition times for each of the three runways to the nominal ETA FG , and selecting the minimum of the three resulting values.This ETA RWY represents the earliest possible time of arrival for an aircraft provided that the aircraft could fly to the runway with no delay.For example, consider the list of aircraft shown in Table 1, which represents a portion of a single arrival rush where AAL1150 has been designated as the lead aircraft in the bank, and the number of aircraft in the bank has been specified as five.The number in the first column represents the sequence number or position of the aircraft within the arrival rush when the aircraft are time-ordered according to increasing ETA RWY .Each arrival rush or traffic sample consists of 108 aircraft, and in the example in Table 1 the aircraft belonging t o the defined bank range from the 57th aircraft t o the 65th aircraft in the arrival rush (AAL1554).The resulting bank aircraft are denoted by bold text for purposes of illustration.This example shows that aircraft belonging to other airlines are interspersed among the arrival aircraft which comprise the bank.The second column is the aircraft identifier and the third column is each aircraftÕs corresponding minimum ETA RWY .The fourth column shows the priority ranking which is assigned to each of the aircraft belonging to the bank based on this preferred order of arrival. Table 1 Bank definition and preferred arrival orderThe actual order of arrival for aircraft in a traffic rush period is generated by adding the Center arrival error to the nominal ETA FG .The Center arrival error represents the uncertainties in the NAS which cause the same flight to arrive in Center airspace at different times on different days.Because the minimum ETA RWY is calculated by adding a TRACON transition time to the ETA FG , the minimum ETA RWY will also vary.As a result, when the aircraft are ordered according t o increasing ETA RWY , the actual order for the bank aircraft will differ from the preferred arrival order.In addition, the number of aircraft interspersed among the arrival bank may vary because the variation in arrival time is modeled for all aircraft in the traffic rush, not only those belonging to the specified bank.Table 2 shows the resulting estimated arrival order for the specified bank when a Center arrival error having a range of up to +/-5 minutes is added to the traffic sample. FCFS SchedulingThe FCFS scheduler is intended to approximate the sequencing and scheduling algorithms presently used in CTAS at the Ft.Worth Center.A detailed description of the actual scheduling algorithm can be found in [6].Aircraft are sequenced and scheduled to be first-come-first-served at both the feeder gates and runways while meeting feeder gate and runway threshold separation constraints.Because scheduling is done in time rather than distance, the prescribed minimum separation criteria are translated into minimum time separations at both the feeder gates and the runway threshold.For aircraft crossing the feeder gate, the minimum in-trail separation requirement for aircraft is 5 n.mi., which is translated to a 60second time separation for purposes of this simulation.The separation criteria at the runway threshold are a function of both aircraft weight class and landing order as determined by the FAAÕs wake vortex safety rules.Airport acceptance rate (AAR) is taken into consideration by limiting the number of aircraft which are allowed to enter the TRACON in sliding ten minute intervals, and the scheduler balances flights between runways t o minimize overall delay.The FCFS sequence is established by time-ordering arrival aircraft according to increasing ETA RWY .Beginning with the first aircraft in the sequence, each aircraft is tentatively scheduled to each of the three runways, while ensuring that the prescribed minimum time separation between aircraft at the runway thresholds is met for each subsequent aircraft.The runway which results in the earliest scheduled time of arrival for the aircraft at the runway (STA RWY ) is then chosen as the landing runway .Scheduling to the runway automatically provides the correct amount of traffic to load the runways equally when traffic is heavy (runway balancing), and directs aircraft t o the closest available runway.The scheduled time of arrival at the feeder gate (STA FG ) is determined by subtracting the sum of the TRACON transition time and any TRACON delay from the previously calculated STA RWY .Finally, if STA FG Õs for two flights are less than the required 60 seconds apart, the scheduled times