Modeling passenger travel and delays in the National Air Transportation System

Transcription

1 Modling passngr travl and dlays in th National Air Transportation Systm Cynthia Barnhart Dpartmnt of Civil and Environmntal Enginring, Massachustts Institut of Tchnology Douglas Faring Oprations Rsarch Cntr, Massachustts Institut of Tchnology, Vikrant Vaz Dpartmnt of Civil and Environmntal Enginring, Massachustts Institut of Tchnology Abstract: Many of th xisting mthods for valuating an airlin s on-tim prformanc ar basd on flight-cntric masurs of dlay. Howvr, rcnt rsarch has dmonstratd that passngr dlays dpnd on many factors in addition to flight dlays. For instanc, significant passngr dlays rsult from flight cancllations and missd connctions, which thmslvs dpnd on a significant numbr of factors. Unfortunatly, lack of publicly availabl passngr travl data has mad it difficult for rsarchrs to xplor th natur of ths rlationships. In this papr, w dvlop mthodologis to modl historical travl and dlays for U.S. domstic passngrs. W dvlop a discrt choic modl for stimating historical passngr travl and xtnd a prviously-dvlopd grdy raccommodation huristic for stimating th rsulting passngr dlays. W rport and analyz th stimatd passngr dlays for calndar yar 2007, dvloping insights into factors that affct th prformanc of th National Air Transportation Systm in th Unitd Stats. Draft compltd August 2 nd, Introduction Ovr th past two yars, flight and passngr dlays hav bn on th dclin du to rducd dmand for air travl as a rsult of th rcnt conomic crisis. As th conomy rbounds, dmand for air travl in th Unitd Stats is also xpctd to rcovr (Tomr & Punts, 2009). Thus, aftr a brif rpriv, th U.S. will onc again fac a looming transportation crisis du to air traffic congstion. In calndar yar 2007, th last yar of pak air travl dmand bfor th conomic downturn, flight dlays wr stimatd to hav cost airlins $19 billion (U.S. Congrss Joint Economic Committ, 2008) compard to profits of just $5 billion (Air Transport Association, 2008). In 2007, passngrs wr also svrly impactd, with th conomic costs of tim lost du to dlays stimatd at $12 billion according to th Joint Economic Committ rport. A similar analysis prformd by th Air Transport Association stimatd th

2 conomic costs of passngr dlays at approximatly $5 billion for Whil thr ar diffrncs in mthodologis, th hug discrpancy btwn ths stimats suggsts th nd for a mor transparnt and rigorous approach to masuring passngr dlays. Accuratly stimating passngr dlays is important not only as a mans to undrstand systm prformanc, but also to motivat policy and invstmnt dcisions for th National Air Transportation Systm. Anothr important considration is that nithr of th passngr dlay cost stimats listd abov includs th dlays associatd with itinrary disruptions, such as missd connctions or cancllations. Analysis prformd by Bratu and Barnhart (2005) suggsts that itinrary disruptions and th associatd dlays rprsnt a significant componnt of passngr dlays. Thir analysis was prformd using on month of propritary passngr booking data from a lgacy carrir. Th challng in xtnding this analysis systm-wid is that publicly availabl data sourcs do not contain passngr itinrary flows. For xampl, on a givn day, thr is no way to dtrmin how many passngrs plannd to tak th 7:05am Amrican Airlins flight from Boston Logan (BOS) to Chicago O Har (ORD) followd by th 11:15am flight from Chicago O Har (ORD) to Los Angls (LAX), or vn th numbr of non-stop passngrs on ach of ths flights. Instad, th passngr flow data that is publicly availabl is aggrgatd ovr tim, ithr monthly or quartrly, and rports flows basd only on th origin, connction, and dstination airports. Th mthodologis w dvlop in this work ar prcisly to addrss ths limitations. Byond th analysis of historical passngr dlays, w xpct our approach to b valuabl in xtnding passngr analyss to othr contxts whr prviously only flight information has bn availabl. For xampl, much of th rsarch on traffic congstion considrs only flight dlays, du to both th lack of passngr data and th complxitis associatd with passngr-cntric objctivs. Thus, to ncourag furthr passngr-cntric rsarch, w hav mad stimatd passngr itinrary flows for 2007 publicly availabl Litratur Rviw As mntiond abov, our work is largly motivatd by th findings of Bratu and Barnhart (2005). Using on month of booking data from a major U.S. carrir, thir rsarch dmonstratd that itinrary disruptions in th form of flight cancllations and missd connctions contribut significantly to ovrall passngr dlays. To gnrat this rsult, th authors us a passngr dlay calculator to stimat passngr dlays by grdily r-accommodating passngrs travling on disruptd itinraris. 1 For furthr information, plas visit which provids dtaild instructions for accssing th data. 2

3 Th primary challng w addrss in our work is stimating disaggrgat passngr itinrary flows from publicly availabl aggrgat flow data using a small st of propritary booking data. In hr Mastr s thsis, Zhu (2009) attmptd to addrss this problm using an allocation approach basd on linar programming. On challng with this approach is th inability to incorporat scondary factors, such as connction tim, which play an important rol in passngr dlays. Th natur of th xtrm point optimal solutions to th linar programming modl also crats challngs, bcaus a much largr proportion of flights nd up bing ithr mpty or full as compard to th propritary data. Ths limitations hav ld us to apply instad a discrt choic modling approach. In a rlatd contxt, Coldrn, Kopplman and othrs hav applid discrt choic modls to stimat airlin itinrary shars from booking data (Coldrn, Kopplman, Kasurirangan, & Mukhrj, 2003 and Coldrn & Kopplman, 2005). In th airlin itinrary shars stimation problm, th goal is to prdict th shar of passngr dmand for a markt (i.., all air travl from an origin to dstination) that will utiliz ach of a st of availabl itinrary choics. Thus, th itinrary shars problm is mor gnral in that all routs btwn th origin and dstination ar considrd simultanously. In our problm, du to th mannr in which publicly availabl passngr flow data is aggrgatd, w ar intrstd in stimating th shar of passngr dmand for a singl carrir and rout combination across diffrnt itinraris. Nonthlss, th succss of th Coldrn and Kopplman modls suggst that application of a discrt choic modl is rasonabl in this ara. Othr rsarchrs hav prformd passngr dlay analyss without first disaggrgating passngr itinrary flows, but ths approachs tnd to rquir rathr substantial assumptions. Shrry, Wang, and Donohu (2007) stimat passngr dlays by trating all passngrs as non-stop and assuming that all flights on an origin-dstination sgmnt oprat at th monthly avrag load factor. Tin, Ball, and Subramanian (2008) dvlop a structural modl of passngr dlays, but in ordr to us th modl ar forcd to mak unvrifiabl assumptions rgarding ky paramtr valus (.g., th dlay thrsholds for missd connctions). Each of ths approachs would bnfit from accss to stimatd passngr itinrary data from which to nhanc or validat th modl. Additional studis on air transportation passngr choic hav hlpd us dtrmin which faturs to includ in our modl. This, Adlr, Clark, & Bn-Akiva (2006) dmonstrat that passngrs travlling on on-stop itinraris ar snsitiv to connction tims, spcifically xhibiting a disutility associatd with both short and long connction tims. Th rfrncd study by Coldrn & Kopplman (2005) suggsts that passngrs prfr travlling on largr aircraft. Last, rcnt work has shown that flight cancllation dcisions ar affctd by flight load factors th fraction of sats filld on ach flight (Tin, Churchill, & Ball, 2009). This suggsts flight cancllations ar an important factor to considr, bcaus w would 3

