DEFINING DYNAMIC ROUTE STRUCTURE FOR AIRSPACE CONFIGURATION · DEFINING DYNAMIC ROUTE STRUCTURE FOR AIRSPACE CONFIGURATION point of P with respect to Q. 2.2 Intersections Merge and

DEFINING DYNAMIC ROUTE STRUCTURE FOR AIRSPACECONFIGURATION

Shannon Zelinski, Michael JastrzebskiNASA Ames Research Center, University of California Santa Cruz

Keywords: airspace configuration, traffic flow, critical points, routing

Abstract

This paper describes a method for defining routestructure from flight tracks. Dynamically gen-erated route structures could be useful in guid-ing dynamic airspace configuration and helpingcontrollers retain situational awareness under dy-namically changing traffic conditions. Individualmerge and diverge intersections between pairs offlights are identified, clustered, and grouped intonodes of a route structure network. Links areplaced between nodes to represent major trafficflows. A parametric analysis determined the al-gorithm input parameters producing route struc-tures of current day flight plans that are closestto todays airway structure. These parameters arethen used to define and analyze the dynamic routestructure over the course of a day for current dayflight paths. Route structures are also comparedbetween current day flight paths and more userpreferred paths such as great circle and weatheravoidance routing.

Nomenclature

A = airway structureB = boundaryC = clusterD = divergeI = intersectionL = linkM = mergeN = noden = numberP = path or sequence of pointsp = point positionR = route structurer = lateral radial distanceS = airway segmentw = weightz = vertical distanceδ = structure deviationη = boundary proximity percentageλ = structure representationρ = intersection representationσ = standard deviationτ = flight track data time rangeω = filtering threshold

1 Introduction

The current airspace sector design evolved overdecades, driven by human-centered separationassurance and an airway system of ground-basednavaids. The future system is migrating towardmore direct and flexible user-preferred routing.Automation tools and dynamic reconfigurationof airspace boundaries will enable controllers

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SHANNON ZELINSKI, MICHAEL JASTRZEBSKI

to adapt to changing weather and traffic condi-tions and increase controller staffing flexibility.Structure-based abstractions of traffic conditionsare necessary both to trigger and guide airspaceboundary changes and to quickly give controllerssituational awareness. Histon et al [1] identi-fied elements of structure-based traffic abstrac-tion that controllers use to maintain airspace sit-uation awareness. Two key elements identified,standard flows and critical points (where majorflows cross and merge), have been used as inputsin several automated airspace boundary reconfig-uration methods [2, 3, 4, 5]. Complex air trafficnetworks have been developed to study aggregatesystem behavior and robustness to disturbances[6]. Route structure is an abstraction of the airtraffic network based on standard flows and crit-ical points. A method of quickly determiningroute structure is necessary for controllers andairspace configuration to adjust to flexible user-preferred routing.

Several methods have been proposed to de-fine the route structure elements of a given setof flight trajectories. Most methods begin withtwo-dimentional grid structures that capture in-formation about traffic passing through each gridcell. Xue [3] used the heading variance of flightswithin each grid cell to determine if the cell be-longed to a major traffic flow or intersection pointand could be used as an airspace boundary con-straint. Other methods used flight occupancycounts within each grid cell along with othertechniques to bundle flight trajectories into flows[7] or to create an abstract network flow graphof traffic [4]. Of the methods that defined routestructure connections between flows and criticalpoints, Sabhnani et al [7] proposed two top-downapproaches that first identified flows and thendefined their intersections to be critical points,whereas work preceding this paper [8] proposed abottom-up approach that identified critical pointsfirst. Li et al [5] took a short cut by refininga complex route structure generated from flightplans. However, this approach depended uponthe existing airway structure elements found intoday’s flight plans.

This paper extends preceding work [8] by

adding an altitude component to critical pointidentification and linking critical points togetherwith flows to form a route structure. A paramet-ric analysis is performed to determine the algo-rithm input parameters that produce route struc-tures that are closest to today’s airway structure.These parameters are then used to extract and an-alyze the dynamic changing route structure overthe course of a day for current day flight pathsand for more user preferred paths such as greatcircle and weather avoidance routing.