will be altered to meet the required separation at the feeder gate.Table 3 shows the resulting order of arrival when the aircraft are scheduled according to an FCFS sequence.The priority ranking of each bank aircraft is shown in parenthesis following the aircraft identifier.The second and third columns in the table show the FCFS sequence which is input t o the scheduler, with the aircraft time-ordered according to increasing ETA RWY .The fourth and fifth columns are the resulting schedule, with aircraft time-ordered according to increasing STA RWY .Note that the resulting scheduled order of arrival at the runway does not precisely match the FCFS sequence based on ETA RWY which is input t o the scheduler.Because the schedule must meet intrail separation criteria at both the feeder gate and the runway threshold, and the separation criteria at the runway threshold are a function of aircraft weight class and landing order, the FCFS sequence may not be preserved at the runway.Among the aircraft belonging to the designated bank, flights AAL1934 and AAL1428 have shifted positions from the sequence which is input to the scheduler (as have aircraft DAL431 and AAL410, which do not belong to the designated bank).In this case, the position shift has resulted in a scheduled sequence which does more closely match the ideal or desired order of arrival than does the input FCFS sequence based on ETA RWY .However, it is purely fortuitous that the resulting schedule more closely matches the preferred order, and depending on the magnitude of the Center arrival error, the scheduled order may actually deviate further from the preferred order. Priority SchedulingThe priority scheduling algorithm is identical t o the FCFS algorithm with one exception: instead of time-ordering the aircraft according to increasing ETA RWY prior to scheduling, the arrival aircraft belonging to the designated bank are ordered according to their priority ranking, which establishes the bank aircraft in the preferred arrival order.It is important to note that only the aircraft belonging to the bank are reordered according to their priority ranking, and that other aircraft in the traffic sample are still sequenced in an FCFS order based on ETA RWY .By reordering only the bank aircraft and scheduling the remaining aircraft according to an FCFS sequence, the impact of the reordering on scheduling efficiency is minimized.Table 4 shows the resulting order of arrival when the bank aircraft are scheduled according to the preferred sequence of arrival.The second and third columns show the priority sequence which is input to the scheduler, with the bank aircraft ordered according to their priority ranking, and the remaining aircraft timeordered according to increasing ETA RWY .The fourth and fifth columns show the resulting schedule time-ordered according to STA RWY .As was the case with FCFS scheduling, the resulting order of arrival does not match the sequence which was input to the scheduler because the schedule must meet separation criteria at the runway threshold which are a function of aircraft weight class and landing order.Although the resulting scheduled bank order does not precisely match the preferred order, it does indeed match more closely the preferred bank order than does the FCFS schedule shown in Table 3. Order DeviationTo quantify the effectiveness of the priority scheduling method we need a measure of how closely the scheduled order of arrival for a designated bank matches the preferred arrival order.We first define a position shift (PS) for an aircraft as the difference between the aircraft position in the preferred bank order and the sequence number in the scheduled bank order. PS N N PREFERRED SCHEDULED = -where N is the sequence number of the aircraft within the bank Table 5 illustrates the calculation of the PS for each of the aircraft in the bank defined in Table 1.The position shift of each aircraft is calculated for both FCFS scheduling (Table 3) and priority scheduling (Table 4).Note that a positive PS indicates that an aircraft is scheduled ahead of its preferred position in the bank, and a negative position shift indicates that an aircraft is scheduled behind its preferred position in the bank.For example, the sequence number of flight EGF628 in the preferred order of arrival is 2 while its sequence number in the FCFS schedule is 5 and its sequence number in the priority schedule is 3.This results in a PS of -3 for the FCFS schedule and -1 for the priority schedule and reflects the fact that EGF628 is scheduled 3 slots behind its preferred