Combining Control by CTA and Dynamic Enroute Speed Adjustment to Improve Ground Delay Program Performance

Transcription

1 Eleventh USA/Europe Air Trffic Mngement Reserch nd Development Seminr (ATM2015) Combining Control by CTA nd Dynmic Enroute Speed Adjustment to Improve Ground Dely Progrm Performnce Jmes C. Jones, Dvid J. Lovell Deprtment of Civil nd Environmentl Engineering nd Institute for Systems Reserch University of Mrylnd College Prk, USA Abstrct Over the pst severl yers there hve been proposls nd discussions regrding move from the use of controlled times of deprture (CTDs) to controlled times of rrivl (CTAs) for ground dely progrms (GDPs) in the U.S. In this pper we show tht, by combining control by CTA with the judicious use of en route speed control, significnt improvements to GDP performnce cn be chieved. Our nlysis of this problem includes both new GDP control procedures nd lso new flight opertor GDP plnning models. While the bility to chieve ll the benefits we describe will reuire NextGen cpbilities, substntil performnce improvements could be obtined even with ner-term implementtion. Keywords- Speed Control, Collbortive Decision Mking, Trffic Mngement Inititives, Integer Progrmming I. INTRODUCTION Airports throughout the U.S. Ntionl Airspce System (NAS) regulrly encounter elevted levels of congestion. When fced with inclement wether, the cpcity of irports is often insufficient to ccommodte demnd nd the potentil effects on congestion re prticulrly burdensome. These cpcity/demnd imblnces will often led the Federl Avition Administrtion (FAA) ir trffic mngers to impose Ground Dely Progrms (GDPs) t irports or Airspce Flow Progrms (AFPs) in the irspce. Such inititives reduce the rte of rriving flights into the irport or region of irspce to level more comptible with the resource s reduced cpcity. Specificlly, flights receive lter deprture times from their origin irports commensurte with the rte of rrivl desired by the ffected irport or irspce region. These progrms lower flight opertor opertionl costs nd reduce the worklod imposed on ir trffic controllers by mitigting the potentil resulting irspce congestion. Trffic Flow Mngement Inititives (TMIs) in the U.S., such s GDPs nd AFPs, operte under philosophy known s Collbortive Decision Mking (CDM). In this prdigm, decisions on flight relese times re mde by irlines nd ir nvigtion service providers (ANSPs) in joint decision process. CDM processes involve both informtion shring nd specilized resource lloction mechnisms. [1,2]. GDP plnning procedures universlly strt by considering constrints on irport rrivl rtes nd set corresponding rrivl flows, which generlly re converted to specific flight rrivl Michel O. Bll Robert H. Smith School of Business nd Institute for Systems Reserch University of Mrylnd College Prk, USA mbll@rhsmith.umd.edu times / CTAs. These in turn re converted to CTDs by subtrcting n estimted flight time from the CTA. The reson this is done is tht CTD is much esier to monitor nd implement thn CTA. Airport tower controllers cn monitor flight deprture times nd prevent controlled flights from deprting erly. On the other hnd, it cn be difficult, costly nd even dngerous to insure set of irborne flights meet CTA constrints. Nonetheless, for mny yers CDM developers nd reserchers hve expressed the gol of controlling bsed only on CTAs. This is ttrctive becuse it gives flight opertors more flexibility nd llows both for more dynmic flight plnning nd greter bility to do system-wide trdeoffs. Even though control by CTA ws n expressed gol erly in CDM development, it hs not yet been implemented. The resons re perhps combintion the implementtion chllenges nd the lck of credible untifiction of the benefits. As both U.S. nd worldwide ir trffic flow mngement moves towrd time-bsed metering nd eventully trjectory bsed opertions (TBO), the use of CTAs for vriety of gols should become routine. Thus, we rgue tht the implementtion chllenges just mentioned should decrese nd eventully go wy. The experimentl results in this pper provide t lest first step in overcoming the second obstcle by demonstrting significnt benefits. CDM procedures were first described in the literture by Wmbsgnss nd Chng et l. [1,3]. A body of reserch hs developed round both GDP plnning nd CDM. One reserch strem hs modeled GDP uncertinty nd incorported stochstic components into integer progrmming models [4,5,6] for GDP plnning. GDP decision support tools now mitigte the impct of wether uncertinty by exempting flights whose origins re outside computed rdius [7]. The theory underlying this process nd extensions re provided in [8]. Other work hs formlized nd then extended CDM resource lloction processes [9]; relted work extended the compression lgorithm to include more comprehensive slot exchnge process [10]. Vossen et l. [11] developed metrics of euity nd then showed how CDM procedures could be improved to deliver better level of euity. CDM ws lter extended for use in multi-resource context by Fering nd Brnhrt [12]. This philosophy hs lso been proposed in deprture ueueing by Briton et l. nd Bhdr et l. [13,14].

