Lagrangian Delay Predictive Model for Sector-Based Air Traffic Flow

Transcription

1 JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS Vol. 28, No. 5, September October 2005 Lagrangan Delay Predctve Model for Sector-Based Ar Traffc Flow Alexandre M. Bayen Unversty of Calforna at Berkeley, Berkeley, Calforna Pascal Greder Swss Federal Insttute of Technology, CH-8092 Zurch, Swtzerland George Meyer NASA Ames Research Center, Moffett Feld, Calforna and Clare J. Tomln Stanford Unversty, Stanford, Calforna A control theoretcal model of sector-based ar traffc flow s derved usng hybrd automata theory. Ths model s Lagrangan, because t models the propertes of the system along ts trajectores. A subset of ths model s used to generate analytc predctons of ar traffc congeston: A dynamc sector capacty s defned and derved that s used forpredctng the tme t takes to overload a gven porton of arspace. Ths result lnks the Lagrangan approach wth Euleran models, whch account for temporal varatons of parameters n a fxed volume. To determne the accuracy of predctons, an ar traffc flow smulator s desgned and valdated. The smulator s then used to show that flow schedulng and conflct resoluton may be decorrelated by reducng arcraft densty. Nomenclature a = vector [a1 0,...,a0 N ]ofntal arc length dstances for N arcraft a 0 = ntal arc length dstance of arcraft from San Francsco Arport along arrval route b = vector [b 1,...,b N ] for N arcraft used for computng ndvdual b b = varable used to compute mode swtchng tme of arcraft d LOS = dstance at whch a loss of separaton (LOS) occurs dmn = mnmum dstance from arcraft to any other arcraft n sector f () = penalty functon for arcraft separaton (assocated to dmn for all ) J = cost functon encodng ar traffc control (ATC) controller acton and sector state J {gven acton} = cost assocated to {gven acton} of controller (vector for spacng, shortcut, etc.) for arcraft M = Mach number N = total number of arcraft n sector of nterest at gven tme, N = N(t) N choce = number of arcraft selected for analyss by smulator Receved 20 December 2002; accepted for publcaton 10 December Copyrght c 2005 by the Amercan Insttute of Aeronautcs and Astronautcs, Inc. All rghts reserved. Copes of ths paper may be made for personal or nternal use, on condton that the coper pay the $10.00 per-copy fee to the Copyrght Clearance Center, Inc., 222 Rosewood Drve, Danvers, MA 01923; nclude the code /05 $10.00 n correspondence wth the CCC. Assstant Professor, Department of Cvl and Envronmental Engneerng, 711 Davs Hall; bayen@ce.berkeley.edu. Member AIAA. Nachdplomstudum n Betrebswssenschaften Student; currently Assocate, McKnsey and Co., Alpenstrasse 3, 8065 Zurch, Swtzerland; pascal greder@mcknsey.com. Research Scentst, Mal Stop ; gmeyer@mal.arc.nasa.gov. Assocate Professor, MC 4035, Department of Aeronautcs and Astronautcs and Courtesy Assocate Professor, Department of Electrcal Engneerng, 028A Durand Buldng; tomln@stanford.edu. Member AIAA. N lmt = dynamc capacty of sector of nterest N moved = total number of arcraft moved at smulator teraton n LOS = number of LOS for arcraft that would happen wth gven set of maneuvers n maneuver = number of maneuvers smulator can assgn to arcraft at any gven tme R = set of real numbers R ψ = rotaton matrx of angle ψ for headng changes Tbreach = boundary condton breach tme of arcraft T lmt = saturaton tme of sector of nterest TOA pred = predcted tme of arrval (TOA) of arcraft [at termnal radar approach control (TRACON)] TOA real = actual TOA of arcraft (at TRACON) t block = tme at whch meterng condton s mposed t swtch = tme at whch arcraft undergoes mode swtch by ar traffc control (ATC) v current headng = velocty vector of gven arcraft at ts current headng v max = maxmum arcraft speed v mn = mnmum arcraft speed v nom = nomnal arcraft speed w gven acton = weght (penalty) assocated to gven acton of controller x = dstance to destnaton arport along flght plan x ex = dstance from arport at whch meterng s appled x = poston of arcraft x swtch = locaton at whch arcraft undergoes mode swtch by ATC L = requested outflow separaton for mergng traffc n regon of nterest L n = mposed nflow separaton for cross traffc n regon of nterest L out = requested outflow separaton for cross traffc n regon of nterest T act = tme perod for one teraton of smulator TLOS = tme untl next predcted occurrence of loss of separaton for arcraft T out = outflow perod of regon of nterest (one arcraft every T out tme unts) 1015

2 1016 BAYEN ET AL. Introducton THE Natonal Arspace System (NAS) s a large-scale, herarchcal, nonlnear dynamc system. At the top of the control herarchy, a sngle Ar Traffc Control System Command Center (ATCSCC) n Herndon, Vrgna, supervses the overall traffc flow (Fg. 1). Ths s supported by 22 (20 n the contnental Unted States) Ar Route Traffc Control Centers [(ARTCCs) or smply, Centers] at the lower control layer, organzed by geographcal regon up to 60,000 ft (Refs. 1 6). Each Center s subdvded nto sectors, wth at least one ar traffc controller responsble for each sector. The maxmum number of arcraft that can be n a sector s a functon of the sector geometry and the procedures used for controllng traffc. Typcal values are between 10 and 20 arcraft. The ar traffc controller s responsble for preventng losses of separaton (LOS) between arcraft, keepng them separated by more than 5 n mle horzontally; 1000 ft vertcally below 29,000 ft; and 2000 ft vertcally above 29,000 ft. For arcraft flyng under nstrument flght rules, the ar traffc controller has access to the arcraft s flght plan and may revse the alttude; provde temporary headng assgnments; and amend the route, speed, or profle to attempt to mantan effcency and to keep arcraft separated. The current control structure s presented n Fg. 1. Exstng NAS modelng tools span the modelng of runway and arport capacty and termnal operatons, through arspace operatons and conflct resoluton, 7,8 to human factors and man machne ntegraton. References 9 and 10 are surveys of NAS modelng and conflct detecton and resoluton methods. A recent tool, Future ATM (Ar Traffc Management) Concepts Evaluaton Tool (FACET), 11,12 provdes a NAS smulaton tool from a traffc flow management (TFM) pont of vew. FACET can also be used for playng back recorded enhanced traffc management system (ETMS) data. [Data are collected from the entre populaton of flghts wth fled flght plans n the NAS. ETMS data are sent from the Volpe Natonal Transportaton System Center to regstered partcpants va the arcraft stuaton dsplay to the ndustry electronc fle server. A fle contanng all recorded data s generated. It dsplays for each arcraft the current flght data (tme, poston), as well as the fled flght plan (n terms of navgaton ads, arways, fxes, etc.). The update rate of the measurements s of the order of 1 mn.] The goal of the present research s to develop a model that complements exstng tools by provdng a control theoretc component for modelng the nfluence of ar traffc control (ATC). Whereas the addtonal logc requred to model the actons of the ar traffc controller does not pose a sgnfcant computatonal problem f the arcraft densty n the arspace s low, t becomes an ssue as the densty ncreases. (The growth of computatonal cost s exponental wth arcraft number per sector.) The long-term goal of ncreasng capacty, as well as safety, n the NAS cannot be acheved wthout an n-depth analyss of the appled control logc and modelng the current arspace wth suffcent accuracy. Such a model would mprove ATC delay predcton and, thus, enable a wde array of applcatons. In ths paper, a model, as well as analytc and smulaton results, of the arcraft and controller actons wthn a sector of arspace are presented. The Lagrangan approach s based on the trajectores of the arcraft and trajectory dependent aggregate quanttes such as the average number of arcraft n a porton of arspace, as well as ther momentum and speed. Although several NAS models n the lterature are trajectory based, 11,13 18 they are explctly related to an Euleran framework. The Lagrangan model developed n ths paper s lnked wth Euleran models. 