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I. Introductionn the current national airspace system, design of sectors have evolved over a long period of time based on incremental addition of new technologies and procedures for air traffic control.Each sector has a fixed capacity.When these capacities are exceeded by traffic demand, traffic flows are restriced to bring the demand below capacity.The concept in Ref. 1 suggests that instead of restricting traffic, which causes delays, airspace capacity can be increased by partitioning the airspace differently.Motivated by this concept, several methods for airspace partitioning that are described in Refs. 2 through 6 have been developed.These methods use some measure of controller workload to guide the design.In the future, with increased level of automation, airspace design might not be guided by controller workload considerations.Depending on how different the future design is from the current design, the controller's ability to actively separate aircraft might be limited.It might be useful to carry some of the design features of the current system into the future one, if some role for human controller is envisioned in the future air traffic control system.The motivation for computing metrics for the existing sectors is to capture some of the design features of the current sectors.Since the design of current sectors is based on the routes of flight and controller workload considerations, metrics related to controller workload can be expected to capure the design features.][9][10][11] These studies are limited to sectors in few centers.A comprehensive study of sectors in all the twenty centers is unavailable.In this paper, thirty-three traffic and geometric metrics from Refs. 7 to 11 are computed for 364 higher altitude sectors in each of the twenty centers, and in eight geographical regions.Higher altitude sectors were chosen because the benefits of airspace partitioning are expected to be realized in these sectors first.Data presented in this paper describes the design of the current sectors and will be found to be useful for comparing the designs of future airspace partitions.The paper is organized as follows.Section II describes the method for computing the metrics for each sector.The maximum number of aircraft in sectors obtained using simulated track-data are compared with those obtained using actual track-data in this section.Evaluation of sectors based on the traffic metrics is described in Section III and on geometric metrics in Section IV.Finally, the paper is summarized in Section V.
II. Computational MethodThis section describes two methods for computing the fifteen sector traffic metrics as a function of time.The first method processes the actual track-data, and the second method processes simulated traffic data.The main benefit of using actual track-data is that they best represent traffic resulting from the demand and capacity constraints of the particular day.These data reflect flow control and separation assurance actions, and airline operational control actions such as: cancellations and creation of new flights.Along with their benefits, they suffer from some data-quality issues discussed in Ref. 12 that can lead to erroneous values of the metrics.Simulated traffic data do not suffer from many of the data quality issues, but they do not include all of the realworld effects.Trajectories of aircraft are simulated using mathematical models; they can be expected to differ from those actually flown.Simulated traffic data have to be compared against actual traffic data for validation.These limitations not withstanding, a simulation offers far greater flexibility in designing scenarios, including future traffic growth scenarios, for evaluating the desired metrics.Simulation also provides a mechanism for eliminating control actions inherent in the real system.For example, aircraft are permitted to violate separation minimums, which only happen as an operational error in the real system.Given a choice between using actual position data, "track-data," and simulated data, it is often desirable to use the actual track-data because they represent reality.Due to this reason, ten of the fifteen measures have been computed using the actual track-data derived from a recorded Airline Situation Display to Industry (ASDI) file.The remaining five metrics, number of jet aircraft, number of non-jet aircraft, conflict-count, average airspeed and variance in airspeed, were computed using position data simulated using the Airspace Concept Evaluation System (ACES) with flight-plans extracted from the same ASDI file.The reason for using simulated data is that the information needed for computing these metrics is provided in the flight plan and not in the actual track-data.
A. Track-DataThe ASDI subsystem of the Enhanced Traffic Management System (ETMS) 13 disseminates real-time air traffic data, associated with different message types, to aviation industry.Of the different ASDI messages and supported data types described in Ref. 13, only the track/flight data-block messages, TZ messages, were used for computing the traffic metrics.TZ messages contain time-stamp, ARTCC identifier, aircraft identification (ACID), groundspeed, altitude, latitude and longitude.Over 9 million TZ messages were extracted from the recorded ASDI file, containing 48-hours of traffic data spanning the period from zero Coordinated Universal Time (UTC) on 17 March 2006 to zero UTC on 19 March 2006.Traffic data for these days were selected because of high traffic-volume, low weather impact and low delays.It should be noted that the traffic patterns vary from day to day and from season to season depending on demand, capacity, wind patterns and weather.Numerical values of the metrics in the sectors can be expected to vary based on the traffic pattern.The results presented in this paper are for a nominal day, which is defined as a high-volume, low-weather, and low-delay day.The time-sorted TZ messages were stored in data structures based on ACID.Data structures were then examined for each ACID to determine all the flights associated with that ACID.Individual flights were identified based on temporal gaps in the associated time-stamps.A temporal spacing of over thirty minutes was assumed to be due to a different flight.After identifying each flight, duplicate messages within one-minute periods were removed.This reduced the data by about 15%.Each flight's latitude, longitude and altitude derived from TZ messages were used to determine the sector the flight was in at each instant of time, where the sectors were as defined in May 2007 ETMS adaptation data.An efficient procedure for locating aircraft in a sector, described in Ref. 14, was used to identify the sectors.The latitudes and longitudes were then transformed into Cartesian coordinates with respect to a horizontal frame of reference using Oblique Stereographic Projection. 