The remainder of this paper is organized asfollows. Section 2 describes the method of defin-ing route structure from flight tracks. A paramet-ric analysis identifies optimal method parametersin section 3. Sections 4 and 5 analyze route struc-tures from dynamically shifting time windows oftraffic, and from alternate user preferred routing,respectively. Finally, conclusions are presentedin section 6.

2 Defining Route Structure

This section describes how flight track data areprocessed to define a route structure. First in-dividual intersection points were generated frompairs of flights within lateral and vertical prox-imity of one another. Intersection points withinanother set of specified lateral and vertical prox-imity of one another formed cluster points. Clus-ters were further grouped into nodes to simplifythe structure. Finally, links were placed betweennodes with the nominal paths of flights formingeach link representing flow paths.

2.1 Proximate Points

The first step in route structure generation iden-tifies points on pairs of flight tracks that comewithin a specified proximity of one another.Let P = p1, ..., pn be an ordered set of lati-tude/longitude/altitude/time coordinates describ-ing the trajectory of flight P. Similarly, let Q =q1, ...,qm describe the trajectory of flight Q. Forall points within a specified time range, any pointin P that comes within a lateral radius rI and ver-tical distance zI of any point in Q is a proximate

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DEFINING DYNAMIC ROUTE STRUCTURE FOR AIRSPACE CONFIGURATION

point of P with respect to Q.

2.2 Intersections

Merge and diverge intersections classify the in-teractions between pairs of flights. When twoflights come within a specified proximity of oneanother, their paths merge. When two flightsoriginally within a specified proximity of one an-other are no longer within the specified proxim-ity, their paths diverge. For every consecutive se-quence of flight track coordinates on P that areproximate to Q, the first point is a merge intersec-tion, and the last point is a diverge intersection.For every intersection on P with respect to Q, anintersection is also identified on Q with respect toP.

Boundary intersections occur where flightscross a given airspace boundary. Any two con-secutive points on a flight track that are in differ-ent specified airspace regions, such as sectors orcenters, produce boundary intersections. Theseare not necessary to generate a route structure.However, if a route structure is generated for onlya specified bounded region, boundary intersec-tions make it possible to identify flows that enteror exit the region.

Rather than storing single instances of inter-section, flight track points are tagged as mergeand diverge intersections with respect to multipleother flights and as boundary intersections whenstraddling a boundary. Each flight track pointtagged with merges defines a merge intersectionIMi with position p(IMi) identical to the trackpoint position and with weight w(IMi) equal tothe number of individual merges identified withrespect to other flights at this track point. Adiverge intersection IDi is defined similarly. Aboundary intersection IBi is different only in thatw(IBi)≡ 1 because a single track point cannot in-tersect the same boundary multiple times. Thismethod allows a single flight track point to de-fine up to three intersections, one of each type.

2.3 Clusters

Clusters characterize groups of intersectionswithin close spacial proximity. Each intersec-

tion may belong to only one cluster in an in-tersection to cluster (I → C) mapping. Theposition p(Ci) and weight w(Ci) of cluster Ciare the centroid and sum weight of the inter-sections within Ci, respectively. Sets IM, ID,and IB are clustered separately to form sets ofmerge clusters, CM = {CM1,CM2, ...}, divergeclusters, CD = {CD1,CD2, ...}, and boundary clus-ters, CB = {CB1,CB2, ...}, respectively.

An agglomerative clustering technique wasused because it handles data outliers well and au-tomatically determines the final number of clus-ters. Pairs of intersection points are clusteredin order of increasing lateral distance if they arewithin rC and zC of each other. Each groupedpoint pair is replaced by the group centroid forconsideration in the next clustering iteration. Theprocess repeats until all groups with centroidswithin rC and zC of each other are clustered.Boundary intersections are different enough frommerge and diverge intersections, that unique clus-tering parameters, rCB and zCB , are used to clusterboundary intersections.

The resulting set of clusters may contain nu-merous low weight outliers, caused by randomtraffic, which should be filtered. A differentweight threshold should be used for filtering dif-ferent time ranges of flight track data analyzed.Let τ be the flight track data time range and letωC be a rate threshold such that cluster Ci is fil-tered if w(Ci) < τ·ωC. This way, the same ωCmay be used for various τ with similar filteringeffect. Because boundary cluster weights are de-termined by instances of flights crossing a bound-ary rather than instances of flight pair intersec-tions, a unique ωCB filters boundary clusters.