19,20 Euleran approaches are control volume based. Thus, they account for temporal fluctuatons of quanttes n a gven volume, for example, the number of arcraft n a sector as a functon of tme. The connecton between these two approaches s made through the concept of sector dynamc capacty that s ntroduced n ths paper and that s related to flow rate constrants 14 and complexty metrcs. 21 The Lagrangan model presented here can be used to study the effect of arcraft flow densty requrements at sector boundares, due to, for example, mles-n-tral requrements at arports. (The termnology n mles n tral s a standard term used by ATC. It means that arcraft follow each other separated by n mles.) Ths model makes t possble to predct how the current system mght react to mposed flow condtons. Gven a set of flght plans, the model enables evaluaton of the effectveness of dfferent controller polces n mnmzng delays. Ths paper has two components: 1) arspace modelng and analyss and 2) valdaton and smulaton. In the frst part, a hybrdsystem-based model for a controlled sector s presented. Hybrd means that the model allows for contnuous and dscrete behavor at the same tme; t wll be defned more precsely later. The hybrd system model for each arcraft encodes smple arcraft dynamcs under the dscrete acton of the ar traffc controller. The number of such actons s large but fnte and conssts of smple nstructons such as turn to headng of 30 deg, hold current headng, fly drect to Coaldale (OAL) vhf omn-drectonal range (VOR), and ncrease speed to 450 kn. Ths model s analyzed and used to defne the concept of sector dynamc capacty. Ths concept facltates the predcton of the tme t takes to overload, that s, to reach the maxmum authorzed number of arcraft n that sector, gven sectors of arspace, and thus makes delay predctons possble. If ar traffc controllers are assumed to use a subset of ther avalable control actons, the delay predcton results are then related to Euleran approaches. In the second part of ths paper, the earler results are valdated aganst real data. Because the results cannot be tested on the real ATC system drectly, a smulator of the system s desgned and mplemented n C++ nterfaced wth MATLAB. Ths smulator conssts of the mathematcal model derved n the frst part of the paper, augmented wth a logc for swtchng between the dfferent controller states. Ths model attempts to reproduce the actons of a human ar traffc controller by mnmzng cost functons defned over sectors. Ths smulator was valdated by comparng the smulated data aganst ETMS data. It s shown that the analytcal predctons for sector capacty are effectvely observed n smulatons. Fnally, the smulator s used to dentfy flow condtons under whch conflct resoluton decorrelates from meterng problems, that s, scheduled tme of arrval. Ths result has mplcatons for numerous ATC flow management technques that rely mplctly on ths assumpton. 14,19,22,23 The data presented n ths paper pertan to several sectors wthn the Oakland Center, located n Fremont, Calforna. The methodology, however, s general and would apply to any other en route porton of the NAS. Jeppesen 24 hgh-alttude en route charts were used for modelng the Oakland Center arspace. The controller model and cost functon have been desgned based on several hours Fg. 1 Control herarchy n current structure of NAS.

3 BAYEN ET AL of observatons of sector controllers for gven sectors at the Oakland Center. The approxmatons that have been made for the study n ths paper are noted throughout. Whereas the model s general, most of the scenaros consdered do not represent normal traffc flow. Ths s because of the nterest n modelng delay propagaton of the system under stress. Hence, the traffc scenaros modeled represent heavy traffc flow along arways. The contrbutons of ths paper are a new mathematcal model for arspace sectors, based on hybrd system theory; an analytcal soluton to the Lagrangan problem of delay propagaton n the network of arways and ts lnk wth Euleran approaches; and the concept and use of sector dynamc capacty. From the applcaton pont of vew, the novelty les n the valdaton of a control theoretc model of the human ar traffc controller and n the valdaton of the analytcal predctons aganst real data. Fnally, the decorrelaton results shown by the smulatons are new. Ths paper s organzed as follows: In the next secton, the model used for arcraft dynamcs and ar traffc controller actuaton are presented. Ths model s used to predct the propagaton of arspace congeston and to defne sector capacty. In the followng secton, the desgn of the smulator, ts use n valdatng the analytcal predctons, and ts use n demonstratng the decorrelaton between conflct resoluton and flow meterng are presented. Fg. 3 Vsual dsplay of smulator, traffc n Oakland ARTCC. Ar Traffc Flow Modelng and Analyss The structure of the NAS s complex, wth a multtude of nteractng agents and technologes for arcraft montorng, flow management, communcaton, and human-centered automaton. For the present work, only the features that are mportant for delay predcton are modeled. The porton of the Oakland ARTCC modeled contans fve sectors. These sectors surround the Bay termnal radar approach control (TRACON), whch controls arcraft on ther approach nto San Francsco, San Jose, and Oakland arports. The Bay TRACON s the fnal destnaton of the traffc consdered. A sector s modeled by a porton of arspace contanng arcraft under the control of a sector controller (Fgs. 2 and 3). Wthn each sector, navgaton nfrastructure, consstng of arways, wayponts, and navgaton ads, s used to gude the flow n desred patterns. Therefore, the structure of the arspace s modeled and used even f t s observed that more than 40% of the arcraft devate from ther fled flght plan. The model permts arcraft to fly at dfferent alttudes, but not to clmb or descend. Alttude changes are not crucal for ths analyss, but arcraft acceptance rates at destnaton arports are. Future models mght ncorporate alttude changes, though, because they sometmes mpact workload, for example, n the presence of cross traffc. The applcablty of the current model s, thus, lmted to sectors n whch most of the traffc s arrval traffc, as n Ref. 14, for