position in the bank using FCFS scheduling, and 1 slot behind the preferred position using priority scheduling.Because we are interested in how closely the overall bank order matches the preferred order, we want a single measure which will indicate the deviation from the preferred order for a bank of any length.We then define the order deviation (OD) for a bank as the algebraic sum of the absolute value of the PS for each aircraft in the bank divided by the number of aircraft in the bank. OD PS= ∑ | | # of bank aircraft # of bank aircraftIt can be seen from this definition that if the OD for a bank of aircraft equals zero, then the scheduled bank order is the same as the preferred bank order.More importantly, the larger the value of the OD, the further the scheduled bank order deviates from the preferred order.This will allow us to easily compare the relative effectiveness of the FCFS and priority scheduling methods in producing the preferred order of arrival.The order deviations for each scheduling method using the example in Table 5 are calculated below.Because the priority scheduling scheme results in the designated bank arriving in an order which more closely matches the preferred arrival order, the OD for the priority scheduled bank is smaller than that for the FCFS scheduled bank.ODFCFS = + -+ + + = | | | | | | | | | | . 0 3 1 1 1 5 1 2 ODPRIORITY = + -+ + + = | | | | | | | | | | . 0 1 1 0 0 5 0 4In order to investigate the statistical performance of the two scheduling methods, a large number of traffic samples are generated for a specified bank.To compare the effectiveness of FCFS scheduling and priority scheduling for a large number of traffic samples, we define the average OD as the sum of the ODÕs for each traffic sample divided by the number of traffic samples. OD Simulation Inputs/OutputsInputs to the fast-time simulation include the aircraft identifier of the lead aircraft in the bank, the size of the bank, the number of traffic samples, the range in Center arrival error, the airport configuration, and airport acceptance rate.In order to determine the statistical performance of the FCFS algorithm and the priority algorithm, 500 traffic samples are generated for each designated bank.Each traffic sample is comprised of 108 jet and turboprop aircraft, 72 of which are AAL or EGF flights.In this simulation the modeled airport configuration is south flow for DFW.Because the traffic model is limited to a single arrival rush period, and because of the manner in which a bank is defined, banks cannot be formed at or near the end of the arrival rush period.For example, if the bank length is specified as 20, and the designated lead aircraft is the 100th aircraft in the arrival rush, no bank will be formed because there are not enough aircraft following the lead aircraft to form a bank.Although we attempt to form banks across the entire range of the traffic rush period, this cannot be done for the reasons just outlined.The output of the fast-time simulation includes the average OD as well as histograms of the position shifts for each bank of aircraft.Total delays and histograms of individual delays for all aircraft in the traffic rush are generated as well.Results can then be compared for the FCFS scheduling algorithm and the priority scheduling algorithm. Results and DiscussionThe primary measure of success of the priority scheduling algorithm is the closeness of the match between the scheduled order of arrival and the preferred order of arrival.Figure 1 is a plot of the average order deviation for a bank size of 20, a range in Center arrival errors of +/-5 minutes, and an AAR of 96 aircraft/hour.For a designated bank whose lead aircraft has a nominal ETA FG given on the x-axis, a corresponding pair of ordinates shows the average OD for the bank using FCFS scheduling and priority scheduling.Figure 1 confirms that the priority scheduling algorithm significantly reduces the average OD from that of the FCFS scheduling algorithm.Note however, that while the OD for each bank is less using the priority scheduling algorithm, the OD is still non-zero for each bank.In other words, while the resulting bank order using priority scheduling matches much more closely the preferred order than does the FCFS order, the scheduled bank order does not precisely match the preferred order.Because the schedule must meet in-trail separation criteria at the runway threshold, and the separation criteria are a function of both weight class and landing order, the preferred order of arrival may not be preserved at the runway.Figure 1 shows