4 xpct fwr passngrs to hav bn bookd on cancld flights. That is, though w do not xpct passngrs to prdict cancllations, in hindsight, cancllations provid valuabl information rgarding th historical distribution of passngrs across itinraris. 1.2 Contributions Th contributions of our rsarch fall broadly into two catgoris: i) an approach for disaggrgating publicly availabl passngr dmand data, and ii) an analysis of historical passngr dlays using ths disaggrgat passngr itinrary flows. Th outlin of th papr follows this structur. In Sction 2, w dscrib th componnts of th passngr itinrary allocation procss. First, w join passngr and flight data from multipl sourcs into a larg Oracl databas. Nxt, w procss th data to stablish th ncssary inputs for passngr allocation, such as potntial itinraris and flight sating capacitis. Last, w dvlop a discrt choic modl for passngr itinrary allocation, training and validating th rsults using a small st of propritary booking data. In Sction 3, w utiliz th disaggrgatd passngr itinrary flows to analyz domstic passngr dlays for First, w xtnd th passngr dlay calculator dvlopd by Bratu and Barnhart (2005) to support a multi-day, multi-carrir rbooking procss. Nxt, w analyz th snsitivity of our approach and validat th calculatd dlays against thos stimatd from th propritary booking data. Last, w analyz passngr dlays from 2007 to dvlop furthr insights into th rlationship btwn flight dlays and passngr dlays and dvlop a simplifid rgrssion-basd approach for stimating passngr dlays dirctly. W conclud th papr with a discussion of othr problms to which this data is ithr alrady bing applid or could b applid in th futur. 2 Passngr Itinrary Allocation In this sction, w dscrib th procss of allocating passngrs to individual itinraris. W considr an itinrary to b a squnc of conncting flights that rprsnts a on-way trip, including schduld dpartur, connction (if any), and arrival tims. Thus, round-trip travl would b rprsntd by two on-way itinraris. To dscrib this procss, w first dfin th following trminology. carrir-sgmnt: th combination of an oprating carrir, origin, and dstination, whr th oprating carrir provids non-stop flight accss btwn th origin and dstination; and 4

5 carrir-rout: a squnc of carrir-sgmnts that rprsnts th flight path a passngr could travl from th origin of th first carrir-sgmnt to th dstination of th last carrir-sgmnt. With ths dfinitions in mind, w can dscrib passngr itinrary allocation as th ffort to combin carrir-sgmnt dmand data that is aggrgatd monthly with carrir-rout dmand data that is aggrgatd quartrly to allocat passngrs to plausibl itinraris. For xampl, a plausibl on-stop itinrary would b taking th 7:55am Amrican Airlins flight from Boston Logan (BOS) to Chicago O Har (ORD) followd by th 11:15am flight from Chicago O Har (ORD) to Los Angls (LAX) on Thursday, August 9 th. Th carrir-sgmnt data would tll us how many passngrs travld on Amrican Airlins flight lgs from BOS to ORD and ORD to LAX in August, whras th carrir-rout data would tll us how many passngrs travld on Amrican Airlins from BOS to LAX conncting in ORD in th 3 rd quartr of Not that whn w discuss itinraris in this papr, w ar including both th spcific dats and tims of travl in our dfinition of an itinrary. In Sction 2.1, w dscrib ach of th data sourcs in dtail, followd by a dscription of th data procssing in Sction 2.2. In Sction 2.3, w dscrib th mthodological cor of our papr th discrt choic modl usd to allocat passngrs to itinraris. Last, in Sction 2.4, w validat th discrt choic allocations against a small st of propritary booking data. 2.1 Data Sourcs Th U.S. Burau of Transportation Statistics (BTS) provids a walth of data rlatd to airlin travl (Burau of Transportation Statistics). Th Airlin Srvic Quality Prformanc (ASQP) databas provids plannd and ralizd flight schduls for many airlins. Rporting is mandatory for all airlins that carry at last 1% of U.S. domstic passngrs. For calndar yar 2007, th databas contains information for 20 airlins, ranging from Aloha Airlins with 46,360 flights to Southwst Airlins with 1,168,871 flights. BTS also maintains th Schdul B-43 Aircraft Invntory which provids annual lists of aircraft in invntory for most airlins. Most importantly for our purposs, th Schdul B-43 provids th sating capacity for ach aircraft, matching approximatly 75% of th flights in ASQP by tail numbr. W cannot match 100% of flights this way, bcaus tail numbr information is somtims inaccurat or non-xistnt in both ASQP and Schdul B-43. Th Fdral Aviation Administration (FAA) maintains th Enhancd Traffic Managmnt Systm (ETMS) databas, which includs schdul information for all flights trackd by air traffic control. This databas is not publicly availabl, du to th prsnc of snsitiv military flight information, but a filtrd vrsion was mad accssibl for th purposs of this rsarch. Th bnfit of this databas ovr ASQP is that, in addition to th plannd and ralizd flight schduls, it contains th Intrnational Civil 5