2 A first-order filter with altitude time-history input was used to generate time-history of climb/descent rate of each flight.Time, Flight ID, climb/descent rate, position and the sector corresponding to the position were input into a MySQL 15 database.This database was then queried to extract data related to flights in each sector and to sort them in time.These time-sorted data were then used to determine the numbers of aircraft in climb, in cruise, and in descent, and their sum (total number of aircraft) in the sectors.The data and the results are for 364 higher altitude sectors shown in Fig. 1.Each of these sectors has a floor of 17,100 feet altitude or higher.Fifty of the sectors have a floor between 17,100 feet and 24,000 feet; the rest have a floor at or above 24,000 feet altitude.The ceilings of these sectors are between 24,000 feet and 99,900 feet altitude.Several sectors in Salt Lake, Minneapolis, New York, DC, Boston and Los Angeles centers (see Fig. 1) were not included in the analysis because their floors are below 17,100 feet altitude.
B. ACES SimulationACES is a comprehensive computational model of the national airspace system consisting of air traffic control and traffic flow management models of ARTCCs, terminal-radar-approach-controls (TRACON), airports and the air-traffic-control-system-command-center (ATCSCC). 16It simulates flight trajectories through the enroute-phase of flight, where enroute-phase for jet aircraft is above 10,000 feet.A queuing model simulates surface movement and flight through terminal airspace.Traffic flow management and air traffic control models in ACES use airport and sector capacity thresholds for delaying flights, while they are on the ground and during their enroutephase.Some of the ACES outputs are arrival and departure counts at airports, trafficcounts in sectors and air traffic system performance metrics including arrival, departure, enroute and total delays.Earlier validation studies in Refs.17 and 18 have shown that ACES generates realistic delays and airport operational metrics similar to those observed in the real-world.Due to these capabilities, ACES was chosen for simulating traffic.
Simulation InputsACES simulation inputs include files containing capacity data (airport arrival and departure capacities, and sector capacities), traffic data (scheduled departure times and flight-plans), and adaptation data (sector/center geometric data).The actual airport arrival and departure rates specified at the 74 major U. S. airports on 17th and 18th March 2006 were specified as airport capacities in ACES.Sector capacity data were derived from the ETMS data tables.Sector capacity is defined as the maximum number of aircraft allowed in a sector at any one time during a fifteen-minute time interval.Capacity values, known as Monitor Alert Parameter (MAP), are used in the ETMS to trigger traffic flow management initiatives for demand reduction.Capacity thresholds are set to ensure that air traffic controllers are able to separate aircraft traversing the sector airspace.MAP values and the number of sectors with those values out of 364 higher altitude   1.Flight-plans for the simulation were derived from the same ASDI file used for computing the traffic-count metrics discussed in the previous subsection.Flight connectivity data relating the same physical aircraft to two or more flights segments were obtained from the Bureau of Transportation Statistics (BTS) for the two days.Airline flight-numbers, aircraft tail-numbers and the associated flight-plans for all flights were included in the ACES input file.Scheduled departure times derived from the BTS data were assigned as departure times.Proposed departure times from flight-plan messages in the ASDI data, or actual departure times in ASDI data minus average taxi times associated with airports of departure were assigned as departure times when scheduled times were not available in the BTS data.After assigning scheduled departure times for flights, an ACES simulation was run without airport and sector capacity constraints to compute unconstrained arrival times of flights at their destination airports.These were then set to scheduled arrival times at destination airports.A series of steps described in Ref. 19 were then taken to ensure that flight connectivity was preserved and that the arrival and departure schedules were compatible with turnaround-time requirements, time required for unloading aircraft after arrival at the gate and preparing it for departure.Final traffic schedule was generated after making the required flight schedules and tail-number changes.Sector and center geometry definitions needed for the simulation were obtained from the May 2007 ETMS adaptation data.
Simulation OutputsACES writes out identification information (ID) and position coordinates of flights that are in each sector to an output database at the specified rate during simulation.After completion of the simulation, flight IDs associated with a sector and their position time-histories were extracted from the database for computation of the five traffic metrics, number of jet aircraft, number of non-jet aircraft, conflictcount, average airspeed and variance in airspeed.This process was repeated for every sector.
C. Comparison of Tack-Data and ACES Simulation ResultsGiven that there are differences between the actual traffic data from the field and ACES simulated data, it is necessary that a comparison between the values of metrics obtained by processing actual track-data and ACES simulation be done for establishing the validity of the results.This was accomplished by comparing 1) the total number of aircraft in higher altitude airspace and 2) numbers of higher altitude sectors grouped according to the peak total-counts (trafficcounts), peak climb-counts, peak cruise-counts and peak descent-counts in each hour simulated by ACES with those obtained by processing track messages.Numbers of aircraft in sectors shown in Fig. 1 were retrieved from the simulation output and added together to compute the total number of aircraft in ten-second intervals.This time-history is shown with that of the actual number of flights in Fig. 2. Observe that the ACES simulation starts with all aircraft on the ground, whereas in the actual air traffic system there are always flights that are airborne.Figure 2 shows that the simulated traffic catches up with the actual traffic.The general trends of simulated and actual traffic are similar for the twenty-four hours between eight UTC on 17 March 2006 and eight UTC on 18 March 2006 (location marked 32 UTC in Fig. 2).Some of the differences between the time-histories are attributable to the issues with simulated and actual flight data discussed earlier in this