2 Speed control hs been widely studied for vriety of ir trffic mngement pplictions. At the tcticl level Neumn nd Erzberger [15] described vriety of seuencing nd spcing lgorithms designed to reduce fuel consumption nd en route/rrivl dely. These lgorithms lid the foundtion for the Trffic Mngement Advisor (TMA) system currently used t mny irports cross the country to mnge flights up to 200 nmi from the irport. An enhnced version of the system clled The Terminl Are Precision Scheduling nd Spcing System (TAPSS) ws lter developed [16]. The technology ws lso proposed for coopertive use in Trffic Flow Progrms [17]. Crrier-centric pproches such s The Airline Bsed En Route Seuencing nd Spcing tool hve lso been proposed. The tool sends speed dvisories to the Airline Opertions Centers (AOC)s to llow crews to more ctively mnge their speeds en route [18]. In recent yers, the horizon for such ir trffic mngement inititives hs lso moved frther wy from the irport. Airservices Austrli developed the ATM Long Rnge Optiml Flow Tool (ALOFT) to llow pilots to control speeds up to 1000 nmi wy from the irport. In so doing, they chieved n estimted fuel svings of nerly 1 million kg in 2008 [19]. Since then, they hve lso used dditionl metering fixes to better mnge trjectory nd rrivl time uncertinty [20]. Delt Airlines chieved n estimted $8 million in fuel svings over 20-month period using disptch monitored speed control progrm known s Attil[21]. At Schiphol, ground bsed plnning system tht interfced with ircrft through dtlink ws used to remove vectoring in their nighttime opertions [22]. Knorr et l. [23] identified substntil inefficiencies in the terminl phse of flights nd chrcterized the benefit pool chieved by trnsferring terminl delys to the en route phse of flight. Jones et l. [24] developed bi-criteri integer progrmming model to fcilitte dely trnsfer wy from terminl irspce nd demonstrted tht substntil proportion of the potentil dely trnsfer benefit could be relized through this pproch. Speed control mesures hve lso been proposed for cpcity lloction in GDPs. Delgdo nd Prts showed tht it ws possible to bsorb some of the dely ssigned to flights within the GDP en route nd mintin the plnned level of fuel consumption [25, 26, 27]. The uthors lso showed tht by flying erlier nd t slower speed, considerble portion of the imposed dely could be recovered in the event of n erly GDP cncelltion. Jones nd Lovell showed tht speed control could lso be used to help curb the exemption bis in GDP slot ssignments [28]. In this pper, we consider replcing the use of CTD with CTA in GDP plnning nd control. The principl chnge is conceptully uite simple: flights nd, by ssocition, flight opertors, re ssigned CTAs rther thn CTDs. When GDP is revised, the ssigned CTAs rther thn the ssigned CTDs re djusted. Becuse of dded flexibility provided by the use of CTAs, we lso propose the elimintion of GDP flight exemptions, insted llowing flight opertors to effectively mke exemption decisions regrding their own flights. To effect these chnges we only need to mke minor chnges to the existing CDM/GDP lloction procedures. We propose new flight opertor GDP plnning model, specificlly scenrio-bsed stochstic integer progrmming model tht determines cncelltion nd substitution pln for ech crrier. The model mtches the crrier s flights to the ssigned rrivl cpcity (CTAs). In doing this, it tkes into ccount the bility to djust flight speeds en route, e.g. the model might ssign flight n erly deprture time, consistent with reltively slow speed but nticipte the bility for the flight to increse its speed should the wether cler t the destintion nd dditionl cpcity be ssigned to the crrier. The integer progrmming models builds on the prior literture on stochstic models for GDP plnning nd the use of speed control extends the work of Delgdo nd Prts. In Section II we provide description of the CDM GDP process nd our modifictions to it. We lso provide bckground on ircrft fuel burn chrcteristics nd how they impct speed control processes. In section III we present our models long with our methodologicl ssumptions. In Section IV we pply our models to cse study bsed on dt obtined t Atlnt Hrtsfield-Jckson Airport nd demonstrte the bility of our models to improve flight opertor performnce metrics. II. BACKGROUND A. CDM Assignment Prctices The CDM resource lloction mechnism for GDP plnning consists of three components: cpcity lloction, schedule djustments, nd slot exchnge. As discussed bove, while control is executed bsed on CTD, plnning is done bsed on CTA. Specificlly, rrivl cpcity is llocted to crriers using mechnism known s Rtion-by-Schedule (RBS). In RBS, flights re ssigned to rrivl slots bsed on the order they ppered in the originl schedule. This procedure provides n euitble initil lloction nd removes incentives for crriers to report inccurte informtion. Once cpcity hs been ssigned, schedule djustments re typiclly performed by llowing irlines to cncel nd substitute flights bsed on their own priorities. To improve the overll footprint, n inter-irline substitution procedure known s compression is used fcilitte trdes. A notionl digrm of the process is shown in Figure 1. Figure 1: Flight ssignment under CDM frmework When GDP is issued t n irport, ir trffic mngers t the Air Trffic Control System Commnd Center (ATCSCC) decide the plnned cpcity nd durtion of the GDP bsed on the predicted conditions over the course of the dy. They lso determine the rdius of exemption for the GDP. This exemption rdius defines the set of flights tht will receive ground delys. Once this prmeter hs been determined there re three pools of flights tht re ffected. Flights inside the exemption rdius receive ground delys bsed on their order in the schedule. Flights on the ground outside of the rdius re exempted from the GDP nd receive no delys. In ddition, ll

3 flights lredy in the ir, regrdless of their origin, re exempted from the GDP. Figure 2 illustrtes n exmple RBS lloction where the two exempt flights identified on the left re both irborne t the time of lloction. After the RBS lloction, crriers my freely substitute flights bsed on their own priorities. They my lso choose to cncel flights nd mke substitutions using the vcted slots. A notionl exmple of this process is shown in Figure 2b. Here, AA hs chosen to cncel AA561 nd move AA321 into its slot. AA lterntively could hve chosen to swp the slots of the two flights. In either cse, once the pproprite rrivl chnges were mde, the rrivl times (CTAs) would be converted to deprture times (CTDs) nd pproprite ground delys. Although DAL nd UA both lso hve two slots, they re unble to mke ny chnges since in ech cse one of their two slots is occupied by n irborne flight whose rrivl time cnnot be djusted. If DAL nd UA could ressign the slots of their irborne flights, then ech irline could improve the number of flights rriving less thn 15 minutes fter their scheduled rrivl time. An exmple of this exchnge is shown in Figure 2c. Figure 2: An exmple of flight lloction in Distnce Bsed Rtion-by- Schedule. Exempt flights receive priority. Figure 2c: Cncelltion nd Substitution process without exemptions. Delt nd United cn subsitute nd improve their on-time