6 Aviation Organization (ICAO) aircraft quipmnt cod for ach flight. Using th ETMS databas, w ar abl to dtrmin th ICAO aircraft cod and sating capacity for many of th 25% of ASQP flights that could not b matchd through Schdul B-43. Thr ar two BTS datasts that w dpnd on for passngr dmand information. Th first is th T-100 Domstic Sgmnt (T-100) databas, which contains passngr and sat counts for ach carrir-sgmnt and quipmnt typ aggrgatd monthly. For xampl, from this data w can s that in Sptmbr 2007, Amrican Airlins prformd 79 dparturs from BOS to ORD using Boing s with 14,852 sats availabl and 11,215 passngrs. T-100 is a particularly usful databas in that it contains information on both passngr counts and aircraft typs. If th variation in sating capacity is sufficintly low for a carrir-sgmnt, w stimat th sating capacity of ach matching flight by dividing th numbr of sats availabl by th numbr of dparturs prformd. W say that th variation in sating capacity is sufficintly low if th cofficint of variation (th standard dviation dividd by th man) is lss than 2.5%. By combining T-100 with th data from Schdul B-43 and ETMS dscribd abov, w ar abl to stimat accurat sating capacitis for approximatly 98.5% of th ASQP flights. For th rmaining 1.5% of ASQP flights, bcaus th variation in sating capacity is high, w us th T-100 data to stimat a sating capacity that is slightly highr than avrag. For ths flights, th sating capacity w us quals th avrag sating capacity across th matching T-100 rows plus on standard dviation to account for variation across aircraft typs. Th scond passngr dmand databas w dpnd on is th Airlin Origin and Dstination Survy (DB1B), which provids a 10% sampl of domstic passngr tickts from rporting carrirs, including all of th carrirs in ASQP, aggrgatd quartrly by rmoving information on flight tims. For xampl, in th 3rd quartr of 2007, 128 passngr tickts wr sampld that includd a on-way trip on Amrican Airlins from BOS to ORD to LAX. W us this data to dtrmin th approximat numbr of monthly passngrs travlling on ach non-stop or on-stop carrir-rout. Th last data st w us contains propritary booking data from a larg ntwork carrir for th 4 th quartr of This data is usd for training our passngr flow stimation modl and for validating our rsults. All of th data sts, including th propritary booking data, ar joind using a larg Oracl databas. 2.2 Data Procssing Thr ar two data procssing stps that ar prformd prior to th discrt choic allocation of passngrs to itinraris. Th first stp is stimating th st of potntial itinraris on which passngrs might hav travlld. Ths itinraris will b usd to crat th choic sts in th discrt choic allocation modl. Th scond stp is stimating th numbr of passngrs travlling on ach carrir- 6

7 rout for ach month. Ths passngrs will b allocatd to matching itinraris using th discrt choic allocation modl dscribd in th nxt sction. W gnrat th st of potntial itinraris for th yar basd on th flights in ASQP and th carrirrouts rprsntd in DB1B. For th purpos of our analysis, w includ only non-stop and on-stop itinraris. Itinraris with mor than on stop account for only 2.5% of th on-way trips in DB1B. A non-stop itinrary is gnratd for ach flight in ASQP, whras a on-stop itinrary is gnratd only for valid flight pairs. Th ruls w us for dtrmining valid flight pairs ar as follows: 1. Th carrir-rout rprsntd by th flight pair xists within DB1B. This filtrs out nonsnsical routs, such as BOS IAH PVD (Boston to Houston to Providnc), but allows for multicarrir and cod-shar itinraris as long as at last on DB1B passngr utilizd th corrsponding multi-carrir carrir-rout. 2. Th plannd connction tim (th diffrnc btwn th plannd dpartur tim of th scond flight and th plannd arrival tim of th first flight) is at last 30 minuts and not mor than 5 hours. 3. For a givn first flight and matching carrir-rout, w gnrat at most 2 connctions. This nsurs that passngrs ar not assignd to a much longr connction whn multipl shortr connction tims ar availabl. Passngr utility associatd with connction tim is also xplicitly considrd within our discrt choic allocation modl. Using th 2007 ASQP and DB1B data sts, this procdur lads to 273,473,424 itinraris, of which 7,455,428 ar non-stop. Ths itinraris ar stord in our Oracl databas for as of qurying during passngr flow stimation. W stimat th numbr of passngrs travlling ach month on ach carrir-rout as follows. 1. First, for ach carrir-sgmnt, s, w calculat a monthly scaling factor, α s. Th scaling factor is calculatd as th ratio btwn th monthly carrir-sgmnt dmands spcifid by T-100 and th 10%-sampl quartrly carrir-sgmnt dmands calculatd from DB1B. For all itinraris rprsntd in th DB1B 10% tickt sampl, w aggrgat th numbr of passngrs on ach carrir-sgmnt. If DB1B sampld across carrir-sgmnts uniformly, including intrnational itinraris, and thr wr no monthly variations across carrir-sgmnts in T-100, w would xpct this ratio to qual 3.33 for all carrir-sgmnts. That is, w would xpct 3.33 tims th DB1B sampld, quartrly carrir-rout dmand to b a good stimat of th total, monthly carrir-rout dmand (i.., multiplying by 10 to account for th sampling and thn dividing by 3, 7

8 th numbr of months in a quartr). Instad, bcaus DB1B sampls only domstic itinraris and thr ar no guarants that th sampling is xactly 10% for ach carrir-sgmnt, w find that th calculatd ratio varis around a man of approximatly For ach on-stop carrir-rout rprsntd in DB1B, w stimat th monthly passngr dmand by first scaling th 10%-sampl quartrly DB1B passngr counts by th minimum α s across th corrsponding squnc of monthly carrir-sgmnts. Bcaus w us th minimum scaling factor across all carrir-sgmnts in th carrir-rout, this approach undrstimats th numbr of on-stop passngrs. W prfr this approach, bcaus othr approachs caus th scald thn aggrgatd carrir-rout dmands to xcd th original carrir-sgmnt dmands (i.., thy allocat too many passngrs on th carrir-sgmnt). To rsolv th undrcounting of on-stop passngrs, w subsquntly apply a uniform scaling to all carrir-rout dmands to nsur that th prcntag of on-stop passngrs is consistnt with DB1B. 3. For ach non-stop carrir-rout rprsntd in DB1B, w calculat th monthly passngr dmand by subtracting th passngr allocatd on all matching carrir-routs basd on th stimatd on-stop dmands in stp 2 from th total carrir-sgmnt dmands providd by T-100 th on-stop dmands stimatd in stp 2 for all carrir-routs that contain th corrsponding carrir-sgmnt. Not that bcaus som on-stop carrir-rout passngrs ar not abl to b allocatd to matching itinraris (.g., du to lack of availabl sats), w wait to calculat th nonstop carrir-rout dmands until th on-stop allocation is complt. This nsurs that, whn aggrgatd by carrir-sgmnt, our stimatd carrir-rout dmands match th original T-100 data st. In th nxt sction, w dscrib th discrt choic allocation modl w us for allocating th monthly carrir-rout passngrs to th gnratd itinraris. 2.3 Discrt Choic Allocation As dscribd in th prvious sction, for ach month and carrir-rout, w stimat passngr dmands and gnrat a st of potntial passngr itinraris. Nxt, w stimat th numbr of passngrs corrsponding to ach itinrary. For ach itinrary choic, i, w assign a passngr utility, u(x i ), basd on faturs of th corrsponding itinrary. Thn, for ach passngr, w randomly slct an itinrary choic from th ons matching th passngr s carrir-rout according to th proportions, P(i), dscribd by th discrt choic multinomial logit function in Equation 2.1. =, itinraris. (Equation 2.1) 8