section.Figure 3. Sectors with peak traffic-count in the first five levels, listed in Table 2, using actual track-data.For comparison based on peak traffic-counts, aircraft were counted in each higher altitude sector.The maximum of 60 values, one for each minute, provided the maximum number of aircraft, peak trafficcount, using actual track data for that hour.Figures 3 and4 show the number of sectors with peak traffic-count values in the first five levels listed in Table 2 during each one-hour period.The graphs in the figures viewed in conjunction with Fig. 2 show that as traffic increases, there are fewer sectors with low peak traffic-counts as would be expected.The maximum numbers of sectors for the four graphs, Level 2 through 5, in Fig. 3 were found to be 217 at 28:00 UTC, 190 at 22:00 UTC, 85 at 23:00 UTC and 12 at 18:00 UTC.In Fig. 4 these are 222 at 29:00 UTC, 176 at 24:00 UTC, 55 at 23:00 UTC and 12 at 17:00 UTC.The information contained in the individual graphs in Figs. 3 and4 can be combined and presented in terms of a vertically stacked bar chart for each one-hour period of the day.Such bar charts provide cumulative information as explained by the following example.Consider the bar charts obtained by processing the actual trackdata shown in Fig. 5.Of the eight levels listed in Table 2 and included in Fig. 5, only levels one through five are visible in the bar charts.Numbers of sectors with a peak traffic-count of four aircraft or less are shown in the bottom bar charts.Numbers of sectors with the next higher level are placed on top of this layer, and so on.Cumulative counts obtained by summing the levels below each chosen level determine the numbers of sectors with peak traffic-counts below the thresholds implicitly defined by levels in Table 2.For example, the top of Level 2 histogram at 23:00 UTC indicates that at any time of the day, at least 99 sectors have a peak traffic-count of nine aircraft or less.This is defined as the lower cumulative count.The maximum value of the top of the Level 2 histogram is 364 sectors at 10:00 UTC.This maximum value is defined as upper cumulative count.Table 3 summarizes these results obtained using actual track-data and ACES simulation.The time-histories shown in Figs. 3 and4 compare reasonably well; they show that similar peak traffic-counts are obtained in approximately the same number of higher altitude sectors using actual track-data and ACES simulated track-data.Values listed in the second and third  2, using ACES data.Figure 5. Time-history of bar charts of number of sectors grouped in eight peak traffic-count levels using track-data.Table 3. Numbers of sectors with peak traffic-counts below thresholds using ACES simulation compared to those obtained using track-data.3 also suggest that the peak traffic-count statistics computed using actual track-data and ACES are comparable.Analysis of peak climb-counts, peak cruise-counts and peak descent-counts using actual track-data and ACES simulated data also compared well.
III. Traffic MetricsA considerable amount of research has been devoted to the synthesis of traffic dependent metrics and their application to modeling sector complexity and air traffic controller's workload. 8,9Traffic metrics that were found to be especially pertinent for modeling workload perceived by controller in Ref. 8 are listed in Table 4.These metrics were computed for today's higher altitude sectors shown in Fig. 1 and the results are presented in the following subsections.
A. Traffic-count MetricsPeak traffic-count or the maximum number of aircraft has been found to be the most important contributor to controller workload.Research has found that controller activity and attentiveness are highly correlated to peak traffic-count. 10Maximum number of aircraft in higher altitude sectors computed using actual track-data were discussed in Section II.The time histories of the numbers of sectors with peak traffic-count levels were shown in Fig. 3 and the corresponding bar charts were shown in Fig. 5.Maximum numbers of aircraft in the climb phase (peak climb-count), in the cruise phase (peak cruise-count), and in the descent phase (peak descent-count) were computed in the same manner as the peak traffic-count in a sector.Aircraft with a climb rate of 200 feet/minute or more were considered to be climbing and those with a descent rate greater than or equal to 200 feet/minute were considered to be descending.Aircraft with climb or descent rates less than 200 feet/minute were considered to be cruising.Maximum number of jet aircraft and non-jet aircraft (turboprops and piston-props) in each hour in every sector were computed using ACES simulated track-data at ten second intervals.Since actual track-data do not contain aircraft type information, flight plans do, ACES simulated track-data that are based on flight-plans were used.Although it is possible to relate actual track-data to the flight-plans using the aircraft IDs that are common to both the message types, it does require an efficient data structure, significant memory and computation.ACES simulated data were also used for computing conflict-counts.Since jet aircraft cruise at approximately 8 miles/minute, trajectory data generated by ACES were written to the output database at tensecond intervals.Aircraft within each sector were selected from the database for checking conflicts, which means that conflicts between aircraft in neighboring sectors were not checked.This limitation arose because the database did not contain information on which sector is next to which one.Not knowing the sector neighborhood relationship meant that the only way to check for all such conflicts was to consider all the flights at each time-  3).Cumulative counts out of 364 counts listed in the last two columns are based on the time history of bar charts of numbers of sectors in peak climb-count levels like the one shown in Fig. 5. Cumulative counts were discussed earlier to explain the contents of Table 3.The value of 364 in the sixth and seventh columns indicates that at no time were there more than 14 aircraft in climb in a higher altitude sector.Tables 6 through 10 should be interpreted in the same way as Table 5. Observe that the thresholds in Tables 9 and 10 are not the ones in Table 2. Since there are far fewer non-jet aircraft and conflicts compared to the number of aircraft in a sector, the thresholds for non-jet aircraft counts and conflict-counts have a smaller range compared to those in Table 2.The time to conflict is computed as the ratio of the range to the range-rate (time derivative of range).The average time-to-go, defined as C12 in Ref. 8, considers each aircraft in the sector one at a time for determining the aircraft with which it is predicted to conflict.Next, the time-to-go is used for identifying those aircraft (conflict set) with which conflict is predicted in the near term (for example, in less than ten minutes).Minimum time-to-go is then determined for each conflict set, summed and divided by the number of sets to compute the average.Minimum values of the 1) two horizontal separation metrics, 2) two vertical separation metrics, and 3) one timeto-go metric were computed for each hour using actual track-data.Time histories and historgrams of sectors were created in the same manner as discussed for the traffic-count metrics.The trends in these data are summarized in Tables 11 through 15.The category no-conflict in Tables 11 and12 means that aircraft in the sector were outside each others vertical bounds, therefore horizontal separation was not computed for them.Horizontal separation is measured in nauticalmiles and the vertical separation is measured in feet.Time-to-go is measured in seconds.The categories no-conflict in Tables 13 and14 means that aircraft were outside each others horizontal bounds, and 'at most one aircraft' in