performnce. The dvntges illustrted by these exmples underlie the one component of the benefits tht cn be chieved by combining control by CTA with dynmic speed djustments. Similr improvements to the performnce of the compression lgorithm cn be chieved by llowing djustments to irborne flights. We note second source of benefits hve the sme origin s those investigted by Delgdo nd Prts [25,27], nmely the bility of irborne flights to more uickly rect to increses in rrivl cpcity resulting from wether chnges. B. Fuel Burn Implictions of Speed Chnges The reltionship between fuel efficiency (specific rnge) nd Mch number is illustrted in Figure 4. In this reltionship, s the Mch number of the ircrft increses, its fuel efficiency will lso increse to point known s the mximum rnge, beyond which it begins to decline. In generl, the shpe of this curve in the vicinity of the optimum is reltively flt. The fltness of this curve implies tht the speed of the ircrft cn be djusted (within resonble rnge) to bsorb the intended dely with miniml increse in fuel burn. Specific Rnge NM/ton Mximum Rnge Figure 2b: Cncelltion nd Substitution process in current CDM frmework. Mch Number Figure 4: Vrition in Aircrft fuel efficiency with speed. In [25] it ws suggested tht GDP flights receive n erly relese time nd fly t the minimum possible speed such tht

4 their specific rnge could be mintined. In the event tht the wether clers prior to the end of the GDP, the flight cn get in the ir erlier nd cn fly fster to recover some of the dely. In [27] the sme uthors exmine the effect of the exemption rdius on GDP performnce when pplying their originl ide. In [28] speed control ws pplied to the exempt flights while flights inside the rdius received only ground delys. Ech of these studies exmined trdes between delying flights in the ir nd delying flights on the ground but in ll cses the ssignments were mde by the ANSP. They serve s significnt first step, however, s these trde-offs my be more effective when they re performed by the crriers. If flight on the ground receives 15-minute reduction in dely t the expense of flight in the ir, the benefit to tht flight is irrelevnt if the crrier decides to cncel the flight on the ground. For resons such s this we would like to propose more crrier-centric lterntive to these strtegies. In the following section we present model designed to llow crriers to control their own flights using combintion of ground dely, speed control nd cnceltions. We describe the frmework for the models nd context in which we envision the ssignment process operting. III. NEW MODELS AND ARCHITECTURE In this section, we describe our CTA-bsed rchitecture (III-A), present our new irline optimiztion model to support the irline cncelltion nd substitution process (III-B) nd describe the model used to represent compression nd revisions in our experiments (III-C). A. Architecture The previous two sections hve described in generl terms the modifictions tht we envision to mjor components of the process. Here we more specificlly define the rchitecture nd explin some of the importnt chnges. While the new process uses the RBS mechnism, the exemption rdius is eliminted. Once cpcity is llocted to crriers, ech crrier cn use both speed control nd ground delys to mnge their substitution nd cncelltion decisions. Since no exemption rdius hs been imposed, crriers must be more strtegic bout their substitution process becuse in the event of n erly wether clernce they will wnt to tke dvntge of cpcity increses, e.g. by speeding up irborne flights. Our scenrio bsed stochstic model (Section III-B) is designed to fcilitte tht end. Ech scenrio ccounts for possibility of the wether clering t different times nd the ssocited increse in cpcity. The gol is to position the flights in slots tht llow them to mke the best use of cpcity under ll scenrios. The fct tht slot ssignment nd the effective use of speed control re key to evluting the impct of this new pproch implies tht proper evlution of its effectiveness reuires experiments tht involve GDP revisions. The mnner in which we model revisions is discussed both lter in this section nd in Section III-C. TABLE I gives the bsic steps in our CTA-bsed rchitecture. TABLE I: CTA-Bsed Flight Assignment Architecture Step 1 [FAA]. 1: Assign slot to ech irborne flight bsed on the flight s expected time of rrivl. 1b. Assign slot to ll flights on the ground using RBS. 1c. Crete list of slots (nd CTAs) owned by ech irline bsed on the lloction from both steps 1 nd 1b. Step 2 [Airlines]. Execute cncelltion nd substitution processes nd djust flight-to-cta ssignments. Assign deprture time to ech flight Step 3 [FAA]. Execute compression, djusting ssignments nd filling ny unusble slots. This process looks lmost identicl to the existing process illustrted in Figure 1. However, there re some subtle differences. First, none of the flights on the ground t the strt of the GDP re exempted. Second, when the irlines perform their cncelltions nd substitutions, nd lso when the FAA performs compression (steps 2 nd 3), both irborne flights nd flights on the ground should be considered. The considertion of flights in the ir imposes substntil new informtion reuirement: the (possibly very tight) limits on the degree to which their rrivl times cn be djusted. Third, tody the ssignment of deprture time (CTD) is performed by subtrcting nominl flight time from the CTA. Under this new pproch the irlines hve substntil flexibility in ssigning the deprture time, e.g. s in Delgdo nd Prts [25,27], ssuming n initil slow speed while nticipting possible speed-ups if wether conditions chnge. This dded irline flexibility implies tht when the irlines perform their cncelltion nd substitution process, they hve rich set of lterntives to consider nd the opportunity to improve performnce. In the next section, we present n optimiztion model to ddress this new irline decision problem. Another very importnt chllenge ssocited with this new pproch is the mnner in which GDP controls re dynmiclly updted over time. Tody vriety of possible GDP revisions might tke plce s wether conditions chnge t the destintion irport. Perhps the simplest is cncelltion of the GDP in the event of clernce of poor wether. If this occurs, ll issued ground delys re immeditely rescinded nd the impcted flights cn immeditely tke off. An euivlent ction in CTA-bsed rchitecture would be to llow flights on the ground to immeditely deprt nd flights in the ir increse their speed, to the extent fesible, in order to rrive t n erlier time if this is desired. It is difficult to ssess priori whether such complete cncelltion might ever be pproprite under CTA-bsed system. However, it is cler tht new GDP revision models nd controls will be reuired. In prticulr, it is likely tht revisions will be reuired not only bsed on mjor chnges in conditions t the destintion irport but lso more minor disturbnces tht impct the flight times of en route flights. It is likely tht such models could build on the recent experience with irborne speed control [17,18,19,20,21,22] nd the growing body of reserch [23,24,25,26,27,28] on the topic. Of course, this lso reltes to current efforts on time-bsed metering nd TBO.