9 Th utility function, u( ), w us for our discrt choic modl includs paramtrs for th intraction of th local tim of dpartur and day of wk, paramtrs for a picwis linar function of connction tim (to modl th disutility associatd with short and long connction tims), as wll as paramtrs for flight cancllations and sating capacitis. To dscrib th utility function, w first dfin th following notation: day x i = th day of wk for itinrary i with Sunday = 1 and Saturday = 7; tim x i = th local tim of dpartur for itinrary i; connct x i = th connction tim for itinrary i with connct x i = 0 for non-stop itinraris; cancl x i = 1 if any flight in itinrary i was markd as cancld in ASQP, 0 othrwis; sats x i = th minimum sating capacity for th flights in itinrary i; n T = th n th four-hour daily block of dparturs, with T 1 = 1:00 4:59am and T 6 = 9:00pm 12:59am th following day; c m = th m th thrshold for th picwis linar utility for connction tim in minuts with c 0 = 0, c 1 = 45, c 2 = 60, c 3 = ; and I ( ) = th indicator function for th xprssion argumnt. Using this notation, th mathmatical formulation of th itinrary choic utility function is providd in Equation 2.2. In th quation, th scond sum rprsnts th picwis linar utility associatd with connction tims, with ( ) + indicating th positiv part of th innr xprssion, i.. max{0, }. 7 6 day tim ( i ) dn I ( xi = d) I ( xi Tn ) d= 1 n= 1 u x = + 3 m= 1 ( min { xi, cm} m 1) connct connct + cancl cancl sats sats m c + xi + xi. (Equation 2.2) W includ flight cancllations in our modl, bcaus all ls bing qual, a carrir is mor likly to cancl a flight with fwr passngrs than on with mor. This is intuitivly rasonabl bcaus thr is a significant cost associatd with rbooking th disruptd passngrs. Thus, in hindsight, w would xpct fwr passngrs to hav bn schduld to travl on itinraris that includ a cancld flight. This dcision is additionally supportd by th passngr dlay validation w prform in Sction 3.2. Additionally, w includ th minimum sating capacity on th itinrary as a masur of aircraft sizs. Th discrt choic modl rprsntd by Equation 2.2 is stimatd with BIOGEME (Birlair, 2003) using on quartr of th propritary booking data from a singl major carrir xtndd to includ unslctd itinraris from our st of gnratd itinraris. Adding in th unslctd itinraris is 9

10 important to accuratly assss th disutility associatd with vry long connctions. Without ths itinraris it would appar that th vry long connctions ar mor strongly prfrrd, bcaus unslctd altrnativs would not appar in th choic st. Whn xtnding th booking data, w considr only th gnratd itinraris with connction tims of on hour or longr to liminat choic st issus du to airport-spcific minimum connction tims. Additionally, this approach nsurs that th distribution of connction tims in our allocation aligns with th distribution of connction tims in th booking data. Bcaus thr ar oftn hundrds of choics for ach month and carrir-rout, w us sampling of altrnativs to limit th siz of th choic st to 10 altrnativs for ach obsrvation, whr ach passngr in th booking data rprsnts a singl obsrvation. Sampling of altrnativs limits th computational ffort rquird to train th modl whil still nsuring consistnt paramtr stimats. Thr is substantial litratur on sampling of altrnativs ranging from gnral applications (Bn-Akiva & Lrman, 1985) to spcific considrations in a rout choic contxt (Frjingr, Birlair, & Bn-Akiva, 2009). Th stimatd paramtr valus and statistics from this modl ar listd in Tabl A1.1 in Appndix 1. All of th paramtr stimats ar significant at th 0.99 confidnc lvl using a classic Studnt s t-tst, xcpt for 5,3, which is xtrmly clos to zro. Th ovrall modl is also xtrmly significant, with a liklihood-ratio tst valu of highly unlikly to occur undr a χ 2 distribution with 46 dgrs of frdom (corrsponding to a p-valu of lss than ). Additionally, w fl that th paramtr stimats ar subjctivly rasonabl suggsting th highst utility for travl on Sunday, Thursday aftrnoon, and Friday, and th lowst utility for lat night and pr-dawn travl. Using th stimatd paramtrs of this modl, w calculat th utility associatd with ach of th gnratd itinraris and thn, for ach passngr, w sampl a [0, 1] uniform random variabl to slct an itinrary allocation basd on th proportions calculatd using Equation 2.1. Whn a flight bcoms full, w rmov all corrsponding itinraris from th choic st and updat th xpctd proportions for th rmaining itinraris. Bcaus of this stp, th ordr in which carrir-routs ar procssd is an important issu, as carrir-routs procssd first ar mor likly to find sats availabl on all flights. Thus, to maintain th aggrgat conncting prcntag in th allocation, w procss on-stop passngrs bfor non-stop passngrs. Within ach group (i.., on-stop or non-stop), w procss a singl passngr at a tim. Passngrs ar procssd in a random ordr, which rducs ordr-basd biass in th rsults (.g., having no sats availabl for carrir-routs that ar procssd last). To dtrmin th random ordr, w sampl a [0, 1] uniform random variabl to st a priority for ach individual passngr and thn sort th passngrs according to ths prioritis. 10