C. Flow MetricsThe three flow metrics discussed in this section are, average transit-time, average airspeed and the variance in airspeed of aircraft in the sector.Sector transit-time is defined as the time taken by the aircraft to cross the sector.The difference between the entry and exit times, obtained by processing the actual track-data provided the transit-time.Average transit-time for each sector was obtained by considering the transittime of all the aircraft that went though the sector during the 24-hour period.Figure 6 shows the histogram of the average transit-time in minutes of 364 higher altitude sectors.The minimum, mean, standard-deviation, and maximum values of the distribution shown in Fig. 6 were found to be 2.8 minutes, 8 minutes, 2.8 minutes and 21 minutes.Average airspeed was computed every ten-second in each sector using the ACES simulated data.Maximum average-airspeed within each hour was computed with 360 such values.Time histories and bar charts of sectors were then created with the maximum average-airspeed values.Results are summarized in Fig. 7 and Table 16.Observe that airspeed of higher altitude traffic generally lies in the 400 knots to 500 knots range.Like the average airspeed, the variance of airspeed (knots 2 ) was computed at ten-second intervals and then the maximum value was selected for each hour for each sector.Variance of airspeed is defined in Eq. 26 in Ref. 8. Time history of the bar charts of sectors with the maximum airspeed-variance in six-levels is shown in Fig. 8. Table 17 lists the five-levels, minimum, maximum, average, and maximum number of sectors at each of the five-levels, and the cumulative lower and upper bounds obtained using the bar charts in Fig. 8.The computations done with airspeed could have also been done with groundspeed, which is available in the actual track-data, but it was not used because groundspeed depends on winds, which vary from day to day.Airspeed on the other hand is a function of aircraft performance characteristics and is independent of winds.
IV. Geometric MetricsGeometric metrics are described in this section.Sector geometry features such as airways, navigational aids and airports define the kind and the frequency of tasks performed by the controller.Therefore, they contribute to controller workload directly and operational errors indirectly. 10,11Sector geometry metrics, including those proposed in Refs. 10 and 11, considered in this study are listed in Table 18.Data resulting from computations on higher altitude sectors are discussed in the subsections below.Geometric metrics listed in Table 18 are grouped into five categories.The first category "Geographical Location" consists of metrics one through three.The second category "Sector Dimensions" consists of metrics four through seven.The third category "Shape Attributes" consists of metrics eight through ten.The fourth category "Route Attributes" comprises of metrics 11 through 15.The last category "NeighborhoodAttributes" contains metrics 16 through 18.
A. Geographical LocationThe number of higher altitude sectors in each center was determined from the first three characters of Sector IDs of sectors with a base of 17,100 feet and above.For example, "ZAB37" indicates that the sector belongs to the Albuquerque center (ZAB).Counting all these sectors shown in Fig. 1 with the same first three letters provided the number of sectors in each center shown in Table 19.The 20 centers listed in Table 19 are organized in eight geographical regions listed in Table 20.The number of sectors in each region is obtained by summing the values corresponding to the centers that form the region.These results are given in the fourth column of Table 20.The numbers of lowaltitude, high-altitude and super-high-altitude sectors as defined in May 2007 ETMS adaptation data were found to be five, 248 and 111, respectively.The five low-altitude sectors had a base at or above 17,100 feet altitude.
B. Sector DimensionsTo determine the dimensions of each sector, the volume of each subsector was computed.A subsector is defined as a polygonal prism with a boundary defined by a polygon and a constant height.The complex geometric shape of a sector is achieved by placing subsectors on top, and to the side of other subsectors.The volume of a sector is the sum of the volumes of its subsectors.Figure 9 shows the histogram of the volume of sectors, in cubic-nautical-miles.Height of each sector was determined by subtracting the lower bound of the lowest subsector from the upper bound of the highest subsector.The distribution of the heights of the sectors is shown in Fig. 10.The histogram in Fig. 10 shows a bi-modal distribution with sector below 16,000 feet and above 56,000 feet.Dividing sector volumes with sector heights resulted in the reference-areas of the sectors.The distribution of the sector reference-areas is shown in Fig. 11.Reference-lengths of the sectors were obtained by taking the square-root of the reference-areas.The histogram of the reference-lengths is given in Fig. 12.Minimum, mean, maximum and standard deviation values of sector volume, height, reference-area and reference-length are summarized in Table 21.