5 In the current reserch we hve not ttempted to ddresses ll the nunces of GDP revisions under CTA controls. This would certinly represent nother significnt reserch contribution. Rther, to estimte the benefits of this new rchitecture, we evlute reltively simple scenrio in which wether clers t rndom time nd use n optimiztion model [9] tht represents the combined effect of RBS nd compression in ressigning CTAs bsed on the newly vilble cpcity. This model is described in Section III-C. B. Model to Suport Airline Subsitution nd Cncelltion Process Under the new rchitecture nd considering both the possibility of en route speed djustments nd no flight exemptions, ech irline hs more control over the disposition of its own flights. Since GDPs re often cncelled prior to their plnned end time, it behooves irlines to hedge between the prospect of erly nd on-time cncelltion. Such hedging is effectively done tody by the FAA through the exemption rdius. The chllenge for n irline lies in positioning flights in the pproprite slots to best del with ll possibilities. To do so we dpt stochstic models developed erlier [4,5,8] from n FAA/ANSP perspective to the perspective of specific irline. To understnd this model, consider the deterministic cse where the set of vilble slots, i.e. the CTAs ssigned to tht irline, is known with certinty, e.g. s described in [10]. This is simple ssignment problem where flights re ssigned to slots llowing for the possibility tht some flights my be cnceled t cost. Since this model is solved by specific irline, we cn ssume the vilbility of rich cost function tht tkes into ccount vrious fctors regrding flight, crew nd pssenger sttus, pssenger count, etc. Cpcity uncertinty is modeled using set of scenrios: ech scenrio is chrcterized by the time t which tht scenrio becomes known, the revised set of slots, i.e. dditionl cpcity represented by the ugmenttion of the existing slots with set of dditionl slots, nd probbility. An dditionl set of vribles indictes how the initil ssignment is djusted when the new cpcity becomes vilble. In defining the dt underlying this model, the differences in constrints underlying irborne flights nd flights on the ground must be tken into ccount. For exmple, if flight ws ssigned CTA of 4:00 nd, t the time the new scenrio ws effective tht flight ws irborne, then the flight might be restricted to revised CTAs not erlier thn 3:50 bsed on limittions on speedup options (no more thn 10 minutes). On the other hnd, if flight on the ground ws ssigned CTA of 4:00 nd tht flight still hd one hour to serve on its ground dely, then tht flight could be ssigned ny deprture time within the next hour nd in order to meet ny new ssigned CTA between 3:00 nd 4:00. The ir crriers should ssign both CTA nd deprture time to ech flight. For the present experiments, we ssume the deprture time ssigned is the erliest possible deprture time tht cn meet the ssigned CTA. This pproch provides mximum flexibility where wether scenrios only llow for cpcity increses. We recognize tht idelly the optimiztion model should contin both deprture time nd rrivl time vribles we leve such model to future reserch. This model certinly hs some substntil dt reuirements, most notbly the scenrio informtion. There re two spects to generting the slot lists for ech scenrio. The first is defining the set of slots vilble to ll crriers nd the second is how those slots re ssigned to ech crrier. There hs been prior reserch on the first spect, but this certinly would hve to be dpted to this new context. For the purposes of this pper, we use representtive/stylized informtion tht cptures the essentil spects of the problem setting. Regrding the second spect, we use bsic RBS relloction tht (by necessity) cnnot tke into ccount the sttus (nd slot ssignment) of ech crrier s flights. Thus, this relloction must be viewed s n pproximtion; however, it only impcts cost ssigned to the initil slot ssignment nd so it impcts only the ulity of the solution nd not its fesibility. We cn judge the overll ulity of our pproch by the results of our simultion experiments. We lso note tht some ir crriers might wish to use other processes; thus, this model could be viewed s surrogte for ny number of internl irline decision support processes. The specific integer progrmming problem formultion is given below. Note tht this model includes subscript for irlines in prctice, ech irline will solve its own model. Prmeters: F The set of ll flights vilble to irline A The set of ll irlines S - The set of ll slots vilble to irline E f The set of ll slots vilble to flight f t stge 1 prior to first probble end of the GDP vilble to irline P f The set of ll slots vilble to flight f t stge 1 following the first probble end of the GDP vilble to irline K fs The set of ll slots vilble to flight f t stge 2 in scenrio from slot s vilble to irline d Cost of delying flight f to slot s owned by irlines in scenrio c f The cost of cncelling flight f operted by irline p The probbility of scenrio occurring Vribles: 1if flight f of irline is ssigned to slot s x 0 otherwise 1if flight f of irline is cncelled y f 0 otherwise 1if flight f of irline is ssigned to slot s z in scenrio 0 otherwise