2.4 Nodes

Nodes are at the top level of intersection group-ings and serve as the end points for links repre-senting traffic flows. Crossing traffic flows mayform merge and diverge clusters very close toone another or merge or diverge clusters may ex-ist very close to the boundary. Therefore, nodesare used to represent groups of clusters of mixedtype. Building a network of flows between nodes

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rather than individual clusters significantly sim-plifies and strengthens the resulting route struc-ture.

Each cluster may belong to only one node.A boundary node refers to any node contain-ing a boundary cluster. Interior nodes refer tonodes without any boundary clusters. The po-sition p(Ni) of node Ni is the centroid of allclusters within Ni. Node weight w(Ni) is thesum weight of all clusters within Ni. Nodes canalso be expressed as groups of intersections be-longing to its clusters (I → C → N ≡ I → N).The spacial size of node Ni is measured by thethree dimensional standard deviation, σ(Ni) =(σx(Ni),σy(Ni),σz(Ni)), of all I within Ni fromp(Ni).

A different method is used to group clustersinto nodes than intersections into clusters. Ini-tially each cluster defines a unique node. Nodeswith overlapping σ are too close with respectto their spacial size to serve as traffic flow endpoints. Therefore, if the distances between nodesd(Ni,N j) < σ(Ni) + σ(N j) in all three dimen-sions, then clusters within Ni and N j are groupedinto a single node. Additionally, if a single trackpoint defines multiple intersections grouped tounique nodes, these nodes are grouped into a sin-gle node.

2.5 Links

Links are directed connections between pairs ofnodes representing traffic flow. Through I → Nmappings, all flights with track points definingintersections, may be expressed as a sequence ofnodes along the flight trajectory. Let Li j specifya set of flight segments from Ni to N j. Only seg-ments between consecutive nodes along a flighttrajectory are considered. Let link weight w(Li j)be the number of flight segments in Li j. LetP(Li j) specify the nominal path or flow path ofall segments in Li j. Link paths may curve andbend around special use airspace or weather asthey travel between nodes. The sample rate usedto define link paths is one point every 8 nmi. Thissample rate is similar in distance to the 1-minuteresolution flight tracks analyzed.

As with clusters, the resulting set of links mayhave many low weight outliers which should befiltered. Let ωL be a rate threshold such that linkLi j is filtered if w(Li j) < τ·ωL. Filtering linksalso has an additional filtering effect on nodes.Boundary nodes with less than one link and in-terior nodes with less than two links are filtered.If nodes are filtered, links are recalculated andthe process iterates until the number of nodes andlinks stabilizes.

3 Parametric Analysis

There are a number of parameters described insection 2 that affect the fidelity of the resultingroute structure. Route structure links and nodesare functionally equivalent to today’s airways andtheir intersections. Results from a range of pa-rameters are analyzed to find values that produceroute structure similar to today’s airway struc-ture.

Flight tracks used to generate the route struc-tures were 1-minute resolution simulated trajec-tories of flight schedules and filed flight plansfrom a high traffic volume, good weather Tues-day on 4/21/2009. This analysis focused on highaltitude tracks in Kansas City Center (ZKC) dur-ing the peak four hours, approximately 15:30-19:30 ZKC local time. Because the ZKC highaltitude sector floor was 24,000 ft, only tracks at24,000 ft and above were considered.

There are four types of airways in the US.V-routes (below 18,000 ft) and J-routes (above18,000 ft) are classic airways using ground-basednavaids. T-routes (below 18,000 ft) and Q-routes(above 18,000 ft) are newer area navigation orRNAV-based airways. This analysis focused onthe 38 J-routes and 2 Q-routes in high altitudeZKC shown in Fig. 1.