C. Shape AttributesAspect-ratio, the ratio of the length to width, of the sectors was determined by computing the moments of inertia of the sectors.Prior to the computation of moments of inertia, centroids of the sectors had to be computed.Since a sector is composed of subsectors, the centroid of each subsector was determined first, and then, these centroids were weighted with the volumes of the subsectors to obtain the centroid of the sector.The moment of inertia tensor of  each subsector was computed with respect to the frame of reference located at the centroids, and then the parallel axis theorem was employed to determine the moment of inertia tensor with respect to the frame of reference located at the centroid of the sector.These moment of inertia tensors were then summed up to determine the moment of inertia tensor of the sector.Mathematical expressions for computing the centroid and the moment of inertia tensor for a two-dimensional polygonal object are given in Ref. 20.These equations were extended to three-dimensional polygonal prisms for generating the results discussed here.The eigenvalues of the moment of inertia tensor are the principal moments of inertia about the principal axes, which are the eigenvectors corresponding to the eigenvalues.If 11 I , 22 I and 33 I are the principal moments of inertia, the dimensions of a rectangular prism with the same principal moments of inertia as the sector (polygonal prism) are:( )3 1 ; 12 ! ! " = i I S V l ii i (1)where, ( )33 22 11 2 1 I I I S + + =and V is the volume of the sector.The aspect-ratio is given by the ratio of dimensions in Eq. (1), j i l l / such that j i ! .Figure 13 shows the distribution of the aspect-ratio of the 364 sectors.Sectors with an aspect-ratio close to one are of square shape, while the sector with an aspect-ratio closer to seven is a highly elongated rectangle.The minimum, mean, maximum and standard deviation aspect-ratio are 1.0, 2.0, 6.6, and 0.86, respectively.Reference 7 notes that the traffic pattern is usually highly parallel and less complicated in elongated sectors.If the principal moments of inertia are distinct, the principal axes are uniquely specified.If two or all three of the principal moments are the same, there is no choice of a preferred axis.Once the three principal axes were obtained, the two principal axes with larger projections on the horizontal plane were selected.Of these, the one with the larger eigenvalue was chosen as the preferred axis of the sector. Figure 14 shows the preferred axis of the sectors.This figure shows that most of the sectors are aligned along East-West direction.Along the East and West Coasts, sectors are oriented in the North-South direction.It is interesting that the sectors are aligned along the major traffic flow directions.The number of subsectors in a sector is an indicator of the shape complexity of the sector.Table 22 lists the number of sectors containing the same number of subsectors.This table shows that most of the sectors have a single subsector.One sector has 13 subsectors.The mean and the standard deviation of the number of subsectors were found to be 1.7 and 1.4.
D. Route AttributesThree types of navigation aids were counted to determine the number of navigation aids in sectors.These three types of radio navigation aids commonly employed by aircraft for navigation along routes are Very-High-Frequency Omnidirectional Range (VOR), VOR collocated with Distance Measuring Equipment (VOR-DME), and VOR collocated with Tactical Air Navigation System (VORTAC).The known latitude and longitude of each navigation aid were used for locating it in the sector. Figure 15 shows the distribution of sectors as a function of the number of navigation aids enclosed within their boundaries.There are a total of 1055 navigation aids.Some of these are shared by multiple sectors.Six sectors had no navigation aids and one sector had a maximum of 14 navigation aids.The mean and standard deviation of the number of navaids in a sector is 3.9 and 2.3.Next, the number of intersections in sectors was computed.Intersections are defined as locations where airways, Victor Airways and Jet Routes, intersect.Intersections are specified by latitude, longitude and altitude.This makes it possible to locate them in sectors.Figure 16 shows the histogram of sectors based on the number of intersections enclosed within the sectors.Sixty-four sectors had no intersections, 328 sectors had ten or fewer intersections, 36 sectors had more than 10 intersections, and one sector had 22 intersections.Mean and standard deviation were determined to be 4.3 and 4.1 intersections.Airways in sectors were determined using the association between the intersections and airways.Since an airway can be associated with several intersections within a sector, each associated airway is counted only once.An airway that went across the sector without passing through an intersection in the sector could not be counted.It may be possible to improve the airway count by using the association between the navaids and airways in addition to that between intersections and airways.Victor Airways were counted below 18,000 feet altitude and Jet Routes at or above 18,000 feet altitude.Both were counted in sectors whose base was below 18,000 feet and top above 18,000 feet altitude.A histogram of sectors as a function of the number of airways is given in Fig. 17.Airways were not found in sixty-four sectors because those sectors did not have any intersections.334 sectors had ten or fewer airways while 30 sectors had more than ten airways.The maximum number of airways was found to be 17 in only one sector.Mean and standard deviation values were determined to be 5 and 3.7 airways.Seventy-four major airports in the United States that are in the Federal Aviation Administration's (FAA) Aviation System Performance Metrics (ASPM) 21 were located within the horizontal confines of the higher altitude sectors and counted.Table 23 lists the numbers of sectors and the corresponding numbers of 74 ASPM airports.Eightythree sectors had one or more major U. S. airports.Only 16 sectors had two or more airports.Controllers have to ensure that aircraft do not enter a Special Use Airspace (SUA).This monitoring function adds to controller workload.Prohibited areas, military operations areas, alert areas, warning areas, and national security areas are considered to be SUA.Boundary and height information of the 1017 SUAs obtained from the FAA were used for locating them in sectors.Of the 364 sectors, only two sectors, ZHU 59 and ZDV 47 were found to completely contain one and two SUAs, respectively.The rest partially contained the SUAs.Statistics of sectors partially containing SUAs are discussed in the next subsection.