6 x x, z min p x ss Q s.t. f F z f F x z z fk kk fs, y f F, ss 1 s S f x y d 1 f F 1 s S, s E f F, s E f z f F, s P, Q, Q, Q (1) (2) (3) (4) (5) (6) 0,1 f F, A, s S (7) f F Constrint (2) ensures tht for ech irline, every flight is either ssigned to slot or cncelled. Constrint (3) ensures tht no more thn one flight is ssigned to slot in the first stge of the problem. Constrint (4) ensures tht no more thn one flight is ssigned to slot in the second stge of the problem for ll scenrios. Constrint (5) ensures tht if flight is ssigned to slot in the first stge prior to the first fesible wether clernce time, it must be ssigned to the sme slot in the second stge for ll scenrios. Constrint (6) ensures tht if flight is ssigned to slot in the first stge fter the first fesible wether clernce time, it must be ssigned to slot tht is rechble from tht slot in the second stge. Note tht this constrint, through the definition of K fs, restricts the set of slots to which flight cn be ressigned bsed on flight sttus nd the vrious timing restrictions. Constrint (7) reflects tht our ssignment vribles re binry. Our objective is to minimize the expected cost of the flight delys over ll scenrios plus the cost of flight cncelltions. C. Compression nd GDP Revisions To crry out our experiments, we must both execute compression s prt of the initil lloction process (see Tble I) nd lso perform slot relloction for the cse of GDP revision. Under current prctices revisions re performed using modified ppliction of RBS tht tkes into ccount both flight sttus nd the new set of vilble slots. Compression is lso typiclly performed. Very often combined RBS/compression process is executed clled RBS ++. In [10], n optimiztion model is defined tht provides both the functionlity of compression nd RBS ++. We use this model in our experiments for both the initil compression step nd lso the revision process. This model ctully provides crriers with more flexibility in the ppliction of compression. However, for our purposes here we only wish to mimic the bsic processes. Specificlly, the model employs set of gol slots, with one such slot ssigned to ech flight to be ssigned. To mimic compression the gol slot ssigned to ech flight is the RBS slot for tht flight. Other ssignments cn be used by crriers to implement vrious flight prioritiztion schemes. Prmeters: F The set of ll flights A The set of ll irlines S - The set of ll slots T The set of ll time periods F The set of ll flights belonging to irline f f c f f y f I - The set of ll gol slots belonging to irline R f The set of slots within cceptble for flight f S ft The set of ll slots vilble to flight f in period t t The time corresponding to slot s s f The time corresponding to the gol slot of flight f Vribles 1 if flight f of irline is ssigned to slot s x t in time period t 0 otherwise ss, tt f F, ss, A, tt f F, A, tt 1 min t x (8) f s t s.t. x 1 f F, A (9) t x 1 s S (10) t x 0,1 f F, A, s S, t T (11) t Eution (9) ensures tht every flight is ssigned to exctly one slot. Constrint (10) ensures tht ech slot is ssigned to no more thn one flight. Constrint (11) reflects tht our ssignment vribles re binry. The objective of the model is to lexicogrphiclly minimize the distnce of the flights from their gol slots. It ccomplishes this minimiztion by using coefficients tht grow super-linerly. This mimics the impct of compression, which seeks to find slot s close s possible to the flight s RBS slot in the cse where tht flight cnnot be fesibly ssigned to its RBS slot. IV. A. Experimentl Description RESULTS AND DISCUSSION To conduct our studies we selected dt collected from Atlnt Hrtsfield-Jckson Airport on My 1, The wether conditions were cler nd sunny nd ll runwys were ctive. The dt were obtined from file generted by TFMS in conjunction with n ASDX file, the combintion of which listed flight numbers, crrier, collection time, ETA, scheduled time of rrivl (STA), the origin irport, ctul time of deprture, ircrft position, ircrft type, rrivl time. The irport cceptnce rtes on n hour-by-hour bsis vried from 56 to 101 flights per hour. Since this dtset ws not tken on dy on which GDP ws issued, hypotheticl GDP ws superimposed on the dt. A 5 hour GDP ws ssigned to the irport over the hours of 16:00-21:00 GMT. Flights inside the exemption rdius were ssigned ground delys. Flights on the ground tht originted from irports outside of the rdius s well s flights in the cruise phse of flight t the strt of the GDP were llocted slots over the rnge chievble by the ircrft. The model used flight trjectories observed in the dt over the dy of opertions. Speed control directives were issued over the period of time tht the ircrft reched n ltitude of 35,000 ft. Bsed on these trjectories we clculted the distnce trveled. As bseline cse flights were given nominl cruise speed bsed