3.1 Parameters

There are three types of parameters used to de-fine route structure. The parameters used to de-fine intersection points are rI and zI . The param-eters used to define cluster points are rC, zC, rCB ,and zCB . Finally, parameters ωC, ωCB , and ωL

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Intersection pointAirway segmentBoundary pointZKC sector boundaries

150 nmi

Fig. 1 Airways and their intersections withinhigh altitude Kansas City Center (ZKC).

filter low weight clusters and links. The rangeof intersection and cluster parameters exploredwas designed with aircraft separation tolerancesin mind. En-route lateral and vertical aircraftseparation tolerances are five nmi and 1,000 ft,respectively. Therefore, the analysis consideredvalues of rI , rC, and rCB between three and 30nmi and values of zI , zC, and zCB between 500and 3,000 ft. Recall from section 2 that eachflight pair interaction produces two intersectionpoints, one on each flight trajectory, separated byas much as rI laterally and zI vertically. There-fore, rC ≥ rI and zC ≥ zI to guarantee that thesepoints are clustered. Filtering parameters wereincreased from zero.

3.2 Route Structure Evaluation

Route structure results from each set of parame-ters were evaluated to determine their precisionand accuracy. Precision metrics compare routestructure to the individual flight tracks they rep-resent and accuracy metrics compare route struc-ture to the current airway structure.

Precision metrics include traffic deviationsfrom route structure and route structure intersec-tion representation. Let σr(Li j) be the lateralstandard deviation, of all flight track segments inLi j from P(Li j). Let traffic deviation σr(L) be theaverage of all σr(Li j) weighted by w(Li j).

Route structure intersection representation, ρ,

measures the ratio of flight intersections repre-sented by the final route structure. It is the ratioof sum weight of all nodes over the sum weightof all intersections before cluster filtering. If allfiltering parameters were zero, ρ would alwaysbe one.

Route structure accuracy metrics compareroute structure with airway structure to find theright balance of abstraction and precision. Let Si jspecify the airway segment between airway in-tersections Mi and M j. Just as link nominal pathpoints are positioned every eight nmi along eachpath, airway path points are placed every eightnmi along each airway segment. Let P(Si j) be thesequence of (x,y) points every eight nmi alongSi j. Unlike links, airway segments do not have avertical component or a weight.

Accuracy metrics include deviation and rep-resentation metrics between airway and routestructure. The route structure deviation, δR, isthe average lateral distance of each link nomi-nal path point pk(Li j) from its closest airway seg-ment, weighted by w(Li j). The airway structuredeviation, δA, is the average lateral distance ofeach airway path point pk(Si j) from it’s closestlink.

Airway and route structure representationsare the ratios of each structure found to be clos-est to a piece of the other structure. Let nSi j bethe number of path points on P(Si j). Let nL(Si j)be the number of points from all P(L) identify-ing Si j as the closest airway segment. The airwaystructure representation is defined as

λA =∑min[nSi j ,nL(Si j)]

∑nSi j

.

Similarly, let nLi j be the number of path pointson P(Li j) and let nS(Li j) be the number of pointsfrom all P(S) identifying Li j as the closest link.The route structure representation is defined as

λR =∑ [min[nLi j ,nS(Li j)]·w(Li j)]

∑ [nLi j ·w(Li j)].

This is similar to λA calculation, only λR isweighted by w(Li j).

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Table 1 summarizes the precision and accu-racy metrics. The right column indicates the goalof the parametric analysis to either minimize (-)or maximize (+) each metric. Note that the goal isto minimize all deviation metrics and maximizeall representation metrics.

Table 1 Summary of route structure evaluationmetrics

Precision Metricsσr(L) = lateral traffic deviation -ρ = intersection representation +

Accuracy MetricsδR = route structure deviation -δA = airway structure deviation -λR = route structure representation +λA = airway structure representation +

3.3 Results

The goal of the parametric analysis was to findparameters that minimized σ and δ metrics, andmaximized ρ and λ metrics. A simple optimiza-tion formula was designed to combine the met-rics in Table 1 into a single value to minimize bymultiplying metrics to minimize and dividing bymetrics to maximize.

J =σr(L)·δR·δA

ρ·λR·λA

This function was used to guide the searchfor route structure parameters that produced thesmallest deviation metrics with the largest andmost balanced structure representation metrics.Balanced structure representation metrics en-sured that the airway and route structure networklengths were similar and thus represented trafficat a similar level of abstraction.