11 2.4 Validating Passngr Itinrary Flows Unlik T-100, which includs passngrs travlling on both domstic and intrnational itinraris, our on quartr of propritary booking data includs only domstic itinraris. Thus, th aggrgat passngr counts for ach carrir-sgmnt and month ar significantly lowr than th T-100 data on avrag. Dirct validation btwn th allocation dscribd abov and th propritary data would lad to rsults that ar havily biasd by this discrpancy. Instad, w prform a validation allocation whr w scal th DB1B data (as dscribd in Sction 2.2) by th monthly carrir-sgmnt passngr counts from th booking data (instad of T-100). Using this approach, th total numbr of validation passngrs allocatd is approximatly th sam as th numbr of passngrs rprsntd in th booking data. For validation purposs, w ar primarily concrnd with distributional proprtis of our allocation approach. That is, bcaus w hav no way of dtrmining th actual itinrary for ach passngr, w instad focus on nsuring that our allocation is rasonabl in an aggrgat sns. W do so by comparing aggrgat distributions of our validation allocation against th aggrgat distributions of th propritary booking data. Th distributions w considr ar: 1. Distribution of flight load factor, 2. Distribution of daily avrag load factor, 3. Distribution of prcntag of conncting passngrs, and 4. Distribution of connction tim for on-stop passngrs. For ach of ths distributions, w compar our validation allocation to th booking data and to a randomizd allocation (in which w assum all itinrary utilitis, u(x i ), ar qual). Th randomizd allocation allows us to tst th snsitivity of our approach to th individual paramtr valus of our discrt choic modl. In Figur 2.1, w considr th distribution of flight load factor. In th plot, w buckt flights by load factor in incrmnts of 5%, with th prcntag on th x-axis rprsnting th mid-point of th buckt. Th y-axis lists th prcntag of flights falling into ach buckt. With rgards to load factors, th discrt choic allocation prforms similarly to th randomizd allocation. Each of ths approachs undr-stimats th numbr of flights with load factors btwn 0% and 35% and btwn 75% and 95%, and ovr-stimats th numbr of flights with load factors btwn 40% and 70%. W bliv ths discrpancis ar du to th impacts of rvnu managmnt and our inability to modl pric as a dpndnt fatur in our allocation modl. Nonthlss, ach of ths approachs appars to prform quit wll. 11

12 12% 10% Prcntag of Flights 8% 6% 4% 2% 0% Flight Load Factor (Passngrs / Sats) Booking Data Randomizd Allocation Discrt Choic Allocation Figur 2.1: Distribution of flight load factor for booking data, randomizd allocation, and discrt choic allocation. In Figur 2.2, w considr th distribution of daily avrag load factor th fraction of sats filld ach day. As with flight load factors, daily avrag load factors ar groupd into 5% buckts. In this plot, w s a significant improvmnt using th discrt choic modl as compard to a randomizd allocation. Although th discrt choic modl incrass th sprad of avrag daily load factors, th propritary booking data suggsts vn furthr variability. Th propritary booking data w us is from th fourth quartr of 2007, thus w attribut this additional variability to th impact of holiday travl. Bcaus ach holiday impacts travl diffrntly, and bcaus w hav accss to only on quartr of booking data, w do not attmpt to modl th impact of holiday travl dirctly. 12

13 60% 50% Prcntag of Days 40% 30% 20% 10% 0% Avrag Load Factor (Passngrs / Sats) Booking Data Randomizd Allocation Discrt Choic Allocation Figur 2.2: Distribution of daily avrag load factor for booking data, randomizd allocation, and discrt choic allocation. In Figur 2.3, w considr th distribution of conncting passngrs. That is, for ach flight w dtrmin th prcntag of passngrs on th flight who ar on th first or scond lg of a on-stop itinrary. Th flight conncting passngr prcntags ar subsquntly bucktd as with load factors abov. Othr than th 95% to 100% buckt, both th randomizd allocation and th discrt choic allocation match th booking data wll. Th highr prcntag of flights filld with conncting passngrs is most likly du to our dcision to allocat on-stop passngrs prior to non-stop passngrs (as dscribd in Sction 2.3). If w wr to considr a largr buckt from 85% to 100%, all thr data sts corrspond quit wll (5.5% for booking data, 5.4% for randomizd allocation, and 5.4% for discrt choic allocation). 13

14 35% 30% Prcntag of Flights 25% 20% 15% 10% 5% 0% Prcntag of Conncting Passngrs (Conncting / Total) Booking Data Randomizd Allocation Discrt Choic Allocation Figur 2.3: Distribution of conncting passngrs for booking data, randomizd allocation, and discrt choic allocation. In Figur 2.4, w considr th distribution of connction tims for on-stop passngrs. In this plot, w considr only on-stop passngrs, and buckt ths passngrs by th connction tim btwn th two flights. In this plot, w utiliz 10-minut buckts, with ach point on th x-axis spcifying th mid-point of th buckt. Th y-axis lists th prcntag of on-stop passngrs falling into ach buckt. This plot dmonstrats th powr of th discrt choic modling approach. Using this approach w ar abl to vry accuratly match th distribution of connction tims that xists in th propritary booking data. Th randomizd allocation xhibits no prfrnc towards connction tims, so all variation is du to availability of connctions, with connction tims of an hour to an hour and a half bing th most frqunt. 14

15 16% Prcntag of On Stop Passngrs 14% 12% 10% 8% 6% 4% 2% 0% Connction Tim (Minuts) Booking Data Randomizd Allocation Discrt Choic Allocation Figur 2.4: Distribution of connction tims for booking data, randomizd allocation, and discrt choic allocation. In Sction 3.2, w xtnd our validation to th analysis of passngr dlays. In th contxt of stimating passngr dlays, th numbr of passngrs travling on itinraris with flight cancllations is critical du to th immns impact of itinrary disruptions. Our rsults show that th inclusion of flight cancllations in th modl allows us to pick up on an important factor, namly th tndncy of airlins to cancl flights with fwr passngrs, furthr justifying our discrt choic approach. Ovrall, it appars that th discrt choic modl and randomizd allocation both do quit wll according to systm-wid mtrics such as th distribution of load factors and conncting passngrs. On th othr hand, for mor disaggrgat masurs, such as connction tims or daily load factors, th discrt choic modl appars to dominat th randomizd allocation. 3 Analyzing Passngr Dlays In this sction, w turn our focus from stimating passngr travl to th analysis of passngr dlays. First, in Sction 3.1, w dscrib th procdur w us to calculat passngr dlays basd on th stimatd passngr itinrary flows dvlopd in Sction 2. Nxt, w us th stimatd passngr dlays to furthr validat our allocation approach. In Sction 3.3, w highlight a fw ky findings from our passngr dlay analysis, such as how passngr dlays brak down annually, by carrir, by airport, by tim of yar, by day of wk, and by tim of day. Last, in Sction 3.4, w dvlop a linar rgrssion 15