E. Neighborhood AttributesSectors above, below and to the sides of sectors were counted to determine the number of surrounding sectors.Minimum, mean, maximum and standard deviation of the number of surrounding sectors were determined to be 4, 13.3, 30 and 3.9.Sector 22 in Atlanta Center was found to have 30 sectors surrounding it.There were 202 sectors that had 13 or fewer sectors surrounding them, while 162 sectors had more than 13 sectors surrounding them.The distribution of the sectors as a function of number of surrounding sectors is given in Fig. 18.SUA polygons were related to a data structure of grid cells using the method described in Ref. 14.The mapping of the grid cells to the sectors was then used to identify the set of sectors that the SUAs could be in.The altitude range of the sectors was compared with the altitude range of the SUAs to determine if there was any overlap.Sectors with overlap were deemed to partially or fully contain these SUAs.If a SUA was associated with a single sector, that sector was considered to completely contain that SUA.In instances where the SUA was associated with more than one sector, the SUA was considered to be partially contained in the associated sectors.With the elimination of two sectors that fully contained SUAs, analysis was done on the remaining 362 sectors.SUAs were not found in 268 sectors.Eighty-one sectors were found to have five or fewer SUAs.Only 15 sectors were found to have more than five SUAs.Sector 26 in Houston Center contained 19 SUAs.Table 24 summarizes these results.Distance with respect to the center of the sector to the closest one of the 74 ASPM airports outside the sector was determined by first establishing which of them were within the confines of the sector boundary.These airports were excluded and distances to the airports outside the sector boundary were computed.The minimum of these distances gave the distance to the closest airport outside the sector. Figure 19 gives the histogram of the sectors with respect to distances to the closest airports.The closest airport outside a sector was 20.6 nautical-miles.The average and maximum distances were 116.5 and 422.2 nautical-miles.The standard deviation was 57.8 nautical-miles.A major airport was within 200 nautical-miles from the 335 sectors (both inside and outside the sector).Only 29 sectors were farther than 200 nautical-miles from a major airport.
V. SummaryThis paper was motivated by the problem of determining the design features of the current sectors so that future designs can be compared with the current design.Since the current design is based on tools and techniques used by controllers, a large departure from this design guided by automation needs will have implications in controllers being able to manage traffic in the new sectors.Since this study is focused on current sectors, fifteen traffic metrics related and eighteen geometric metrics related to controller workload were used to characterize the design of current sectors.Numerical values of these metrics were computed for sectors with a base of 17,100 feet and above in the current U. S. airspace.The fifteen traffic metrics were classified into three categories: seven traffic-count metrics, five separation metrics and three flow metrics.The eighteen geometric metrics were classified into five categories: three geographical location metrics, four sector dimension metrics, three shape attribute metrics, five route attribute metrics and three neighborhood attribute metrics.Ten out of the fifteen traffic metrics were computed using actual aircraft position data obtained from the field and the remaining five were computed using simulated aircraft position data.Use of simulated data provided an easy means of computing conflict-count, aircraft type and airspeed metrics.Conflictcounts are difficult to determine from actual data because controllers make sure that aircraft are separated.Only in rare occasions operational errors occur when separation minimums are violated.Aircraft type and airspeed information is available in the flight-plan therefore it is straightforward to carry this information in a simulation.It is possible to relate the flight-plan data to aircraft position update messages using aircraft identification tag that is common to both, but the processing is more involved.Maximum numbers of aircraft in sectors during the 24-hour period were computed using both actual and simulated data.Time histories were presented to show that the results obtained using simulated data compare very well with those obtained using actual data.Data corresponding to the distribution of sectors as a function of the traffic and geometric metric values were provided in tables and in bar charts.These results show that most sectors in the current airspace have fewer than 20 aircraft at any given time.Most sectors have less than five aircraft in climb phase, fifteen in cruise phase and five in descent phase.Most of the traffic at higher altitude sectors is jet traffic.It was shown that about 98% of the sectors have fewer that three pairs of aircraft in conflict in simulation.Horizontal and vertical separation metrics indicated that aircraft fly at the same altitude in most sectors.Airspeed was found to lie in a narrow range of 400 to 500 knots.Sector transit time was found to be normally distributed with a mean of eight minutes and standard deviation of three minutes.The maximum transit time was found to be 21 minutes.A wide variation was found in sector volume, area, height and length.Most sectors were found to be elongated with an aspect ratio of two and aligned with the main traffic flows.The number of subsectors, which is a measure of sector shape complexity, was found to be less than three in most sectors.Of the 364 sectors considered in this study, 328 sectors had ten or fewer airway intersections.Maximum number of airways in a sector was determined to be 17.On an average, a sector was surrounded by 13 other sectors.The maximum number of sectors surrounding a sector was found to be 30.None of the 1017 Special Use Airspaces (SUAs) were found in 268 sectors.Eighty-one sectors had five or fewer SUAs.The maximum number of SUAs in a sector was determined to be 19.A major U. S. airport was found within 200 nautical-miles from each of the 335 sectors.Only 29 sectors were farther than 200 nautical-miles from one of the 74 major U. S. airports.Figure 1 .1Figure 1.View of 364 higher altitude sectors with a floor at or above 17,100 feet altitude.
Figure 2 .2Figure 2. Actual and ACES simulated aircraftcounts.
Figure 4 .4Figure 4. Sectors with peak traffic-count in the first five levels, listed in Table2, using ACES data.
Figure 9 .9Figure 9. Sector volume histogram.Figure10.Sector height histogram.
Figure 11 .11Figure 11.Sector reference-area histogram.Figure12.Sector reference-length histogram.
Figure 12 .12Figure 11.Sector reference-area histogram.Figure12.Sector reference-length histogram.
Figure 13 .13Figure 13.Sector aspect-ratio histogram.Figure14.Preferred axis of the sectors.
Figure 14 .14Figure 13.Sector aspect-ratio histogram.Figure14.Preferred axis of the sectors.
Figure 16 .16Figure 16.Sector intersections histogram.
Figure 17 .17Figure 17.Sector airways histogram.
Figure 18 .18Figure 18.Surrounding sectors histogram.
Figure 19 .19Figure 19.Distance to closest airport outside the sector histogram.
Table 1 .1Sector capacities.MAP No. ofsectors911011151210131514231562164517281882193820222131231
Table 1 .1The average MAP value is approximately 17 and the most frequent MAP value is 18 for data in Table