Table 2 shows the set of optimal parame-ter values identified and used in remaining routestructure analyses. The optimal intersection pa-rameters were very similar to standard separa-tion criteria with rI equalling the lateral stan-dard and zI only 200 ft greater than the verti-

cal standard. As expected, all clustering param-eters were greater than intersection parameters.Boundary intersection clustering required a rCB

almost three times rC. Merge and diverge clus-tering produced much larger weight clusters thanboundary intersection clustering. Therefore, ωCis eight times larger than ωCB . Links were lessseldom formed due to the requirement of fullflight trajectory segments between nodes and be-cause they were iteratively filtered. Therefore, ωLwas never raised above one.

Table 2 Optimal set of route structure generationparameters.

rI = 5 nmi zI = 1,200 ftrC = 6 nmi zC = 2,000 ftrCB = 17 nmi zCB = 2,000 ftωC = 20 w/hr ωCB = 2.5 w/hrωL = 1 w/hr

Table 3 shows the evaluation metrics obtainedusing the parameters in Table 2. In general, σr(L)responded mostly to intersection and cluster pa-rameters. As ωC and ωCB were increased, ρ andλA decreased slightly, and λR increased. Whenthe filtering parameters were increased too much,ρ and λA began to fall more rapidly. The higherλA and λR, the lower there respective δA and δRwere. This is because portions of the unrepre-sented structure began to skew deviation metricswith closest distances to parts of the other struc-ture that clearly did not match. In general, δAtended to be greater than δR because many un-represented links were in similar lateral locationsas other links at different altitudes. The airwaystructure was more prone to skewing δA due tounderutilized airway segments. The optimal pa-rameters were chosen such that λA and λR weresomewhat balanced and as high as possible.

Figure 2 illustrates the route structure gen-erated from the parameters in Table 2. Linksare shown as lines with color indicating linkweight. Nodes are shown as red dots with sizeindicating node weight. Because node weighttends to increase very quickly, the square rootof node weight is shown to better view relative

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Table 3 Evaluation metrics obtained from optimalset of route structure generation parameters.

σr(L) = 1.79 nmi ρ = 0.57δA = 5.81 nmi λA = 0.73δR = 1.67 nmi λR = 0.53

weights. Black and gray lines underlying theroute structure are the same airway segments andsector boundaries, respectively, shown in Fig. 1.The route structure completely overlaps many ofthese black lines. Figure 2 visually confirms theaccuracy metrics from Table 3. It can be seenthat route structure elements that follow the air-way structure, follow closely. Some airway seg-ments do not get enough traffic to be representedat all whereas a few links highlight flows whereno published airway segment exists. Becauseroute structure is altitude specific, Fig. 2 showsseveral instances where links appear to overlap orcross without a node.

Fig. 2 Route structure generated from optimalparameters overlaying airways.

3.4 Robustness Verification

The parametric analysis calibrated route struc-ture parameters to a single day. To demon-strate that these parameters do not need to bere-calibrated, the same parameters optimized for4/21/2009 were used to create route structures forthe peak four-hour periods of three other low-weather Tuesdays spread throughout 2009. Ta-

ble 4 shows the evaluation metrics as well as afew additional metrics for all four days. Ad-ditional metrics include number of flights (n f ),number of links (nL), number of nodes (nN),average link weight (wL), average node weight(wN), and the average lateral standard deviationof points within each node from the node cen-troid (σr(N)). Metrics are grouped into numbers,average weights, representation ratios, and devia-tions. The values for each metric are very similarwhen compared between different days, nor are4/21/2009 metrics always the best. This verifiesthat the chosen set of parameters are robust to dif-ferent days of flight schedules. The same param-eters are used to analyze dynamic route structureand route structures for user preferred routing infollowing sections.

Table 4 Evaluation metrics from the peak four-hour periods of four low weather Tuesdays in2009.