the resulting OD for banks of aircraft beginning at different points in the arrival rush.The average order deviation for the FCFS algorithm first increases and then decreases as the ETA FG of the lead aircraft in the bank increases.The change in average OD for the FCFS schedule is due to changing traffic density and mixture in the arrival rush.As the traffic density increases (estimated times of arrival are more closely spaced), a given arrival error will cause larger position shifts within a bank and thus larger order deviations.By the same token, the traffic mix impacts the order deviation because if non-AAL/EGF flights are interspersed among the bank aircraft, the aircraft comprising the bank will be spaced farther apart.Then, for a given arrival error, the OD for the bank will be smaller because the aircraft are not as closely spaced.The average OD for the priority scheduling algorithm also varies with traffic density and mixture and is most effective in a region where some non-AAL/EGF aircraft are interspersed among the bank aircraft.The effects of AAR, bank size, and Center arrival error on the success of the priority scheduling algorithm are also examined.For the sake of brevity, no plots are shown but important results are summarized here.Results show that for a given Center arrival error and bank size, the priority OD tends to decrease with decreasing AAR, meaning that the priority scheduling algorithm is more effective for a more restrictive AAR.This is actually a characteristic of both the priority scheduler and the FCFS scheduler, and it can be shown that for a lower AAR, either scheduler is better able to preserve the order in which the aircraft are scheduled.Lowering the AAR effectively reduces the airport capacity (because demand remains constant), requiring that the scheduled times of arrival (STAÕs) be spaced farther apart.Because the STAÕs must be spaced farther apart, differences in crossing times or separation criteria are less likely to cause the resulting order to deviate from the order in which the aircraft are scheduled.Therefore the resulting schedule for either algorithm will more closely match the sequence in which the aircraft are scheduled.Results also show that increasing the size of the bank of aircraft does not significantly impact the effectiveness of the scheduling algorithm.However, increasing the magnitude of the Center arrival error for a given bank size and AAR does lead to a decrease in the effectiveness of the priority scheduling algorithm.For purposes of illustration, a histogram of the position shifts for a bank of aircraft led by AAL535 is shown in Figure 2.This histogram, along with the OD values labeled in Figure 1, demonstrate the relationship between average OD and the closeness of the match between the scheduled bank order and the preferred arrival order.Priority scheduling reduces the spread of the position shifts for the designated bank of aircraft.In this case, aircraft belonging to the designated bank are scheduled in the preferred position (position shift = 0) approximately 60% of the time using priority scheduling.Using FCFS scheduling, bank aircraft are scheduled in the preferred position only about 25% of the time.The increase in the number of aircraft scheduled in the preferred position leads to a decrease in average OD for the bank.Because this simulation does not provide any information about the controller workload required to meet the priority schedule, the output of the simulation is used only to investigate the feasibility of the priority scheduling method in terms of scheduling efficiency.However, it can be reasonably assumed that an increase in scheduled delays greater than a certain amount would be unacceptable to air traffic controllers because of the likely adverse effect on controller workload.Similarly, airlines would likely find an increase in scheduled delays which exceeds a certain threshold to be unacceptable from the standpoint of increased costs.While the amount of delay increase acceptable controllers and airlines would have to be determined before a priority scheduling method could be considered practicable, the present simulation provides initial insight into the impact of priority scheduling on scheduling efficiency.This can be measured as the change in average delay per aircraft when priority scheduling is used instead of FCFS scheduling.q q q q q q q q q q q q q q q q q q q q q q q q q For each designated arrival bank whose order deviation is shown in Figure 1, a corresponding pair of points in Figure 3 shows the change in average