example. Fg. 2 ATC sectors modeled for ths study: 32, 33, 34, 13, and 15 wthn the Oakland ARTCC. Fg. 4 Hybrd automaton representng acton of one controller on sngle arcraft. Arcraft Behavor A hybrd model for each arcraft descrbes the evoluton of a system by a set of dscrete modes wth assocated contnuous dynamcs and dscrete swtches, whch enable the system to jump from one mode to another nstantaneously. The moton of arcraft s descrbed as current headng ẋ = dx dt current headng = v (1) where v R 2 s a constant velocty vector held by the arcraft untl the next dscrete swtch, a headng or speed change current headng that changes v. Here, x R 2 s the planar poston of arcraft. Integraton of Eq. (1) over tme produces a contnuous pecewse affne trajectory. Such a model s preferred over a contnuous dynamc model for two reasons. Frst, the tmescale of a change n arcraft behavor, for example, a turn or slow down, s on the order of several seconds, whereas the tmescale of a straght lne porton of the flght s usually much longer, sometmes 15 mn or more; thus, dynamcs of such maneuvers are gnored and only ther effects are consdered (the set of resultng straght lnes). Second, the update rate of ATC montorng s generally not more than 30 s, whch makes the detals of these maneuvers obscure to the ATC. Ths approxmaton s wdely accepted n lterature. 17,22,25 28 Observatons at the Oakland Center showed that a fnte set of maneuvers s used by controllers. Combnatons of these maneuvers result n a conflct-free flght envronment n whch the constrants of the ar traffc flow are met. The maneuvers shown n Fg. 4 are realzed by changng the speed and the headng of the arcraft [rghthand sde of Eq. (1)]. In Fg. 4, each of the eght modes represents

4 1018 BAYEN ET AL. one possble state of the arcraft. The arrows jonng these states are the mode swtches, ntated by the controller. The valdty of models smlar to ths has been confrmed by statstcal studes. 21 1) For speed change, f ATC employs speed control, the arcraft may decelerate or accelerate wthout devatng from ts flght plan, current headng v modfed speed := λ v (2) where λ R + defnes the magntude of the velocty change. The model s desgned to allow a fnte set of speeds, whch means that λ has a fnte number of acceptable values. Ths s because arcraft performance s ted to arspeed and because arcraft thrust s lmted at alttude. Generally, ATC wll not speed up or slow down the arcraft by more than 10% of the current value. 2) The vector-for-spacng (VFS) maneuver conssts of a devaton of the arcraft away from ts orgnal flght plan for a short tme (part 1 of the maneuver) and then a second devaton (recovery maneuver) for brngng t back to ts orgnal flght plan (part 2 of the maneuver). Ths stretches the path that the arcraft must follow and, therefore, results n delay. The maneuver s contaned wthn the extent of the sector. Where R ψ s the rotaton matrx by angle ψ, current headng v part1 := R ψ v (frst-half of maneuver) v part2 := R 2ψ v part1 (second-half of maneuver) (3) 3) In certan stuatons, the ATC wll have the arcraft cut between two arways, a shortcut/detour maneuver that could ether shorten or lengthen the flght plan. The decson to command such a maneuver s often dctated by conflct resoluton, but could also be used to shorten the overall flght tme f sector occupancy allows t (sometmes called drect-to by plots): current headng v shortcut := R ψ v (4) for the duraton of the maneuver, untl the next ATC acton s taken. Here agan, ψ s the headng change angle by whch ATC turns the arcraft to acheve the shortcut. 4) Holdng patterns are used to hold an arcraft n a gven regon of arspace before allowng them to follow ther orgnal flght plan. Ths s modeled by assgnng the arcraft to a predefned zone and keepng t there whle preventng other arcraft from enterng that zone. Lagrangan Analyss of Delay Propagaton n NAS A large proporton of en route and termnal congeston s caused by restrctons mposed at destnaton arports, due to weather or arport arrval departure demand. These restrctons are often mposed as mles-n-tral or mnutes-n-tral meterng constrants, representng the dstance (or tme) requred between arcraft n a flow arrvng to the TRACON. Fgure 5 shows the topology of the nbound flows nto San Francsco Arport (SFO), whch are often subject to ths type of constrant. These constrants tend to propagate backward from the arport nto the arways and result n mles-n-tral constrants mposed at the entry ponts of each sector. For example, n the case shown n Fg. 5, these meterng condtons propagate backward toward the east as follows: TRACON sector 34 sector 33 Salt Lake Center,... In the current system, these restrctons are mposed emprcally. To ensure maxmal throughput nto the TRACON, an understandng of 1) how the traffc jams propagate and 2) what the optmal control polcy should be under these restrctons s needed. These ssues are addressed n the paper. Shock Wave Propagaton A smple Lagrangan model of mergng flows ntroduced earler n Refs. 29 and 30 s used for studyng the phenomenon of shock wave propagaton for meterng the mergng flows of the type shown n Fg. 5. The concept of dynamc capacty appears naturally n the meterng problem, defned as follows. Gven a requred spacng of T out between the arcraft (meterng constrant), compute a controller polcy for routng groups of arcraft to satsfy exactly the meterng constrant at the sector ext pont whle mantanng separaton at all tmes. The task of meetng meterng constrants can be acheved by applyng the varous control optons avalable to the controller (Fg. 4). Consder a very smple verson of the problem, n whch the controller uses only two modes (fast and slow). Several methodologes can be used to map the full automaton shown n Fg. 4 to ths model: See, for example, Refs. 14 and 23. To explan the procedure, consder the followng example. Let the ntal arc length dstance of arcraft be a 0 R along ts arrval route to the arport. An a 0 = 200 means that arcraft has to fly 200 n mle before landng at the destnaton arport. Let x ex R be the locaton at whch the meterng condton s mposed. For example, x ex = 50 means that the meterng s appled 50 n mle from the arport. It s possble to assume wthout loss of generalty that the arcraft are numbered n order of arrval. (The a 0 are ndexed n ncreasng order.) Assume that all arcraft are ntally at maxmum speed v max and that ATC slows down arcraft to ts mnmum speed v mn for meterng (Fg. 6) at a locaton x swtch at tme t swtch, whch s unknown for now (Fg. 7). Ths scenaro s represented as a dash dot lne n Fg. 4. The condton that each arcraft cross the meterng pont x ex at exactly t block + ( 1) T out s mposed, where t block s the tme at whch the meterng condton s ntated. The moton of arcraft under the meterng constrant s descrbed by the followng knematc equatons: x (t) = a 0 + v max t f t [ ] 0, t swtch (5) ( ) ( ) x (t) = x t swtch + vmn t t swtch f t [ ] t swtch, t block + ( 1) T out (6) In the precedng formula, the orgn of tme s taken wthout loss of generalty at t 0 = 0. The assumpton of contnuty of x (t) enables Fg. 5 Overlay of trajectores mergng nto SFO (11 h of traffc). Fg. 6 ATC control for mergng flow.