2/10 4/21 7/14 11/10n f 1,098 1,054 1,059 1,064nL 285 315 284 268nN 129 138 121 125wL 9.46 9.83 9.87 10.77wN 510.80 554.88 545.07 604.38ρ 0.52 0.57 0.51 0.56λA 0.73 0.73 0.75 0.72λR 0.60 0.53 0.58 0.59σr(L) 2.26 1.79 2.07 2.05σr(N) 4.69 4.69 5.07 4.78δA 4.45 5.81 5.47 4.78δR 1.71 1.67 1.73 1.86

4 Dynamic Route Structure

One of the main potential benefits of route struc-ture is that it may be generated dynamically tovisualize how the structure changes with time.Figure 3 shows multiple route structures from4/21/2009 by shifting the four-hour time windowin two-hour increments from the peak four-hoursshown in Fig. 2. In some instances, links andnodes move slightly, but for this good weather

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Fig. 3 Dynamic route structure shifted every two hours.

day, most of the route structure dynamics areincreases and decreases in weight. Nodes andlinks appear and increase in weight up to the peaktime period, after which they begin to decrease inweight and disappear. Tracks from time rangesoutside of the peak-10 hours to peak+6 hoursshown did not produce any route structure.

The numbers of flights, links, and nodes (n f ,nL, and nN) for each of the route structures fromFig. 3 are shown in Fig. 4. Average link and nodeweights (wL and wN) are shown in Fig. 5. Bothlink and node numbers and weights correlate withthe number of flights, especially nodes.

Figure 6 shows intersection, airway, and routestructure representations (ρ, λA, and λR) for eachof the route structures from Fig. 3. Intersectionand airway representations increase with numberof flights, whereas route structure representationdecreases. This is because as segments of the air-way structure saturate, more and more flows areformed in places where no airway has been pub-lished.

Average deviation metrics are shown in Fig.

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7. The average lateral standard deviations of in-tersection points for their node centroids (σr(N))and flight tracks from their link paths (σr(L)) arestable with respect to number of flights. Thesemetrics depend far more on the route structuregeneration parameters than the track data pro-cessed. Route structure deviation from airwaysis also very stable. However, airway deviationfrom route structure correlates heavily to route

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structure representation. Structure deviation met-rics are more accurate when representations arehigh. The δA inaccuracies introduced by unrep-resented airways are more prominent because theairway structure is stable and covers all of ZKC,whereas the route structure becomes more local-ized as λR decreases. With extremely localizedroute structures such as at peak+6, unrepresentedairway segments in West ZKC introduce large er-rors because the closest links are far away in EastZKC.

5 User Preferred Routing

This section compares route structures for severaldifferent routing options. The same 4/21/2009flight schedules used to generate filed flight plan

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tracks in section 3 were used to generate greatcircle tracks and weather rerouted tracks for thesame peak four-hour time period (15:30-19:30 lo-cal) in ZKC.

5.1 Great Circle Routing

The route structure of great circle flight tracksresulted in significantly lower intersection repre-sentation than that of flight plan tracks when us-ing parameters from Table 2. When the clusterfiltering parameters were reduced to increase in-tersection representation to a value similar to theflight plan route structure, the number of linksand nodes quadrupled with no increase in aver-age link weight and a decease in average nodeweight. Figure 8 shows great circle route struc-tures with the original parameters on top and re-duced cluster filter parameters on the bottom. Inaddition to increased numbers of links and nodes,Fig. 8 shows how lowering the cluster filters sig-nificantly shortened the average link length. Thisreaffirms the integrity of the originally chosen pa-rameters. The total number of flight pair inter-sections was actually quite similar between flightplan and great circle routing. Great circle routingsimply spread these intersections out more ran-domly such that only 21% of the traffic intersec-tions were stable enough to form a structure.

Figure 8 also shows how great circle routestructure rarely conforms to the airway structure.

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Fig. 8 Great circle route structures for origi-nal and reduced cluster filters.

The largest nodes are in different places than theflight plan route structure and are often close tosector boundaries. If the future airspace systemis to support user preferred routing, route struc-tures like these will enable designing airspace toaccommodate them.

5.2 Weather Avoidance Reroutes

User preferred reroutes around weather weresimulated [9] for both original flight plans andgreat circle routing. The simulated weather werestationary contours of percent likelihood that aflight would avoid the area [10]. These weathercontours blocked several airways in SoutheastZKC.