16 modl to stimat passngr dlays dirctly, allowing us to bypass th passngr allocation and dlay calculation procdurs for crtain stimation tasks. 3.1 Passngr Dlay Calculator Th procdur w us for calculating passngr dlays is an xtnsion of th passngr dlay calculator dvlopd by Bratu and Barnhart (2005). In ordr to calculat th passngr dlays associatd with th stimatd passngr itinrary flows, th authors usd th ralizd flight schduls in ASQP, which provid information about flight dlays, flight cancllations and divrsions. Th original passngr dlay calculator was applid to only a singl carrir, and thus assumd a dfault passngr dlay valu for passngrs accommodatd on a diffrnt carrir. For th purpos of our study, involving all of th 20 ASQP-rporting domstic carrirs, w xtnd th algorithm to stimat th dlays for passngrs rbookd on a carrir diffrnt than plannd. Th first stp in passngr dlay calculation is to dtrmin which passngrs hav had thir itinrary disruptd and thrfor nd to b r-accommodatd to thir final dstinations. A non-stop itinrary is disruptd only if th corrsponding flight is cancld or divrtd. A on-stop itinrary is disruptd if on or both of th two flights is cancld or divrtd, or if th first flight is dlayd to such an xtnt that th corrsponding passngrs ar unabl to mak thir connction to th scond flight (w assum this is th cas if th availabl connction tim is lss than 15 minuts). For non-disruptd itinraris and th corrsponding passngrs, th passngr dlay is simply qual to th (non-ngativ) flight dlay associatd with th last flight in th itinrary. Not that for passngrs on non-disruptd on-stop itinraris this mans that dlay on th first lg is absorbd into th plannd connction tim. If an itinrary is disruptd, ach of th passngrs on th itinrary must b r-accommodatd from th point of disruption to th final dstination of th itinrary. W assum that ach of ths passngrs is raccommodatd on th bst availabl altrnativ itinrary, whr bst is dfind as th altrnativ schduld to arriv th arlist. Th passngr dlay for ths passngrs is thn th tim thy rach thir final dstination minus th plannd arrival tim, ignoring ngativ valus. Thus, th primary work of th passngr dlay calculator is th r-accommodation of passngrs whos itinraris hav bn disruptd. Disruptd passngrs ar r-accommodatd in an ordr basd on th itinrary s tim of disruption. For cancld or divrtd flights, w us th plannd dpartur tim as th tim of disruption. For missd connctions, w us th actual arrival tim of th first flight as th tim of disruption. Not that rathr than ignoring th divrsions, w trat thm th sam as cancllations. This is not du to any limitations with th algorithm, but to th fact that th dstination to which th flight is divrtd is not providd in ASQP. Th numbr of flight divrsions is qual to about 10% of th numbr of flight cancllations (or 16

17 about 0.23% of total flights), so w do not xpct th mthod of handling divrsions to impact th final rsults significantly, as long as thy ar not ignord ntirly. Undr this assumption, th point of disruption for cancld or divrtd flights is th origin of th flight, whras for missd connctions, th point of disruption is th plannd conncting airport. On challng in calculating passngr dlays is that th ASQP databas dos not includ all possibl flight options, such as thos of non-rporting carrirs. Thrfor, in ordr to b consrvativ in our stimats, w put a limit on th r-accommodation dlay for ach disruptd passngr basd on th tim of disruption. For passngrs disruptd during daytim hours, btwn 5:00am and 5:00pm, w limit th r-accommodation dlay to 8 hours. For passngr disruptd during vning or pr-dawn hours, btwn 5:00pm and 5:00am, w st th limit to 16 hours to allow for r-accommodation th following day. Thn, in ordr to r-accommodat ach passngr, w chck if thr ar any valid rcovry itinraris amongst th 273,473,424 itinraris gnratd in Sction 2.2. A rcovry itinrary is valid if it dparts from th point of disruption at last 45 minuts aftr th tim of disruption (to allow tim for rbooking and transfr), has availabl sat(s), and is schduld to arriv at th passngr s final dstination in tim to satisfy th r-accommodation dlay limit. W first sarch for itinraris that us airlins matching th original itinrary (.g., th two carrirs on a multi-carrir on-stop itinrary), along with any subcontractd or parnt airlins. For xampl, whn a Continntal itinrary is disruptd, w look for rcovry itinraris on Continntal or ExprssJt (or any combination of th two). If w ar unabl to find a valid itinrary using ths airlins, w attmpt to r-accommodat th passngrs using any valid itinrary across all carrirs. If w ar unabl to find an altrnativ at this point, w assign th passngr a dlay qual to th r-accommodation dlay limit, assuming that h or sh will b r-accommodatd in som othr fashion. For passngrs who ar rcovrd on a nw itinrary, th passngr dlay is calculatd basd on th actual arrival tim of th rcovry itinrary. Not that w allow disruption chaining, that is w allow for th possibility that th rcovry itinrary to which a passngr is assignd may in turn gt disruptd and th passngr may b rquird to b rbookd again. Although w allow such disruption chaining in our passngr dlay calculator, w maintain th r-accommodation dlay limit throughout. Thus, passngrs ar oftn dfaultd to th r-accommodation dlay limit aftr a scond disruption. This nsurs that our disruption chains do not bcom ovrly long, bcaus in many cass airlins hav knowldg of futur disruptions at th tim of r-accommodation (.g., a svr wathr vnt that is projctd to last throughout th day). 3.2 Validating Passngr Dlays In this sction, w validat against thr potntial sourcs of rror in our nd-to-nd approach for stimating passngr dlays. First, w considr th snsitivity of our passngr dlay stimats to th r- 17