5 BAYEN ET AL Fg. 7 Shock constructon: arcraft trajectores are represented n (x, t) plane. Fg. 8 Swtchng curve (shock) for vanshng traffc congeston. us to solve for t swtch and x (t swtch ) := x swtch. The condton for the system (5) and (6) to have a physcally acceptable soluton s a 0 [x ex v max (t block ( 1) T out ), x ex v mn (t block ( 1) T out )] (7) When Eq. (7) s met, the analytcal soluton of Eqs. (5) and (6) provdes the locaton of the edge of the congeston front n space and tme, x swtch t swtch = x ex v mn t block ( 1) L a 0 v max v mn = a 0 + v [ max xex v mn t block ( 1) L a 0 v max v mn (8) where L := v mn T out s the metered spacng at the outflow of the sector. At a gven tme t, the metered stream conssts of the set of arcraft such that t swtch t. These arcraft have already been slowed down (Fg. 6) and congest the arspace they occupy. It follows drectly from Eq. (8) that the congested porton of arspace, that s, the stream of arcraft metered at T out n Fg. 6, wll not grow n length f the two followng condtons are met: x swtch + 1 t swtch < t swtch + 1 L < a 0 a < x swtch (v mn / L) < [ v max /( a 0 a Condton (9) s a suffcent condton for traffc congeston to decay, whch can be observed by nspecton of the slope of the swtchng curve of ponts (x swtch, t swtch ) dsplayed n Fgs. 7 and 8. The swtchng curve can also be called a shock wave, whch tradtonally refers to the movng nterface between a medum of hgh densty )] ] (9) and a medum of low densty (n the present case, densty of arcraft). In Fg. 7, x denotes the dstance to the meterng pont (SFO). The lnes are the trajectores of the arcraft n the (x, t) space. The postons of arcraft are represented every 1000 s as dots. Once they have passed through the shock, they are separated by v mn T out. The pont (x m, t m ) s the farthest reachable pont by ths traffc congeston. Note that the slope of the lnes changes through the shock. The slope dfference can hardly be seen vsually because the speed change s small. Equaton (9) s a local property of the problem n that t depends only on a 0 a and not on all of the arcraft. The second equaton n Eq. (9) corresponds, n fact, to a one-dmensonal dscretzed steady Lghthll Whtham Rchard equaton, whch appears naturally n hghway congeston problems. 31 Ths result s obtaned through a Lagrangan analyss, whch lnks t to Euleran approaches such as those n Refs. 19 and 20, whch are based on conservaton equatons. It relates local propertes of the flow (drecton and speed of propagaton congeston, arcraft densty on an arway) to global quanttes (here, the trajectores of the arcraft). Ths s mportant because t, thus, enables one to lnk quanttes that are easy to access (flght plans and, thus, trajectores) to densty (and, thus, sector counts), whch are harder to predct. Ths result s llustrated n Fg. 7: The arcraft trajectores are represented n the (x, t) plane. They orgnate at t = 0 from the horzontal axs (whte crcle on each trajectory). After some amount of tme, the arcraft may be swtched to speed v mn at locaton (x swtch, t swtch ) (shaded crcle on each trajectory). Ultmately, they reach x ex, the entrance of TRACON (black crcle). The condton that each arcraft reaches x ex exactly at the scheduled tme of arrval s restrctve. From the TFM (a set of ARTCC controllers n charge of flow management at the center level) pont of vew, the actual crossng tmes are not mportant, but the flow rate s. Therefore, t s meanngful to pose the problem as follows. Gven {a 0} [1,N], compute the swtchng polcy that delvers at most one arcraft every T out satthe locaton x ex whle mantanng separaton and that mnmzes the arrval tme of arcraft N. Ths problem may be posed as a lnear program. 1) Mnmze the arrval tme of arcraft N whle 2) separatng the arcraft by more than T out at x ex, wth 3) at most one swtch between the ntal poston a 0 x ex and the ext x ex of the consdered arspace as follows: 1) Mnmze [0, 0, 1]b 2) subject to b v mn ) wth T out... T out a b (v mn /v max )a + (1 v mn /v max )x ex [1,...,1] T where a = [a 0 1,...,a0 N ]T and b = [b 1,...,b N ] T. Note that the rghthand sde of part 2 can be changed to [ T 1,..., T N ] T to account for tme-varyng meterng condtons. The advantage of ths formulaton s that any lnear objectve functon may be gven and optmzed. In the present case, the objectve functon s the arrval tme of the last arcraft n the stream. Condtons for shock monotoncty (9) derved earler are stll vald locally for any soluton derved wth the precedng lnear program. Sector Overload Predctons When the analyss of the precedng secton s used, the dynamc capacty of a sector can be predcted. Consder the worst-case

6 1020 BAYEN ET AL. scenaro: An nbound stream of arcraft, wth each arcraft at v max speed, s separated n tme by T n, such that the second condton n Eq. (9) s volated. For the example shown n Fg. 6, such a stream would cause the traffc congeston to propagate from sector 34 to sector 33. Let l be the arc length dstance of the porton of the arrval arway contaned n sector 34 n Fg. 6. Assume that the sector s ntally empty. When Eqs. (8) are used, the maxmum number N lmt of arcraft that can be stacked along the length l of the arway n the sector untl ths arway s saturated can be computed. These arcraft are labeled as metered stream n Fg. 6. Fgure 6 shows that approxmately one-half of l s occuped by the metered stream at the tme consdered, and so the number of metered arcraft s approxmately N lmt /2. When the number of metered arcraft reaches N lmt after a tme T lmt, the rest of the arcraft have to be slowed down upstream n sector 33. N lmt and T lmt are gven by N lmt = T lmt = l(v max v mn ) v max