7 on the ircrft performnce listed on the BADA dtbse. This dtbse ws lso used to derive set of speeds t which ech ircrft could fly. In generl we used these speeds s guidelines; however, speeds on ll ircrft were restricted to +/-0.02 of their performnce mximum/minimum. Also, when ircrft were cpble of flying bove Mch 0.85 or below 0.72, ircrft speeds were restricted to mximum of 0.85 or minimum 0.72 respectively. CTAs for ground delyed flights could correspond to ny time t or following the scheduled time of rrivl of the flight. A bseline run ws used to evlute the dely performnce with no intervention. On these runs cpcity ws llocted to irlines using DB-RBS. A deterministic version of the substitution nd cncelltion model ws used which did not ccount for the possibility of erly clernce. A compression model ws then dopted to improve throughput. To understnd the full extent of the performnce we tested the computtion run time of ech model using dul core system with four Intel Xeon X5535 processors nd 12 GB of memory in 64 bit environment. The models were coded in Python 2.7 using GUROBI solver. B. The Cost of Dely nd Cncelltion If this proposed scheme were implemented, ech irline would compute the cost of dely bsed on their internl cost mesures; however, to perform computtionl experiment we needed to find suitble proxy. In this pper we chose to strt with the cost model presented in Vkili nd Bll [29], which drws from ATA dt nd models from Metron Avition. The model ssumes tht the direct operting cost per minute of block time is free during the first 15 minutes. After 15 minutes the cost jumps to $64 in the ir nd $32 on the ground. Since our irborne dely is essentilly free from fuel cost stndpoint nd fuel typiclly ccounts for roughly hlf the dely costs we decided to use n eul cost for ground nd ir dely. Updting for yerly chnges in dely costs we found the cost on both the ground nd the ir ws $40[30]. The Vkili nd Bll pproch lso ssumes tht the cost per minute of pssenger dely is $34.88 per hour or $34.88/60 = $ per minute. Since the irlines do not suffer the sme degree of impct s customers on per minute bsis the pproch pproximtes the cost by multiplying pssenger cost by 1/6 nd uses cost of $0.1 per minute. Adopting the sme process using 2013 pssenger costs we find tht the dditionl irline cost is $0.125 per minute, per pssenger. An expression for the cost function is show below: C( x, P) 0 x P x x M PM 15 x M 14 p p where P is the number of pssengers on the flight nd M p is the mximum mount of time before the dely cost levels off. When the cost levels off it does not mtter whether the irline delys the flight n dditionl minute or dy. Thus we ssume the cost to cncel flight is the cost t level off. Aircrft specifictions were used to determine the number of pssengers on given ircrft. Using the 2013 verge reported in IATA our nlysis ssumed lod fctor 0.8 on ll flights [31]. We set M p to vlue of 90. p C. Effect on Airlines Metrics with no GDP cncelltion To better study the distribution of dely we reduced the number of flights to consider just the 5 lrgest crriers. A bseline run ws performed using conventionl GDP procedure. Cpcity ws llocted with DB-RBS nd cncelltions nd substitutions were mde using deterministic model. The resulting performnce for GDP with Plnned Airport Arrivl Rte (PAAR) of 40 is shown in TABLE II. The percentge of cncelltions remined reltively consistent cross crriers rnging between 25% nd 33.33%. Delt nd AirTrn, however, both exhibit stronger dely performnce in trditionl GDPs. This is understndble s Delt nd AirTrn both control lrger pool of exempt flights thn regionl crriers nd those with smller presence t the irport. To evlute CTA-bsed rchitecture nd new plnning modes, we used 5 cpcity profiles. The set consisted of complete GDP nd wether clernces of 15, 30, 45 nd 60 minutes erly. Ech scenrio ws ssumed to be eully probble. The results of our test re shown in TABLE III. The tests yielded noticebly different results reltive to the bseline. All crriers reduced their number of cncelltions except for Americn Airlines, which only controlled 3 flights. TABLE II: AIRLINE PERFORMANCE WITH A CONVERTIONAL GDP MODEL Airline Percentge of Flights Cncelled Pssenger Dely Number of Flights Delt (DAL) AirTrn (TRS) Americn Southest Airlines (ASQ) Americn (AAL) Pinncle (FLG) TABLE III: AIRLINE PERFORMANCE WITH CTA-BASED ARCHITECTURE Airline Percentge of Flights Cncelled Pssenger Dely Number of Flights Delt (DAL) AirTrn (TRS) Americn Southest Airlines (ASQ) Americn (AAL) Pinncle (FLG)

8 The performnce dt suggests tht irlines will pproch the two GDP procedures in remrkbly different fshion. In the current frmework crriers re more likely to cncel flights to crete dditionl cpcity nd flexibility s well s reduce dely. In our modifiction crriers hve more opportunity for intr-irline substitution both through speed control nd the lck of n exemption rdius nd re lso ccounting for the benefits chieved in the event of n erly cnceltion. This is not something tht is ssumed in the deterministic plnning cse. Thus crriers will choose to keep greter portion of their slots. Since there re fr fewer cncelltions the crriers re less ffected by ctions of other crriers during compression. This llows crriers to hve more direct control over their performnce. While the exmple bove revels some informtion regrding the reltive effect of our CDM modifiction, it does not provide us with sense of how strong the possibility of erly clernce needs to be to ffect the decision. We rn the model with nother set of scenrios in which the erly clernce intervls were only 7.5 minutes piece. The resulting performnce of both models is shown in Figures 7b. In nerly ll cses the prospect of n erly clernce reduced the number of cncelltions while incresing the pssenger dely crriers with more long hul flights. The mgnitude of the reduction is not uite s prominent, however, s tht of the 15 min scenrios. While