delay for the AAL/EGF aircraft in the arrival rush, and for the non-AAL/EGF (ÒOthersÓ) aircraft in the arrival rush.Figure 3 shows that the change in delays due to priority scheduling varies with the position of the bank in the arrival rush, and that the greatest delay increase occurs for a bank which starts near the beginning of the arrival rush.This is attributable to the changing traffic density and traffic mixture in the arrival rush, and to the fact that all aircraft following the bank lead aircraft may be impacted by the reordering of the bank aircraft before scheduling.Because a larger number of aircraft may be impacted by the reordering, the aggregate increase in delays will be greater for a bank which begins earlier in the arrival rush.The average delay increase then diminishes as the ETA FG of the lead bank aircraft increases, and priority scheduling in some instances results in a slight decrease in average delay per aircraft.In these instances the priority schedule is actually more efficient than the FCFS schedule.The priority scheduling algorithm has the smallest impact on scheduling efficiency in regions where arrivals are not closely spaced and banks have non-AAL/EGF flights interspersed among the bank aircraft.Although a scheduling method which takes into account user preferences would ideally have no impact on scheduling efficiency when compared with FCFS scheduling, Figure 3 shows that for certain traffic conditions, the priority scheduling method results in little or no decrease in scheduling efficiency.v v v v v v v v v v v v v v v v v v vv v v vv v 0 0.5Any type of scheme which allows the introduction of user preferences into the arrival flow management process must ultimately be fair to all air carriers.In light of this, we are particularly interested in determining whether the priority scheduling of flights belonging to one airline disproportionately impacts the scheduled delays of aircraft belonging to other airlines.Examination of the delay increases for AAL/EGF flights in Figure 3 shows that for most of the banks, the delay increase for AAL/EGF flights in the arrival rush is greater than the delay increase for the non-AAL/EGF aircraft.By reordering only the aircraft belonging to the designated bank and scheduling all other aircraft according to an FCFS sequence, the impact of reordering on aircraft belonging to other airlines is minimized.This strategy also minimizes the impact of the reordering on scheduling efficiency, and in some instances results in improved efficiency by decreasing scheduled delays.The effects of AAR, bank size, and Center arrival error on the change in scheduled delays are also examined.For a given bank size and Center arrival error, when priority scheduling is used instead of FCFS scheduling, the change in average delay per aircraft tends to increase as AAR is increased.Results are similar to those seen in Figure 3 with the greatest change in delay occurring for banks which begin early in the arrival rush, and the change in delays decreasing for banks which are positioned later in the arrival rush.Increasing the magnitude of the Center arrival error for a given bank size and AAR substantially increases the change in delays for banks of aircraft arriving early in the rush period, while not significantly impacting the change in delay for banks arriving later in the traffic period.Finally, results show that the change in delays due to priority scheduling is largely unaffected by an increase or decrease in the size of the arrival bank.q q q q q q q q q q q q q q q q q q q q q q q q q v vv v v v v v v v v v v v v v v v v v v v v v v Concluding RemarksThis paper introduces the concept of priority scheduling as a means of taking into consideration airline arrival preferences in sequencing and scheduling algorithms for air traffic control automation.Priority scheduling is defined as a method of scheduling a bank of arrival aircraft according to a preferred arrival order instead of according to an FCFS order based on estimated time of arrival at the runway.A fast-time simulation originally developed for statistical evaluation of CTAS sequencing and scheduling algorithms has been modified for use in this investigation.Because this simulation does not provide any information about the controller workload required to meet the priority schedule, the output of the simulation is used only t o investigate the feasibility of the priority scheduling method in terms of scheduling efficiency and how closely the bankÕs scheduled arrival order matches the preferred arrival order.Results