v mn ( T out T n ) (10) l v max v mn v max T n v mn T out T out T n (11) The foregong results have been obtaned by accountng for how long t takes for congeston to grow by a length of l and how many arcraft are needed n the process. In mathematcal terms, the result s obtaned by solvng for N lmt and T lmt n the followng equatons: xn swtch lmt x1 swtch = l and tn swtch lmt t1 swtch = T lmt, where the swtchng tmes and locatons are related by Eq. (8). If arcraft are ntally present n the sector, these two quanttes can be modfed by replacng l by the dstance to the last arcraft n the sector. N lmt s referred to as dynamc capacty because t depends on nflow and outflow condtons n addton to geometrc parameters. Also note the followng 1) As v mn v max 0, N lmt 0 because arcraft cannot be slowed down to meet the meterng constrants; ths means that f ths porton of arspace s already congested, no further arcraft can be handled by t. 2) As T out T n 0, N lmt and T lmt :Ifthe nbound flow s almost metered, lttle addtonal control s requred for meetng the meterng constrant at the outflow boundary. As a consequence, the number of arcraft requred to saturate ths arspace becomes large, and the tme t takes to saturate ths sector grows accordngly. The swtchng curve (x swtch, t swtch ) generated usng Eq. (8), for example, n Fg. 8, can be used to compute the maxmal extent of traffc congeston along the arway. The edge of the traffc congeston, called x m, obtaned at t m,gves the worst stuaton obtaned from the ntal confguraton a 0 of the arcraft. For the scenaro n Fg. 8, the traffc congeston does not propagate more than 300 n mle upstream from the destnaton of the arcraft x ex. Therefore, meterng s not requred upstream from that pont. Because such nformaton s unavalable currently to the ATC, controllers pass the meterng restrctons upstream, whch leads to flow neffcency, or vrtual overloads. Valdaton Aganst ETMS Data The mathematcal models descrbed n the precedng sectons are now valdated usng a realstc smulaton. The desgn of a smulator and ts valdaton aganst ETMS data are also dscussed n the next subsecton. In the followng subsecton, the analytcal predctons derved earler are valdated usng the smulator. Fnally, n the last subsecton, the smulator s used for dervng condtons on the decorrelaton of flow meterng and conflct resoluton. Smulator Desgn The smulator was desgned followng the observed control actons of the controller at the Oakland ARTCC. Fgure 4 summarzes the model of the control actons observed at the ARTCC. The swtchng logc s mplemented n the form of a cost functon, whch s also descrbed n ths secton. Fg. 9 Program flow of smulator. Overall Program Flow The overall program flow of the smulator s shown n Fg. 9. The nput s a set of fled flght plans that are ether user generated or taken from ETMS data. As n the real system, these flght plans are not conflct-free and usually do not satsfy meterng condtons mposed on the network. Once the program s ntalzed, arcraft poston s obtaned by ntegratng the equatons of moton (1) along the route specfed va the flght plan. As tme advances, conflct, as well as meterng constrants, are dealt wth on a sector by sector bass by predctng forward n tme the actons the controller would choose to resolve conflcts and meet the meterng condtons. Key Data Structures Gven a route of flght and ntal condtons, arcraft dynamc equatons (1) are ntegrated forward to generate the arcraft trajectory. Ths trajectory s then mplemented as a lnked lst of ponts [x, y, z], wth a prescrbed velocty between the ponts, and s subsequently modfed by the ar traffc controller model n the program. The output for each arcraft s the updated lnked lst. The sectors are also mplemented as sets of lnked lsts wth data such as meterng condtons (number of arcraft through a gven boundary per unt tme). Ar Traffc Controller Model ATC control actons are modeled by three levels of prorty: 1) Prorty 1 s that there s no loss of separaton (LOS). The prmary requrement for ATC s to ensure that any arcraft par s always separated by more than 3 n mle horzontally or 1000/2000 ft 5 vertcally. 1 2) Prorty 2 s that meterng condtons are met. The controller needs to ensure that the outbound traffc s adequately separated to meet the meterng restrctons at the next sector (or TRACON). 3) Prorty 3 s the best possble throughput. Controllers wll gve drect routes to arcraft f requested to mnmze ther flght tmes. These prortes may be modeled usng the followng cost functon J: J = cost LOS + cost BC breach + cost delay + cost arcraft actuaton + cost maneuver + cost mn dst (12) Each term of the cost s a weghted functon: N n LOS J = w N LOS ( + T 2 T breach) wbreach LOS = 1 + N = 1 = 2 ( TOA pred TOA real) wdelay + N moved w sngle move + where w s the weght. N J maneuver + = 1 N f ( dmn) wdst = 1