the previous grphs demonstrte significntly different behvior on the prt of irlines, it is uncler wht portion of the chnge is ttributble to the possibility of erly cncelltion vs. the lck of n exemption rdius. To isolte the effect we tested our models both with nd without rdius. In the former cse RBS ws used to generte cpcity while the lter used the DB-RBS lgorithm. The performnce is shown in Figure 8. The results suggest tht when rdius is present lrge crriers such s Delt will reduce the number of cncelltions they impose on their flights; this is lso the cse with Air Trn. This likely ttributble to the significntly lrger number of exempt eligible flights they hve reltive to other crriers. Regionl crriers such s Americn Southest Airlines re negtively ffected by the presence of the rdius nd re forced to cncel more flights to crete substitution opportunities. Figure 8: Effect of the Exemption Rdius on Percentge of Flight Cncelltions. Figure 7: Percentge Flight cncelltion level of Airlines with Conventionl nd Erly Clernce. Figure 8b: Effect of the Exemption Rdius on Pssenger Dely Figure 7b: Pssenger Dely of Airlines for Conventionl nd Erly Clernce Models in minutes. D. Dely Recovery with GDP cncelltion In ddition to the effect our GDP modifictions hve on the propensity of irlines to cncel flights, we lso wnted to study the potentil benefit we could chieve in dely recovery in the event of n erly GDP cncelltion. To test our model we used 5 scenrios in which we ssumed erly clernce times of 0, 15, 30, 45 minutes nd 1 hour. The performnce in ech cse is shown in Figure 9 below. Delt nd AirTrn both

9 experience noticeble reduction in the overll dely s the extent of the erly cncelltion reches one hour. This is not entirely surprising in the cse of Delt becuse they hve greter number of cross-continentl nd interntionl flights thn regionl crriers such s Americn Southest Airlines nd operte more flights thn Americn nd re in better position to recover the dely in the event of cnceltion. Figure 9: Minutes of Pssenger Dely Recovered in ech Scenrio V. CONCLUSIONS AND PERSPECTIVES In this pper we proposed new strtegy for mnging ground dely progrms. The strtegy incorported both Controlled Deprture nd Arrivl Times s well s en route speed control. It lso eliminted the use of n exemption rdius which provides incentives for crriers to crete their own hedging strtegies. To model performnce under our new frmework we dpted stochstic model to ccount for irline hedging. Our nlysis suggests tht under our new set of GDP controls irlines re significntly less likely to cncel flights becuse they hope to recover dely in the event of erly cncelltion. Below we discuss implementtion nd lso suggest implictions on NextGen. A. Ner-Term Implementtion The two biggest chllenges to ner-term implementtion re i) insuring CTA complince (s ws mentioned t the outset) nd ii) modifying the vrious GDP procedures to support the proposed rchitecture. Two types of enforcement cn be envisioned. First, violtions could be monitored nd flight opertors with poor records penlized in vrious wys. Second, s time-bsed metering methods re implemented CTA informtion could be communicted to these systems so tht they could be CTA-wre nd id in insuring complince. Regrding ii), the reserch in this pper s well s the work on vrious speed control mesures could be dpted to provide revision nd dynmic CTA djustment methods pplicble to this context. It is probbly sfe to sy there re no mjor rod blocks, just the reuirement for further development nd experimenttion with the existing concepts. The reserch in this pper lso should provide strting point for irline decision support models. A vriety of pproches (some simpler, some more complex) re possible. There will be new informtion exchnge reuirements including the need for informtion on the limits to which CTAs cn be chnged for irborne flights. Of course integrtion with time-bse metering tools would lso induce new informtion reuirements. It should be dmitted tht in the ner term the full benefits envisioned could not be chieved s they reuire complete flexibility on the prt of ech flight to independently djust its speed. This limittion suggests certin NextGen gols s discussed below. B. Fr-Term Implementtion nd Implictions for NextGen NextGen nd Sesr both express TBO vision in which flight timing will be closely monitored nd controlled. Implicit in this vision is the bility to insure some degree of CTA complince. In fct, one cn view the rchitecture we hve described s (prtil) vision of how GDPs would be migrted to TBO-bsed NAS. NextGen nd Sesr technologies lso should provide the bility for flights to more independently djust their speeds. This in turn should llow for the benefits described in this pper to be more completely relized. It is perhps instructive to consider the underlying opertionl concept of our rchitecture. Note tht, while there is high degree of control over en route flight timing, there is lso n ssumption of high degree of flexibility. This is not comptible with TBO vision in which 4D trjectory is set t the time of flight deprture nd then rigorously dhered to for the reminder of the flight. Our vision clls for high degree of control nd system-wide coordintion mong 4D trjectories coupled with the bility to dynmiclly djust those trjectories to chieve