show that for the simulated traffic conditions, the priority scheduling algorithm results in a scheduled bank order which closely matches the preferred order.Results also show that when compared with FCFS scheduling, priority scheduling will, for certain traffic conditions, substantially reduce deviations from the preferred bank order while causing little or no decrease in scheduling efficiency.Figure 2 Figure 323Figure 1 Average order deviation Figure 33Figure 3 Change in average delays per aircraft when priority scheduling is used instead of FCFS scheduling Table 2 Actual arrival order2 Table 4 Priority Sequence and resulting schedule4SequencePreferredFCFSPositionPriorityPositionNumberOrderScheduleShift forScheduleShift forinFCFSPriorityBankScheduleSchedule1AAL1150AAL11500AAL115002EGF628AAL1934-3AAL1934-13AAL1934AAL14281EGF62814AAL1428AAL15541AAL142805AAL1554EGF6281AAL15540 Table 5 Calculation of position shift for a bank of aircraft5 FCFS SequenceResulting ÒAirline Arrival Prioritization,Ó NAS Status Information Subgroup Memo ALacher DBenfield May 19, 1997 Lacher, A., and Benfield D., ÒAirline Arrival Prioritization,Ó NAS Status Information Subgroup Memo, www.metsci.com/faa/cdm/nassi.html, May 19, 1997. Quarterly Update October - December 2015 LBond 10.1163/2210-7975_hrd-9806-2016016 Ó Journal of ATC October -December 1997 Brill Bond, L., ÒGlobal Positioning Sense II: An Update,Ó Journal of ATC, October - December 1997, pp. 51 -55. Initial Characterization of the 30 kW Miniature Arc Jet (mARC II) at NASA Ames Research Center FNeuman HErzberger 10.2514/6.2020-3108.vid ÒAnalysis of Delay Reducing and Fuel Saving Sequencing and Spacing Algorithms for Arrival Traffic,Ó NASA TM 103880 American Institute of Aeronautics and Astronautics (AIAA) October 1991 Neuman, F. and Erzberger H., ÒAnalysis of Delay Reducing and Fuel Saving Sequencing and Spacing Algorithms for Arrival Traffic,Ó NASA TM 103880, October 1991, NASA Ames Research Center. HErzberger TJDavis SMGreen ÒDesign of Center-TRACON Automation System,Ó Proceedings of the AGARD Guidance and Control Panel 56th Symposium on Machine Intelligence in Air Traffic Management Berlin, Germany 1993 Erzberger, H., Davis, T. J., and Green, S. M., ÒDesign of Center-TRACON Automation System,Ó Proceedings of the AGARD Guidance and Control Panel 56th Symposium on Machine Intelligence in Air Traffic Management, Berlin, Germany, 1993, pp. 52-1 -52-14. ÒDesign and Operational Evaluation of the Traffic Management Advisor at the Fort Worth Air Route Traffic Control Center,Ó 1st USA HNSwenson Europe Air Traffic Management Research and Development Seminar June 17-19, 1997 Saclay, France Swenson, H. N., et al., ÒDesign and Operational Evaluation of the Traffic Management Advisor at the Fort Worth Air Route Traffic Control Center,Ó 1st USA/Europe Air Traffic Management Research and Development Seminar, Saclay, France, June 17-19, 1997. ÒDesign Principles and Algorithms for Automated Air Traffic Managment,Ó AGARD Lecture Series No. 200, Knowledge-Based Functions in Aerospace Systems HErzberger November 1995 San Francisco Erzberger, H., ÒDesign Principles and Algorithms for Automated Air Traffic Managment,Ó AGARD Lecture Series No. 200, Knowledge-Based Functions in Aerospace Systems, San Francisco, November 1995. Delay exchanges in arriving sequencing and scheduling GregoryCarr HeinzErzberger FrankNeuman 10.2514/6.1998-4478 Guidance, Navigation, and Control Conference and Exhibit Boston, MA American Institute of Aeronautics and Astronautics August 10-12, 1998 Carr, G. C., Erzberger, H., Neuman, F., ÒDelay Exchanges in Arrival Sequencing and Scheduling,Ó AIAA Guidance, Navigation, and Control Conference, Boston, MA, August 10-12, 1998. Enabling user preferences through data exchange StevenGreen TsuyoshiGoka DavidWilliams StevenGreen TsuyoshiGoka DavidWilliams 10.2514/6.1997-3682 Guidance, Navigation, and Control Conference New Orleans, LA American Institute of Aeronautics and Astronautics August 10-12, 1997 Green, S. M., Goka, T., Williams, D. H., ÒEnabling User Preferences Through Data Exchange,Ó AIAA Guidance, Navigation, and Control Conference, New Orleans, LA, August 10-12, 1997. ÒFast-Time Statistical Evaluation of Sequencing and Scheduling Algorithms for Multiple Runways FNeuman HErzberger MSchueller Ó to be published as a NASA technical memorandum Neuman, F, Erzberger, H., Schueller, M., ÒFast-Time Statistical Evaluation of Sequencing and Scheduling Algorithms for Multiple Runways,Ó to be published as a NASA technical memorandum. 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