18 accommodation dlay limits dscribd in th prvious sction. Scond, w validat our passngr dlay stimats against thos stimatd from th propritary bookings data. Th purpos of this validation is to nsur that thr ar not important factors missing from our discrt choic allocation. Last, w masur th impact of our discrt choic sampling variation on our aggrgat passngr dlay stimats to nsur that a singl allocation is sufficint for our subsqunt analyss. That is, w want to nsur that at th lvls of aggrgation w ar intrstd in, th varianc btwn sampls is low. As dscribd in th prvious sction, ach tim a passngr is disruptd, th passngr dlay calculator attmpts to r-accommodat th passngr on an altrnativ itinrary for which th plannd arrival tim satisfis th r-accommodation dlay limit. Bcaus ths limits hav bn introducd with th intnt to b consrvativ in our stimats, th rsults ar snsitiv to th limits chosn. In Tabl 3.1, w compar dlay stimats for 2007 utilizing diffrnt r-accommodation dlay limits for daytim (5:00am to 5:00pm) and vning (5:00pm to 5:00am) disruptions. In ach column of th tabl, w list th corrsponding daytim and vning dlay limits sparatd by a /, so 8 hour / 16 hour would rfr to th limits dscribd in Sction 3.2. Evn whn ths limits ar incrasd to 24 hours for both daytim and vning disruptions, w ar still unabl to find altrnativ itinraris for just ovr 8% of th disruptd passngrs, bcaus thr ar ithr no flights or no sats availabl. This xplains why th choic of raccommodation dlay limit has such a significant impact on th stimatd dlay for disruptd passngrs. 6 hour / 12 hour Dlay Limits 8 hour / 16 hour Dlay Limits 12 hour / 24 hour Dlay Limits 24 hour / 24 hour Dlay Limits Avrag Passngr Dlay (min) Avrag Disruptd Passngr Dlay (min) Avrag Daytim Disruptd Passngr Dlay (min) Avrag Evning Disruptd Passngr Dlay (min) % of Passngrs Disruptd 3.3% 3.3% 3.3% 3.3% % of Disruptd Passngrs Rciving Dfault Dlay 33.5% 20.7% 15.5% 8.0% Tabl 3.1: Comparison of dlay stimats using diffrnt daytim / vning dlay limits in th passngr dlay calculator. Of th daytim / vning limit combinations that w tstd, w chos to us th 8 hour / 16 hour dlay limits as th basis for rporting our rsults for th following rasons. First, th 8 hour daytim limit nsurs that passngrs who ar both schduld to arriv and subsquntly disruptd btwn th hours of 5:00am and 5:00pm ar rschduld (ithr on an altrnativ or by dfault) to rach thir dstination 18

19 bfor th following morning. This would not hold if th daytim dlay limit wr largr than 12 hours. Th 16 hour vning limit nsurs that, for passngrs who ar disruptd during th vning, th passngr dlay calculator will considr at last a fw hours worth of rbooking altrnativs th following morning. This would not hold for vning limits of 12 hours or lss. Last, basd on th fact that 20% of th disruptd passngrs ar not r-accommodatd within th systm, w fl that ths ar sufficintly consrvativ valus. Nxt, in ordr to furthr validat our allocation approach, w considr our stimatd passngr dlays alongsid thos stimatd from th propritary booking data. Bcaus th propritary booking data dos not contain information on passngr r-accommodations, w cannot compar our passngr dlay stimats dirctly to actual dlays. Instad, w first stimat th passngr dlays associatd with th propritary bookings data by applying th passngr dlay calculation procdur from th prvious sction. Th intnt of this validation is to nsur that any itinrary-lvl diffrncs in passngr counts ar washd out by th aggrgat passngr dlay calculations. Thus, in Tabl 3.2, w compar th passngr dlay rsults basd on our stimatd passngr flows to thos basd on propritary booking data for on major carrir for th 4 th quartr of For ach of ths two data sts, w list th numbr of passngrs impactd by ach typ of disruption (or lack throf) as wll as th total numbr of hours of dlay accumulatd. For th cas of disruption chaining, w catgoriz disruptd passngrs and thir dlays basd on th caus of th first itinrary disruption (i.., cancllation / divrsion or missd connction). By construction, as dscribd in Sction 2.4, th total numbr of passngrs is vry clos (within 0.4%), but for all othr catgoris, th rror rangs from 2.0% to 4.4%, which w bliv to b quit good. On intrsting rsult is that our stimatd passngr dlays appar to b consistntly biasd high across all catgoris. This suggsts that airlins do (slightly) mor to mitigat passngr dlays than w ar abl to pick up in our allocation approach. For xampl, much lik with cancllations, airlins may choos to push dlays to flights with fwr passngrs. Passngr Counts Dlays (Hours) Caus Booking Data Estimatd Flows Prcntag Diffrnc Booking Data Estimatd Flows Prcntag Diffrnc Flight Dlays Flight Cancllations Missd Connctions 7,113,553 7,141, % 1,968,253 2,007, % 114, , % 933, , % 80,439 77, % 558, , % 19

20 Total 7,308,646 7,337, % 3,460,460 3,553, % Tabl 3.2: Passngr dlays by caus Last, bcaus th passngr itinrary allocation mthodology is basd on a probabilistic allocation, th stimatd passngr flows and hnc th calculatd passngr dlays ar not dtrministic but rathr ar subjct to sampling rrors. For instanc, th validation rsults prsntd in Tabl 3.2 ar for a singl allocation. Thus, it is critical that w also idntify th xtnt of rrors du to sampling. To do this, w prform two allocations using th ntir yar s worth of data and calculat th passngr dlays associatd with ach of ths allocations. To dtrmin th sampling rror, w aggrgat th passngr dlays on a daily, monthly, and annual basis. From ths aggrgatd dlays, w calculat a prcntag rror qual to th absolut valu of th diffrnc dividd by th smallr of th two. In Tabl 3.3, w summariz ths rrors by prsnting th minimum, maximum, avrag and mdian prcntag rror for ach aggrgation lvl. Not that for th annual dlays, thr is just on aggrgatd dlay valu for ach sampl, as opposd to 365 for daily and 12 for monthly. Th tabl dmonstrats that th sampling rrors ar vry low, vn whn calculatd on a daily basis. Morovr, as w would xpct, th rang of sampling rrors dcrass significantly as th lvl of aggrgation incrass. This suggsts that sampling rror is not a significant sourc of concrn, spcially for th lvls of aggrgation w considr in th following sction (.g., annual, by carrir, or by month). Aggrgation Lvl Minimum Maximum Avrag Mdian Daily % % % % Monthly % % % % Annual % % % % Tabl 3.3: Summary of sampling rror in passngr dlay stimats 3.3 Passngr Dlay Rsults In this sction, w first summariz th rsults of our passngr dlay calculations. Nxt, using th rsults of our allocation and dlay calculation procss, w discuss svral ky findings from our analysis. Ths findings srv two purposs: 1) to furthr th undrstanding of th complx prformanc charactristics of th National Air Transportation Systm, and 2) to dmonstrat th bradth of analytical possibilitis basd on th mthodologis w hav dvlopd. In Tabl 3.4, w prsnt various charactristics of our passngr dlay stimats by carrir (and in aggrgat) for calndar yar Th 20 carrirs listd ar thos that ar rprsntd in th ASQP data st. Each passngr is idntifid basd on th carrir oprating th first flight in th itinrary. Passngrs travling on multi-carrir itinraris account for approximatly 8.9% of all passngrs allocatd. As on 20