flight opertor nd ANSP objectives. We feel it is importnt to incorporte this vision into future TBO rchitectures. VI. ACKNOWLEDGMENTS This work ws supported in prt by the FAA through the NEXTOR-II Consortium. REFERENCES [1] M. Wmbsgnns, Collbortive decision mking through dynmic informtion trnsfer, Air Trffic Contr Qurterly 4 (1996), pp [2] Bll, M. O., Hoffmn, R. L., Knorr, D., Wetherly, J., & Wmbsgnss, M. (2001). Assessing the benefits of collbortive decision mking in ir trffic mngement. Progress In Astronutics nd Aeronutics, 193, pp [3] Chng, K., Howrd, K., Oiesen, R., Shisler, L., Tnino, M., & Wmbsgnss, M. C. (2001). Enhncements to the FAA ground-dely progrm under collbortive decision mking. Interfces, 31(1), [4] Richett, O.; Odoni, A. Solving optimlly the sttic ground-holding policy problem in ir trffic control. 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10 [8] Bll, M.O., R. Hoffmn nd A. Mukherjee, 2010, Ground Dely Progrm Plnning under Uncertinty Bsed on the Rtion-by-Distnce Principle, Trnsporttion Science, 44, [9] T. Vossen. nd M. Bll, Optimiztion nd Medited Brtering Models for Ground Dely Progrms, Nvl Reserch Logistics, vol 53, 2006, pp [10] T. W. Vossen, nd M. O. Bll (2006). Slot trding opportunities in collbortive ground dely progrms. Trnsporttion Science, 40(1), [11] Vossen, T., Bll, M.O., Hoffmn, R. nd Wmbsgnss, M., 2003, A Generl Approch to Euity in Trffic Flow Mngement nd its Appliction to Mitigting Exemption Bis in Ground Dely Progrms, Air Trffic Control Qurterly, 11, ( preprint ws published in Proceedings of 5 th USA/Europe Air Trffic Mngement R&D Seminr, 2003). [12] Fering, D., & Brnhrt, C. (2011). Evluting ir trffic flow mngement in collbortive decision-mking environment. Trnsporttion Reserch Record: Journl of the Trnsporttion Reserch Bord, 2206(1), [13] Brinton, C., Provn, C., Lent, S., Prevost, T., & Pssmore, S. (2011, June). Collbortive deprture ueue mngement. In Ninth USA/Europe Air Trffic Mngement Reserch nd Development Seminr. Berlin, Germny. [14] Bhdr, D., Knorr, D. A., & Levy, B. (2012). Benefits of virtul ueuing t congested irports using ASDE-X: A cse study of JFK Airport. Air Trffic Control Qurterly, 20(3), 225. [15] F. Neumn nd H. Erzberger, Anlysis of dely reducing nd fuel sving seuencing nd spcing lgorithms for rrivl trffic, NASA Technicl Memorndum, , [16] H. N. Swenson, J. Thipphvong, A. Sdovsky, L. Chen, C. Sullivn, nd L. Mrtin, Design nd evlution of the terminl re precision scheduling nd spcing system, 9th USA/Europe Air Trffic Mngement R&D Seminr, Berlin, Germny, June [17] S. Grbbe, B. Sridhr, A. Mukherjee, nd A. Morndo, "Trffic Flow Mngement Impct on Dely nd Fuel Consumption: n Atlnt Cse Study," Air Trffic Control Qurterly, Vol, 20(3) pp , [18] P. M. 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Lovell, nd M. O. Bll, En Route Speed Control Methods for Trnsfering Terminl Dely, in 10th USA/Europe Air Trffic Mngement Reserch nd Development Seminr (ATMf2013), Chicgo, Jun [25] L. Delgdo nd X. Prts, En-Route Speed Reduction Concept for Absorbing Air Trffic Flow Mngement Delys, Journl of Aircrft, vol. 49, no. 1, pp , Jn [26] X. Prts nd M. Hnsen, Green dely progrmes, bsorbing ATFMdely by flying t minimum fuel speed. in 9th USA/Europe Air Trffic Mngement Reserch nd Development Seminr (ATMf2011), Berlin, Jun [27] L. Delgdo nd X. Prts, Effect of Rdii of Exemption on Ground Dely Progrms with Operting Cost Bsed Cruise Speed Reduction Cse study: Chicgo O Hre Interntionl Airport, in 10th USA/Europe Air Trffic Mngement Reserch nd Development Seminr (ATMf2013), Chicgo, Jun [28] J. C. Jones, nd D. J. Lovell. "Methods for Curbing the Exemption Bis in Ground Dely Progrms Through Speed Control." intrnsporttion Reserch Record, presented t 93rd Annul Meeting of Trnsporttion Reserch Bord, Wshington DC, USA, Jnury, [29] Pourtklo, Nsim Vkili, nd Michel Bll. "Euitble lloction of enroute irspce resources." Eighth USA/Europe Air Trffic Mngement Reserch nd Development Seminr, Np, CA [30] [31] AUTHOR BIOGRAPHIES Jmes C. Jones is PhD student in the civil engineering deprtment t the University of Mrylnd. He holds B.S. in engineering from Swrthmore College, n M.S. in electricl engineering from the University of Mrylnd nd n M.S. in systems engineering from The George Wshington University. Prior to pursuing his PhD, Jmes held positions t Northrop Grummn nd the RAND Corportion. His reserch focuses on pplying opertions reserch systems engineering methods to solve ir trffic mngement relted problems. Dvid J. Lovell is n Associte Professor in the Deprtment of Civil nd Environmentl Engineering t the University of Mrylnd. He holds joint ppointment with the Institute for Systems Reserch nd n ffilite ppointment with the Applied Mthemtics, Sttistics, nd Scientific Computing Progrm. Dr. Lovell received his B.A. degree in Mthemtics from Portlnd Stte University, nd his M.S. nd Ph.D. degrees in Civil Engineering from the University of Cliforni, Berkeley Michel Bll holds the Den s Chir in Mngement Science in the Robert H. Smith School of Business t the University of Mrylnd. He lso hs joint ppointment within the Institute for Systems Reserch in the Clrk School of Engineering is co-director of NEXTOR-II, n FAA consortium in vition opertions reserch.. Dr. Bll received his Ph.D. in Opertions Reserch in 1977 from Cornell University.