7 BAYEN ET AL ) The LOS cost n LOS s the number of predcted losses of separaton nvolvng arcraft n the current sector wth ts current flght plan. TLOS s the tme untl the frst LOS for arcraft. 2) The boundary condton (BC) breach cost Tbreach s the tme by whch an arcraft volates the T tme separaton constrant from ts predecessor (set to zero f the two arcraft are separated by more than T ). 3) The delay cost, TOA pred TOA real, accounts for the dfference between predcted and actual tme of arrval (TOA) at the last waypont of the flght. Postve delays are penalzed; earler arrvals are favored because they reduce the flght tmes of arcraft. TOA pred and TOA real are computed by ntegraton of the flght plans for each arcraft, respectvely, usng the orgnal and the amended flght plans. 4) The arcraft devaton cost N moved values accounts for the number of flght plan modfcatons chosen n the current soluton. Large N moved are penalzed because the soluton chosen by the ATC s often the smplest. 5) The maneuver cost Jmaneuver accounts for the cost of the maneuver selected for arcraft. Not all maneuvers are of equal preference, and, therefore, they have dfferent costs. It s as easy for a controller to prescrbe a 10% speed change, a VFS, or a shortcut. A holdng pattern s the least preferred opton because t requres constant montorng of the arcraft. Ths s reflected n the choce of weght: Jspeed change J shortcut J VFS J holdng pattern. The rato Jholdng pattern /J speed change s of the order of 10. 6) The mnmal dstance cost f (dmn ) penalzes arcraft dstrbutons n whch arcraft are closely spaced (but do not lose separaton) aganst more sparse dstrbutons. Here, dst max = 7nmle: f ( ) dmn 1 = w dst f dmn < dst max d mn f ( d mn) = 0 otherwse To reflect the three levels of prorty of the ar traffc controller stated earler, the weghts shown n the cost functon J are w LOS w breach 10 4 other weghts 10. Thus, a computaton for mnmzng J frst deals wth losses of separaton, then meterng condtons, and fnally optmzaton of the flow. The characterstcs of the cost functon for a two-arcraft scenaro are llustrated n Fg. 10. At the top of Fg. 10, cost values for all possble maneuver combnatons n a two-arcraft ntersecton scenaro are shown, where the eght maneuvers of Fg. 4 are enabled (thus, generatng 8 2 = 64 possble values of J). Four out of 64 examples are extracted and llustrated n the bottom part of Fg. 10. At pont a n Fg. 10, both arcraft A and B mantan same speed. At pont b, arcraft A takes a shortcut whereas arcraft B mantans the maxmum speed. At pont c, arcraft A makes a VFS at low speed. At pont d, arcraft A s tryng to take a shortcut, whch s not possble n the current flght plan. Because the move s nfeasble, the maxmum cost s assocated to t. The controller model would choose soluton b because t has the lowest cost. The cost J has been truncated at for readablty. To reduce the computatonal tme, the maxmum number of arcraft controlled by the controller model n each tme teraton s lmted to N choce. N choce s chosen accordng to real tme restrctons and computatonal power. If a decson needs to be made wthn 30 s, the value N choce = 8srealstc. The choce of N choce s a tradeoff between runnng tme and control qualty n the smulatons. It was set n the range from four to eght for the smulatons. Arcraft are selected accordng to the followng rule: Arcraft nvolved n LOS are selected frst, then arcraft volatng meterng constrants are selected, and, fnally, the remanng arcraft are selected untl the selecton lst reaches N choce arcraft, or untl there are no more arcraft left to select. In practce, 4 N choce 8was found to be sutable; N choce = 8 results n more complcated maneuvers but makes the smulaton run more slowly. The set of all maneuver combnatons for the N choce arcraft s called the maneuver set. At each teraton of the controller acton loop, an exhaustve search on the maneuver set of the chosen arcraft s run to fnd a set of N choce maneuvers that mnmzes J. The computatonal complexty of fndng the optmal J for N choce arcraft capable of n maneuver possble dscrete maneuvers s O[(n maneuver ) N choce]. Ths complexty can be reduced to O[(n maneuver 2) N choce]asfollows: 1) The cost of the current maneuver has already been computed n the prevous step and, thus, does not need to be recomputed. 2) Two maneuvers are mutually exclusve; therefore, only one needs to be consdered. When the complexty of checkng for conflcts s added, the total computatonal complexty of each teraton becomes O ( ) N 2 (n maneuver 2) N choce where N represents the total number of arcraft n the sector. Because of both the dscretzaton of tme and the restrcton of the search space to a manageable number of arcraft, the search process s not guaranteed to fnd the global optmum. However, t s shown n the next secton that the search does provde a reasonable approxmaton of the controller s actons. The last parameter to adjust s the tme between two successve controller actvatons, T act, the order of whch s from 5 to 30 s, whch s the tme between successve communcatons of ATC wth dfferent arcraft. Controller Model Valdaton Aganst ETMS Data The controller model presented n the precedng secton resulted from observatons of ar traffc controller acton at the Oakland ARTCC. The modelng nto a set of preferred drectves has been expermentally valdated for a dfferent arspace. 21 Note, however, that even f the automaton of Fg. 4 and the cost functon of the precedng secton mplemented n the smulator are consstent wth the observatons, there s no a pror guarantee that the model based on these would replcate the control actons of a human controller. For ths reason, an assessment of how well the controller model descrbes the decson makng of a human controller s needed va comparsons aganst recorded arcraft trajectores. Recorded ETMS data have been used as the source of actual trajectores flown n the NAS. The data extracton process that enabled converson of ETMS data to a readable format for our smulator s descrbed hereafter. Data Extracton Two types of nformaton are provded by the ETMS data: The actual track flown by the arcraft, and the fled flght plans for each arcraft, whch are amended to reflect reroutng. The track poston s provded as lattude/longtude. The fled flght plan s gven n terms of navgaton ads, fxes, and arways, whch can be looked up usng a publc database (URL: Future versons Fg. 10 Top, cost values for all possble maneuvers and bottom, maneuvers a, b, c, d labeled at top.