Figure 9 shows the route structures forthe flight plan and great circle tracks avoidingweather. The weather contours are shown under-lying the route structure with color indicating thepercent likelihood of a flight avoiding the area.Both route structures clearly show links of rela-tively high weight curving to avoid the weather.In the flight plan based route structure, a newnode with weight 10,088 (

√w(N) ≈ 100) ap-

Fig. 9 Route structures for flight plan andgreat circle tracks avoiding weather.

pears just north of the weather. This is muchlarger than the largest weight node (w(N) =6,885,

√w(N) ≈ 83) from the non weather im-

pacted route structure in Fig. 2. Although thenon weather impacted great circle route structureat the top of Fig. 8 does not show any signif-icant structure in the weather location, weatherreroutes sufficiently compressed flight tracks toform the structure around the weather seen at thebottom of Fig. 9.

5.3 Comparative Analysis

Route structures were compared between flightplan and great circle tracks and between origi-nal and weather rerouted tracks. Figure 10 showsprecision metrics for each of these four routestructures. As mentioned in section 5.1, ρ is sig-nificantly lower for great circle routing and num-bers and weights of nodes and links follow a sim-ilar trend. The pre-filtered sum weight of all Iwas actually only 10% less for great circle thanflight plan routing, indicating a similar overallcomplexity in terms of conflict likelihood. How-

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ever, great circle routing spread out these inter-sections such that most were filtered. Weatherreroutes actually caused a slight increase in ρ

for great circle because of the track compress-ing effect of the weather obstacle. Route struc-tures had higher σr(L) for user preferred rout-ing options; σr(L) was higher for great circleroute structures than for flight plan route struc-tures and was higher for route structures withweather reroutes than for routes structure withoutweather reroutes. In contrast, σr(N) was far lessaffected by routing. σr(N) was slightly greaterfor weather reroutes than original routing, fol-lowing a similar although less pronounced trendas σr(L). However, an opposite trend to σr(L)appeared in that σr(N) was slightly less for greatcircle than flight plan routing.

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Fig. 10 Precision metrics comparing flightplan (FP) to great circle (GC) and originalrouting to weather reroutes.

In addition to metrics compared in pervioussections, metrics relating route structure to sec-tor boundaries were compared. Let nL and nN bethe average numbers of unique links and interiornodes, respectively, within each sector. Each ad-ditional link or node within a sector potentiallyincreases the focus split of a controller. Let nLX

be the average number of links entering or ex-iting a sector. A lower nLX is preferred to mini-mize sector handoff workload for controllers. Letn̂L, n̂N , and n̂LX be maximum numbers of links,

nodes, and boundary crossing links, respectively,in a single sector. Figure 11 shows these sectorrelative numbers of links and nodes. The totalnumbers of links and nodes were less for greatcircle than flight plan route structure but greaterfor weather reroutes than original routes. The av-erages in Fig. 11 echo this result. The increasedaverages can be attributed to weather reroutesthat cause flights to fly through a few extra sectorsto avoid the weather. Even though the averagenumber of links per sector was less for great cir-cle than flight plan route structure, the maximumnumber of links was greater due to the shifting lo-cation of links with respect to sector boundaries.The same effect is seen for maximum nodes forweather rerouted great circle tracks.

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Controllers prefer major flows and criticalpoints to be well within sector boundaries. Con-trollers must be aware of not only flights within asector, but also just outside the sector boundary toguarantee separation. Ideally flows should stay atleast five nmi inside the sector boundary to avoidmagnifying flight awareness workload of neigh-boring sectors. Controllers require some time to

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become familiar with a flight entering the sectorbefore it approaches a critical point. The moretime they have, the more efficiently they maycontrol the flow safely through the critical point.Therefore, the length of flow segments from thepoint they enter a sector to when they encountera critical point should be maximized. Let ηLn

be the percent of points along link nominal pathsthat are within five nmi of a sector boundary. LetηNn be the percent of nodes that serve as the endpoint of a link entering a sector within 10 nmi.Let ηLw and ηNw be ηLn and ηNn percentages nor-malized by link and node weights. Figure 12shows these percentages of link and node sectorboundary proximity. ηLn and ηLw do not changesignificantly with weather reroutes but they do in-crease noticeably from flight plan to great circlerouting. Great circle routing affects the locationof links to be more random with respect to sec-tor boundaries. ηNn decreases from flight planto great circle routing due to the significant re-duction total number of nodes. However, the in-crease in ηNw from flight plan to great circle rout-ing shows how the traffic randomizing affect ofgreat circle routing moved some larger nodes tooclose to sector boundaries. This effect is ampli-fied in the great circle weather reroutes.