Table 2 .2Peak traffic-count levels.Level Peak Traffic-Count Range10 -425 -9310 -14415 -19520 -24625 -29730 -348> 34
Table 4 .4Traffic metrics.NumberMetricDataType1Maximum number of aircraftActualCount2Maximum number of aircraft in climbActualCount3Maximum number of aircraft in cruise ActualCount4Maximum number of aircraft inActualCountdescent5Maximum number of jet aircraftSimulated Count6Maximum number of non-jet aircraftSimulated Count7Peak conflict-countSimulated Count8Average horizontal separation betweenActualSeparationaircraft in sector9Minimum horizontal separationActualSeparationbetween aircraft in sector10Average vertical separation betweenActualSeparationaircraft in sector11Minimum vertical separation betweenActualSeparationaircraft in sector12Average time-to-go to conflictActualSeparation13Sector average transit timeActualFlow14Average airspeedSimulated Flow15Variance in airspeed of aircraftSimulated Flow
Table 5 .5Numbers of sectors with peak climb-counts using actual track-data.Level Min. Mean Max. Threshold CumulativeCumulativeLowerUpper1282323363528236321408010359364301515364364
Table 7 .7Numbers of sectors with peak descent-counts using actual track-data.Level Min. Mean Max. Threshold CumulativeCumulativeLowerUpper1323345364532336420194110363364300115364364
Table 8 .8Numbers of sectors with peak jet-counts using ACES data.Level Min. Mean Max. Threshold CumulativeCumulativeLowerUpper171123415734122213421910144363319417515305364402252203523645031225362364600230364364
Table 9 .9Numbers of sectors with peak non-jet-counts using ACES data.Level PeakMin. Mean Max. Threshold CumulativeCumulativeNon-LowerUpperjetCount102022783611202361213661172306364320164333493644304154358364540165362364650026364364
Table 6 .6Numbers of sectors with peak cruise-counts using actual track-data.These distances are added and the average minimum separation is computed.The second horizontal separation metric, C9 in Ref. 8, is the minimum horizontal separation obtained within the altitude bands.It is the minimum of the horizontal distances, rather than the average, computed in the previous metric.The two vertical separation metrics are computed in a similar manner as the horizontal separation metrics.The first vertical separation metric, C8 in Ref. 8, places a horizontal neighborhood of ten nautical-miles around each aircraft in the sector.Vertical separation distance to the closest aircraft in the horizontal neighborhood is computed.The distances are then summed up to determine the average vertical separation.The second metric, C10 in Ref. 8, is the minimum of these vertical separation distances.Level Min. Mean Max. Threshold CumulativeCumulativeLowerUpper1191363405193402241402201017536430701491532436440153620355364502625361364600330363364700035363364800142364364
Table 10 .10Numbers of sectors with peak conflict-counts using ACES data.Level PeakMin. Mean Max. Threshold CumulativeCumulativeConflict-LowerUpperCount10361423471363472117154232222436432045903314364430174143473645404125359364650146362364760027363364870018364364
Table 1111Level Min.Min. Mean Max. Threshold CumulativeCumulativeSeparationLowerUpperRange10-47612216057616025-9156095109321439-165601411911662623644No-041202! 0364364conflictTable 12. Numbers of sectors with minimum minimum-horizontal-separation (nautical-miles) using actual track-data.Level Min.Min. Mean Max. Threshold CumulativeCumulativeSeparationLowerUpperRange10-49326834459334425-91422341011036139-165233901661623644No-041202! 0364conflict. Numbers of sectors with minimum average-minimum-horizontal-separation (nautical-miles) using actual track-data.
Table 13 .13Numbers of sectors with minimum average-minimum-vertical-separation (feet) using actual track-data.Level Min.Min. Mean Max. Threshold CumulativeCumulativeSeparationLowerUpperRange10-999104281353100010435321000-970011224397011223643No-060242! 0364364conflict
Table 14 .14Numbers of sectors with minimum minimum-vertical-separation (feet) using actual track-data.Level Min.Min. Mean Max. Threshold CumulativeCumulativeSeparationLowerUpperRange10-999105287359100010535921000-97005163497011223643No-060242! 0364364conflict
Table 15 .15Numbers of sectors with minimum average-minimum-time-to-go (seconds) using actual track-data.Level Min.Min. Mean Max. Threshold CumulativeCumulativeTime-to-LowerUppergo Range10-11913126211120132112120-2391594144240343363240-35982658360423574360-47911124480483585480-5991724600593616At most399305! 0oneaircraftFigure 7. Time-history of histograms of number of sectors grouped in six peak average-airspeed levels in Table16using ACES data.Table16.Numbers of sectors with maximum average-airspeed (knots) using ACES data.Figure8.Time-history of histograms of number of sectors grouped in five peak airspeed-variance levels in Table17using ACES data.
Table 17 .17Numbers of sectors with maximum airspeed-variance (knots 2 ) using ACES data.Level Max.Min. Mean Max. Threshold CumulativeCumulativeAirspeed-LowerUppervarianceRange10-29331373273033327230-592513318760197358360-8957413890326364490-119018371203613645120-140013141364364
Table 18 .18Sector geometry metrics.NumberMetricCategory1Number of sectors in centersGeographical2Number of sectors in eight airGeographicaltraffic control regions3Sector-type: low, high or super-Geographicalhigh4Sector volumeDimensions5Sector heightDimensions6Sector areaDimensions7Sector lengthDimensions8Aspect ratio -length/widthShape9Principal directionShape10Number of subsectorsShape11Number of navaidsRoute12Number of intersectionsRoute13Number of airwaysRoute14Number of airportsRoute15Special Use Airspace completelyRouteinside16Number of surrounding sectorsNeighborhood17Special Use Airspace containedNeighborhoodpartially18Distance to closest major airportNeighborhood
Table 19 .19Numbers of sectors in centers.Center ID ZAB ZAU ZBW ZDC ZDV ZFW ZHU ZIDZJX ZKC# sectors23251319281817252027Center ID ZLA ZLC ZMA ZME ZMP ZNY ZOA ZOB ZSEZTL# sectors168621181011271022
Table 20 .20Centers in eight regions.RegionsCode Centers# sectorsCentral RegionACEZKC27Eastern RegionAEA ZNY, ZDC29Great Lakes RegionAGL ZMP, ZAU, ZID, ZOB95New England RegionANE ZBW13Northwest Mountain Region ANM ZSE, ZLC, ZDV46Southern RegionASOZME, ZTL, ZJX, ZMA69Southwest RegionASW ZAB, ZFW, ZHU58Western Pacific RegionAWP ZOA, ZLA27
Table 21 .21Summary of sector dimensions.MetricMinimum MeanMaximum Std. Dev.Volume (cubic-1,909 77,775572, 21086,034nautical-mile)Height (feet)4,000 47,54182,85030,164Area (square-1,6789,39745,7786,369nautical-mile)Length (nautical-419321428mile)
Table 22 .22Numbers of subsectors in sectors.# Subsectors# Sectors1224297322465563718391121131
Table 23 .23Numbers of 74 ASPM airports in sectors.# Airports# Sectors02811672103551
Table 24 .24Number of SUAs contained partially in sectors.# SUAs# Sectors# SUAs# Sectors0268711318222291312101481115812363191
		