21 might xpct, th avrag dlay for non-disruptd passngrs is typically quit clos to th avrag flight dlay. Howvr, including disruptd passngrs, an avrag passngr xprincs approximatly twic as much dlay as an avrag flight, du to th impact of flight cancllations and missd connctions. W stimat that flight cancllations ar rsponsibl for approximatly 30% of passngr dlays, whras missd connctions account for approximatly 18%. Carrir Pinnacl Airlins (9E) Amrican Airlins (AA) Aloha Airlins (AQ) Alaska Airlins (AS) JtBlu Airways (B6) Continntal Airlins (CO) Dlta Airlins (DL) Atlantic Southast Airlins (EV) Frontir Airlins (F9) AirTran Airways (FL) Hawaiian Airlins (HA) Amrican Eagl Airlins (MQ) Northwst Airlins (NW) Comair (OH) Flights Avg Flight Dlay (min) Passngrs Avg Passngr Dlay (min) Prcnt of Total Dlay du to Cancllations Prcnt of Total Dlay du to Missd Connctions Avg Disruptd Passngr Dlay (min) 258, ,563, % 26.76% , ,548, % 16.39% , ,727, % 6.06% , ,600, % 7.87% , ,019, % 6.76% , ,566, % 15.17% , ,150, % 22.40% , ,108, % 37.62% , ,780, % 20.36% , ,522, % 20.57% , ,860, % 13.26% , ,393, % 20.14% , ,507, % 23.00% , ,934, % 19.53%

22 Carrir Skywst Airlins (OO) Unitd Airlins (UA) US Airways (US) Flights Avg Flight Dlay (min) Passngrs Avg Passngr Dlay (min) Prcnt of Total Dlay du to Cancllations Prcnt of Total Dlay du to Missd Connctions Avg Disruptd Passngr Dlay (min) 597, ,542, % 26.58% , ,245, % 20.18% , ,894, % 18.55% Southwst Airlins (WN) Exprssjt Airlins (XE) Msa Airlins (YV) 1,168, ,579, % 10.11% , ,531, % 17.58% , ,457, % 21.67% Total 7,455, ,532, % 18.36% Tabl 3.4: 2007 passngr dlays by carrir Using th aggrgatd rsults in Tabl 3.4 combind with th disaggrgatd rsults drivd from our approach, w highlight nin ky findings rgarding th brakdown and causs of passngr dlays. In ach cas, w bgin by stating th finding, and thn providing furthr dtails, including any dfinitions or assumptions, as wll as furthr discussion of th rsult. Ky Finding #1: Th ratio of avrag passngr dlay to avrag flight dlay is maximum for rgional carrirs and minimum for low-cost carrirs, owing primarily to th cancllation rats and th conncting passngr prcntags. As abov, a passngr is idntifid basd on th carrir oprating th first flight in th itinrary. W catgoriz Amrican Airlins (AA), Continntal Airlins (CO), Dlta Airlins (DL), Northwst Airlins (NW), Unitd Airlins (UA), and US Airways (US) as th lgacy ntwork carrirs; JtBlu Airways (B6), Frontir Airlins (F9), AirTran Airways (FL), and Southwst Airlins (WN) as th low cost carrirs; and Pinnacl Airlins (9E), Atlantic Southast Airlins (EV), Amrican Eagl Airlins (MQ), Comair (OH), Skywst Airlins (OO), Exprssjt Airlins (XE), and Msa Airlins (YV) as th rgional carrirs. Across all carrirs in 2007, th ratio of avrag passngr dlay to avrag flight dlay is For individual carrirs, it rangs btwn 1.49 for Southwst Airlins (WN) and 2.99 for Pinnacl Airlins (9E). For th lgacy ntwork carrirs, this ratio rangs from 1.65 to 2.23, with an avrag valu of

23 For rgional carrirs, it rangs from 2.27 to 2.99 with an avrag valu of Last, for low cost carrirs, it rangs from 1.49 to 1.89 with an avrag valu of Th rasons for such disparity bcom clar whn w look at th cancllation prcntags and th prcntags of conncting passngrs. In th yar 2007, th ovrall prcntag of cancld flights was 2.4% and th prcntag of conncting passngrs was 27.2%. Th rgional carrirs had both th gratst prcntag of cancllations (3.4%) as wll as th gratst prcntag of conncting passngrs (39.6%). Low-cost carrirs had th lowst prcntag of cancllations (1.2%) and th lowst fraction of conncting passngrs (17.0%). Lgacy ntwork carrirs fll btwn ths two xtrms, both for th prcntag of cancllations (2.2%) and th prcntag of conncting passngrs (31.0%). As w show latr in Sction 3.4, th prcntag of cancld flights and th prcntag of conncting passngrs ar highly corrlatd with th ratio of avrag passngr dlay to avrag flight dlay. Ky Finding #2: Passngrs schduld to transfr in on of 6 airports: Nwark (EWR), Chicago O Har (ORD), Nw York La Guardia (LGA), Washington Dulls (IAD), Nw York Knndy (JFK) or Philadlphia (PHL), wr xposd to th longst avrag conncting passngr dlays. For ach of ths airports, ovr 10% of schduld conncting passngrs had thir itinraris disruptd. Ths 6 airports wr also among th worst airports with rspct to both avrag dlays for dparting flights and dpartur canclations. W rstrict this analysis to only th conncting passngrs and considr data from th top 50 transfr airports in th U.S. Ths airports account for narly 98.7% of all domstic conncting passngrs in th U.S. On avrag, 12.2% of th passngrs schduld to connct through th 6 airports listd had thir itinraris disruptd compard to just 6.9% at th rmaining 44 airports. Ths airports wr th worst transfr airports in trms of avrag conncting passngr dlay. Across ths 6 airports, th avrag dlay pr conncting passngr of 78.5 minuts was 32.9 minuts mor than that at th rmaining 44 airports (45.6 minuts). Ths 6 airports ar among th 9 worst transfr airports in trms of dpartur canclation rats and th 7 worst transfr airports in trms of avrag dlays for dparting flights. Th worst transfr airports basd on dpartur canclation rats also includs Ragan (DCA), Boston (BOS), and Dallas / Fort Worth (DFW). DFW is also on th list of transfr airports with th worst avrag dlays for dparting flights, rounding out that list. Ky Finding #3: Domstic passngr connctions ar highly concntratd at th top thr transfr airports: Atlanta (ATL), Chicago O Har (ORD), and Dallas / Fort Worth (DFW), rprsnting approximatly 43.2% of plannd passngr connctions. As such, ATL, ORD, and DFW ar rsponsibl 23