!"#

$"#

%!"#

%$"#

&!"#

&$"#

FP FP weather

GC GC weather

Ln Lw Nn Nwη η η η

Fig. 12 Percentages of links and nodes close tosector boundaries.

6 Conclusion

This paper presented a method of defining routestructure from a given set of flight tracks. A para-

metric analysis identified optimal method param-eters to define good weather route structures sim-ilar to today’s published airway structure. Flighttracks simulated from four different days of flightschedules were tested with similar results com-pared to the airway structure. On average, theroute structures deviated only 1.7 nmi from air-ways.

Route structures were generated for four-hourtime windows of track data shifted every twohours to demonstrate how route structure can beupdated dynamically. Links and nodes of theroute structure appeared and increased in weightas flight traffic increased. When airways beganto saturate, more and more links began to appearwhere airways had not been published, but theprecision of the route structure in representing thetrack data remained stable. On average, the stan-dard deviation of flights tracks was 2 nmi fromlinks and 4.7 nmi from nodes.

Route structures of great circle routing dif-fered significantly from flight plan routing. Greatcircle tracks displayed much less structure withlower traffic intersection representation and linkand node weights than flight plan tracks. How-ever, great circle route structure had larger aver-age numbers of links and nodes per sector thanflight plans, as well as a higher percentage of theroute structure close to sector boundaries. Sim-ulated user preferred reroutes around a station-ary weather obstacle produced route structureswith greater numbers of link sector boundarycrossings and average links and nodes per sec-tor. Weather reroutes of great circle tracks re-sulted in a significant increase in larger weightnodes close to sector boundaries. These resultsdemonstrate how dynamically generated routestructures could be useful in guiding dynamicairspace configuration to accommodate trafficvolume changes or weather reroutes. They alsosuggest that while route structure may help con-trollers retain situational awareness under dy-namically changing traffic conditions, it may nothelp in traffic with little structure such as withgreat circle routing.

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[2] Sabhnani, G. R., "Geometric algorithms for dy-namic airspace sectorization," Ph.D. thesis, StonyBrook University, NY, May 2009.

[3] Xue, M. "Three dimensional sector design withoptimal number of sectors," AIAA Guidance,Navigation, and Control Conference and Exhibit,Toronto, Ontario, Canada, August 2010.

[4] Martinez, S., Chatterji, G., Sun, D., Bayen, A. "Aweighted-graph approach for dynamic airspaceconfiguration," AIAA Guidance, Navigation, andControl Conference and Exhibit, Hilton Head,South Carolina, August 2007, AIAA-2007-6448.

[5] Li, J., Wang, T., and Hwang, I. "A spectral clus-tering based algorithm for dynamic airspace con-figuration," 9th AIAA Aviation Technology, Inte-gration and Operations Conference, Hilton Head,South Carolina, September 2009, AIAA-2009-7056.

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[7] Sabhnani, G., A. Yousefi, D.P. Kierstead, I. Kos-titsyna, J.S.B. Mitchell, and V. Polishchuk, "Al-gorithmic traffic abstraction and its application toNextGen generic airspace," 10th AIAA AviationTechnology, Integration, and Operations Confer-ence, Fort Worth, Texas, September 2010.

[8] Zelinski, S. "Defining critical points for dy-namic airspace configuration," 26th InternationalCongress of the Aeronautical Sciences, Anchor-age, Alaska, 2008.

[9] Love, J., Chan, W., and Lee, C.H. "Analysisof Automatetd Aircraft Conflict Resolution andWeather Avoidance," 9th AIAA Aviation Tech-nology, Integration and Operations Conference,Hilton Head, South Carolina, September 2009,AIAA-2009-6995.

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6.1 Copyright Statement

The authors confirm that they, and/or their company ororganization, hold copyright on all of the original ma-terial included in this paper. The authors also confirmthat they have obtained permission, from the copy-right holder of any third party material included in thispaper, to publish it as part of their paper. The authorsconfirm that they give permission, or have obtainedpermission from the copyright holder of this paper, forthe publication and distribution of this paper as part ofthe ICAS2010 proceedings or as individual off-printsfrom the proceedings.

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