		

			
AcknowledgementsThe authors thank Dr. Hak-Tae Lee of University of California Santa Cruz for generalizing the moment of inertia equations from two-dimensional polygons to three-dimensional polygonal prisms and providing the Java program that was used for computing the principal directions and aspect ratio of sectors.We also thank Christopher Gleim from the University of Louisville who as a part of his internship task wrote the computer program for the Special Use Airspace analysis discussed in this paper.
			

			

				


	
		Initial Concepts for Dynamic Airspace Configuration
		
			ParimalKopardekar
		
		
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		10.2514/6.2007-7763
	
	
		7th AIAA ATIO Conf, 2nd CEIAT Int'l Conf on Innov and Integr in Aero Sciences,17th LTA Systems Tech Conf; followed by 2nd TEOS Forum
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		A Weighted-Graph Approach for Dynamic Airspace Configuration
		
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	Martinez, S., Chatterji, G. B., Sun, D., and Bayen, A., "A Weighted-Graph Approach for Dynamic Airspace Configuration," Proceedings of AIAA Guidance, Navigation, and Control Conference, Hilton Head, SC, August 20-23, 2007.



	
		Temporal and Spatial Distribution of Airspace Complexity for Air Traffic Controller Workload-Based Sectorization
		
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			American Institute of Aeronautics and Astronautics
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		10.2514/6.2007-6877
		
	
	
		AIAA Modeling and Simulation Technologies Conference and Exhibit
		Hilton Head, SC
		
			American Institute of Aeronautics and Astronautics
			August 20-23, 2007. 14 July 2008
		
	
	AIAA-2007-6877
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		Build 4 of the Airspace Concept Evaluation System
		
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		Proceedings of AIAA Modeling and Simulation Technologies Conference and Exhibit
		AIAA Modeling and Simulation Technologies Conference and ExhibitKeystone, Colorado
		
			August 21-24, 2006
		
	
	AIAA-2006-6110
	16 Meyn, L., et al, "Build 4 of the Airspace Concept Evaluation System," AIAA-2006-6110, Proceedings of AIAA Modeling and Simulation Technologies Conference and Exhibit, Keystone, Colorado, August 21-24, 2006.



	
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			ShannonZelinski
		
		
			LarryMeyn
		
		10.2514/6.2006-6115
		AIAA 2006-6115
	
	
		AIAA Modeling and Simulation Technologies Conference and Exhibit
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			August 15-18, 2005 18 Zelinski,. August 21-24, 2006
		
	
	Proceedings of AIAA Modeling and Simulation Technologies Conference and Exhibit
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		Impact of Airport Capacity Constraints on National Airspace System Delays
		
			GanoChatterji
		
		
			YunZheng
		
		10.2514/6.2007-7712
	
	
		7th AIAA ATIO Conf, 2nd CEIAT Int'l Conf on Innov and Integr in Aero Sciences,17th LTA Systems Tech Conf; followed by 2nd TEOS Forum
		Belfast, Northern Ireland
		
			American Institute of Aeronautics and Astronautics
			September 18-20, 2007
		
	
	AIAA-2007-7712
	Chatterji, G. B., and Zheng, Y., "Impact of Airport Capacity Constraints on National Airspace System Delays," AIAA- 2007-7712, Proceedings of 7th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Belfast, Northern Ireland, September 18-20, 2007.



	
		Automating the Process of Terminal Area Node-Link Model Generation
		
			Hak-TaeLee
		
		
			ThomasRomer
		
		10.2514/6.2008-7101
		
	
	
		AIAA Modeling and Simulation Technologies Conference and Exhibit
		Honolulu, Hawaii
		
			American Institute of Aeronautics and Astronautics
			August 18-21, 2008. 14 July 2008
		
	
	Lee, H., and Romer T. F., "Automating the Process of Terminal Area Node-Link Model Generation," Proceedings of AIAA Modeling and Simulation Technologies Conference and Exhibit, Honolulu, Hawaii, August 18-21, 2008. 21 URL: http://aspm.faa.gov/aspm/entryASPM.asp [cited 14 July 2008]