8 1022 BAYEN ET AL. Fg. 11 Flght tme comparsons for frst 100 arcraft gong through sector 33 n ETMS data set used. of the smulator mght use recently developed ETMS analyss tools such as those n Ref. 13. Ths study focuses on sector control, therefore, the traffc management unt (TMU) actons are not modeled. TMU operates at the ARTCC level (Fg. 1) and makes strategc flow schedulng decsons that go beyond the control actons of a sngle sector controller. Thus, the smulator needs to be valdated at a scale at whch TMU actons are already ncorporated n the flght plans (typcally one or two sectors). Because ths study focuses on sectors 32, 33, 34, 15, and 13, the flght plans are truncated to be wthn the bounds of these sectors. The estmated TOA n the sector s set to the actual TOA as marked by the track poston. The entrance locaton s taken to be the track poston closest to the pont of ntersecton of the flght plan and the sector boundary. The alttude assgned s the average alttude of the actual trajectory n that sector. Valdaton Comparson of flght tmes. Track postons of the frst 100 arcraft that flew above 33,000 ft for more than 6 mn were extracted from ETMS data. Ther recorded trajectores are extracted as sequences of wayponts that are used as flght plans for the smulatons. Smulatons were run for the followng set of Mach numbers: M {0.6, 0.7, 0.8} correspondng to the observatons n the data for ths alttude. Durng the smulaton, the controller model s nvoked every T act = 10 s. The resultng flght tmes are compared aganst actual flght tmes n Fg. 11. In Fg. 11, the dots are the flght tmes for the ETMS recorded ponts. The sold curve s the result of the smulatons. Two man conclusons can be made. 1) The smulator s able to recreate the flow characterstcs seen n ETMS data and predcts and resolves conflcts when arcraft could be separated by less than 5 n mle at the same alttude. 2) The flght tme comparsons between smulated and ETMS data (Fg. 11) show a good match. The flght tmes provded by the smulator are usually shorter than n ETMS data because the smulator maxmzes the throughput n the sector. The mean devaton was found to be 120 s for flghts wth an average duraton of 1300 s, whch amounts to a 9.2% error. Valdaton of conflct resoluton. A total of 314 arcraft flyng through sector 33 n a tme perod of 10 h was smulated. The fled flght plans were not conflct free to begn wth. The smulator wth the controller model modfyng the trajectory every T act = 20 s s able to provde a conflct-free envronment. [ T act = 10 s or T act = 20 s s on the order of the maxmal actuaton rate of a controller. We choose T act = 20 s n ths partcular case because of the duraton of the computaton (10 h of real tme smulated).] The set of speeds allowed s M {0.55, 0.75, 0.89}. Durng the smulaton, trajectores of 50 arcraft were altered to resolve conflcts. Valdaton of maneuver assgnments. The valdaton so far has shown the correlaton of flow patterns generated by the smulaton and those observed n realty. The next step s to valdate the type of maneuver chosen by the controller model as a consequence of the mnmzaton procedure. There were 314 flghts examned n sectors 33 and 20. Dfferent maneuvers were dentfed for the purpose of valdaton. Arcraft that followed ther flght plans were assgned ther actual routes of flght, and the arcraft that maneuvered to avod conflcts were assgned ther fled flght plans va a set of wayponts. The smulator was, thus, placed n the same stuaton as the human controller. The smulator was able to reproduce correctly 16 out of Fg. 12 Example of maneuver caused by conflct resoluton, reproduced by smulator. 20 maneuvers. [Small-scale maneuvers are less lkely to be executed correctly by the smulator because the probablty of selectng the respectve arcraft at exactly the rght tme s small, whch explans the small dscrepancy between the results. Also, even f the maneuver s executed correctly by the smulator, the resultng flght plan wll look dfferent from the ETMS data because the smulator s restrcted to a sngle angle of devaton (θ = 22.5 deg).] The smulated maneuvers, thus, appear to be reasonable and consstent wth observed controller behavor. These results, thus, consttute a valdaton for the specfc crcumstances of the 20 scenaros nvestgated from the 314 flghts consdered. A more extensve smulaton valdaton mght ncorporate more flghts and scenaros. Also note that observatons realzed at the Oakland Center made such a valdaton sometmes mpossble: It s not uncommon to ask dfferent human controllers to solve the same problem (on paper or n a smulaton) and to get two radcally dfferent answers. Thus, a full match s practcally mpossble. An example of good match s shown n Fg. 12. In Fg. 12, the recorded data (dashed) exhbt an actual shortcut from the fled flght plan (sold). The smulated trajectory (dashed dotted) s a shortcut of the same type. Valdaton of the Analytcal Predctons In ths secton, the analytcal predctons are compared wth smulatons. An example of two backpropagatng shocks, solved wth an extenson of the method explaned earler, s presented. Two streams, each at 10 mles n tral, are subjected to 15 mles-ntral and 20 mles-n-tral outbound condtons. The mles-n-tral restrcton for the second stream starts after all arcraft of the frst stream have reached the TRACON at t = Speeds are

9 BAYEN ET AL a) c) e) b) d) f) Fg. 13 Sector 33, traffc flow for mergng traffc smulaton of Fgs. 15 and 14. a) b) c) Fg. 14 Frst actuaton tmes of, arcraft; breaches n meterng condtons; delays of two streams of Fg. 15. M {0.59, 0.75, 0.89}. The resultng arcraft flows for ths analytc soluton are shown n Fg. 13. In Fg. 13, the radus around the arcraft s 2.5 n mle. The sold lnes represent the arcraft s flght plan. The dotted lnes correspond to maneuvers assgned by the smulator. The sx panels of Fg. 13 show how VFS s used by the smulator to acheve the requred meterng. Fgure 14a shows the frst actuaton tmes of the arcraft, smulated and predcted; Fg. 14b shows breaches n meterng condtons, smulated; and Fg. 14c shows delays, smulated, for the case of the two streams of Fg. 15. Fgure 15 shows shocks generated by two successve streams. The frst shock s steady n tme. (It only propagates backward n space.) It corresponds to a plng up process on a hghway where all vehcles slow down at the same tme. The second shock propagates backward n space and tme (whch s much harder to handle n practce because actuaton must be performed upstream frst). From Fg. 15, one can see that wthn the second stream, the frst 12 arcraft need to be controlled wthn the Oakland Center, whereas the last eght need to be controlled upstream (Salt Lake Center). Because, n general, no knowledge of the requred meterng condtons s propagated upstream, the last eght arcraft would not be moved untl they enter the Oakland Center, and no soluton to ths meterng problem would be found wthout puttng the arcraft on hold.

10 1024 BAYEN ET AL. Fg. 15 Shocks generated by two successve streams. Fg. 16 Two ntersectng streams, 20 mles-n-tral nbound separaton. These results are verfed by smulatng ths flow. In Fg. 14a t can be seen that for the last eght arcraft, the frst actuaton tme n the smulator s hgher than the predcted tme. The controller model s unable to control the arcraft n tme because they are not n ts arspace. Fgure 14b shows that these arcraft are unable to meet the meterng condtons by about 1 mn each. Ths s also shown n Fg. 14c. The delays become negatve; that s, the arcraft arrve n advance. Ths s an llustraton of dstrbuted and decentralzed control: The control occurs n dfferent sectors, and the only communcaton between the sectors s through the meterng condtons. Obvously, the lack of centralzed control (here communcaton and strategc TMU plannng) lmts effcent flow schedulng. Decorrelaton of Flow Meterng and Conflct Resoluton An assumpton that s often made n flow schedulng s that maneuvers for conflct avodance do not mpact meterng when traffc densty s low. Ths property of the flow s demonstrated by smulatng two streams of ntersectng and conflctng arcraft. Fgure 16 shows two streams of arcraft ntersectng at a navgaton ad (Clovs, n Sector 15). Devatons (VFS) are barely vsble n Fg. 16 because of ther small ampltude (5 n mle). One stream s subject to meterng condtons at the boundary of sectors 15 and 34 whereas the other stream s unrestrcted. The goal s to quantfy the mpact of the second stream on the travel tmes of the frst stream through the sector. There were 16 dfferent confguratons nvestgated by selectng combnatons of the same mles-n-tral nflow restrctons for the two streams: L n {15, 20, 25, 30}, and the followng restrctons for the stream headng toward sector 34, L out {15, 20, 25, 30} (Fg. 16). The travel tmes for each stream wthout the presence of the other are compared wth the travel tme when the two streams ntersect. For each confguraton, 10 smulaton runs were made wth the ntal poston of the arcraft perturbed by a unform nose of ampltude 2 n mle. Ths value was chosen to mantan parwse conflcts, and to dsturb the conflct resoluton mechansm to have a vald statstcal sample. Thus, a total of 160 runs was made for the 16 confguratons. (The settngs for these runs are M {0.8, 0.85, 0.89}; the VFS maneuver was lmted to a 5-n mle devaton from the orgnal flght plan. These settngs were chosen to guarantee short flght tmes. The nterval between controller actvaton was set to T act = 20 s.) Ths scenaro represents the stuaton n whch each arcraft from one stream conflcts parwse wth an arcraft from the second stream. It s really a worst-case scenaro because n practce arcraft mght fly at dfferent alttudes. The bound provded here s,

11 BAYEN ET AL a) b) c) Fg. 17 Dfference n delay between separate and smultaneous flow for sector 33 smulatons: a) T due to δttravel crossflow (n seconds) averaged over 10 runs, and c) δtno crossflow (n seconds) averaged over 10 runs. tme travel tme crossflow (n seconds) averaged over 10 runs, b) Table 1 Numercal results for decorrelaton of conflct avodance and flow meterng L n,nmle L out,nmle δt no crossflow travel tme,s δttravel crossflow tme,s T due to,s crossflow thus, conservatve, and hgher arcraft densty mght stll be compatble n practce wth meterng. For each L n L out par, the followng quanttes are computed: no crossflow δttravel tme = 1 N ) ( T no crossflow,bc no crossflow,no BC arcraft Tarcraft N δt crossflow travel tme = 1 N = 1 N = 1 ( T crossflow,bc arcraft T no crossflow,no BC arcraft arcraft T due to crossflow = δt crossflow no crossflow travel tme δttravel tme (13) Here, N = 20 s the total number of arcraft wth 10 arcraft n each no crossflow,bc stream. T represents the travel tme of arcraft n the absence of the other stream, whereas T crossflow,bc arcraft represents the travel tme n the presence of the other stream. The results averaged over 10 runs for each case for the mean dfference n travel tme are shown n Fg. 17. T due to s shown n Fg. 17 for the complete set of ( L n, crossflow L out ) nvestgated here. The numercal values are shown n Table 1. Even though the peak T due to happens for ( L n, L out ) = crossflow (15, 15), the maxmum δttravel crossflow tme happens as expected for ( L n, L out ) = (15, 30), whch s the maxmal nflow/mnmal outflow condton shown n Table 1. Comparng the results of Table 1 for the two values of L n and Fg. 17 shows the predomnance of conflct resoluton over BC for a hgh densty of traffc. (See the last column n Table 1.) The dfference n delay between separate and smultaneous flow s sgnfcantly larger f the arcraft are spaced at 15 n mle when compared to streams wth larger spacng, as shown n Fg. 17. Whereas the dfference per arcraft s always larger than 60 s for the 15-n mle streams, t s always smaller than 60 s for streams wth larger spacng. Wth an average flght tme of 660 s over all scenaros, 60 s corresponds to an average delay of 9% n flght tme. The worst-case dfference (15-n mle nflow, 30-n mle outflow) s more than 21% of the overall flght tme. These numbers are sgnfcant, especally when consderng the possblty of multple ntersectng streams. Note that n Fg. 17a one would ntutvely expect the largest dfference n delay (crossflow vs no crossflow) to happen for ( L n, L out ) = (15, 30), whch s dffcult to acheve. In fact, ths maxmum occurs at ( L n, L out ) = (15, 15). Ths can be explaned by lookng at Fgs. 17b and 17c. In the absence of the second flow, ) the delay accumulated due to the meterng condtons s maxmal for ( L n, L out ) = (15, 30) as expected. In the presence of the second flow, a maxmum appears at ( L n, L out ) = (15, 15), because no crossflow δttravel tme ( Ln, L out) = (15,15) = 0. Thus, these results are consstent. The flows n Fg. 16 represent an extreme example and are only useful for valdatng the performance of the underlyng meterng and conflct resoluton algorthms. Currently, TMU does not take the nfluence of conflct resoluton nto account when makng decsons, because local conflct resoluton maneuvers are not expected to ncrease overall flght tmes sgnfcantly. In some cases ths assumpton s untrue. Therefore, t leads to naccuraces n the predctons of sector occupancy. Sector occupancy s defned as the number of arcraft n a sector n 15-mn nterval bns. Examples have been presented to show that the nfluence of conflct resoluton maneuvers ncreases wth hgher traffc densty. Ths requres nformaton feedback from sector to sector such that separaton and meterng constrants are met. Conclusons A control theoretcal model of sector-based traffc flow usng hybrd automata theory was derved, based on observatons realzed at the Oakland ARTCC. A subset of ths model was used for generatng Lagrangan analytc predctons of the traffc flow such as dynamc sector capacty and the extent of traffc congeston. The defnton of a dynamc capacty of a sector of arspace enabled quantfcaton of the speed of propagaton of congeston as a functon of dynamc varables of the system, such as nbound flow and outbound restrctons, n addton to statc geometrc parameters such as the sze of the sector. These results were lnked to Euleran models of the NAS. Applyng these results enabled the dervaton of condtons under whch the arspace cannot be treated at the level of sngle sector, rather, a centralzed control (communcaton and strategc TMU plannng) would be requred. These predctons were verfed aganst data generated by a valdated smulaton tool. The smulaton tool conssts of a model of human sector controller acton on traffc, mplemented n the form of a cost functon for the dfferent sectors of the arspace n consderaton. Ths cost functon was based on observatons realzed at the Oakland ARTCC as well, whch have been valdated usng ETMS data. Another applcaton of the smulaton tool was demonstrated: Flow condtons under whch meterng can be decorrelated from conflct resoluton were establshed. Overall, the results of the present study suggest that the congeston speed can be correlated to dynamc varables of the system avalable to ar traffc controllers, and condtons under whch centralzed acton s requred to operate the system effcently can be dentfed. Fnally, there exsts a threshold densty of arcraft above whch conflct resoluton cannot be neglected when meterng the flow and preventng the extenson of congeston. Acknowledgments Ths research was supported by NASA under Grant NCC , by the U.S. Offce of Naval Research under Multdscplnary Unversty Research Intatve Contract N , by the