Flight elays Capacity Investent and Welae unde Ai Tanspot Syste Equilibiu by Bo Zou A dissetation subitted in patial satisaction o the equieent o the degee o octo o hilosophy in Engineeing Civil and Envionental Engineeing in the Gaduate ivision o the Univesity o Calionia Bekeley Coittee in chage: oesso Mak Hansen Chai oesso Sae Madanat oesso Jaes oell Sping
Abstact Flight elays Capacity Investent and Welae unde Ai Tanspot Syste Equilibiu by Bo Zou octo o hilosophy in Engineeing Civil and Envionental Engineeing Univesity o Calionia Bekeley oesso Mak Hansen Chai Inastuctue capacity investent has been taditionally vieed as an ipotant eans to itigate congestion and delay in the ai tanspotation syste. Given the huge aount o cost involved justiying the beneit etuns is o citical ipotance hen aking investent decisions. This dissetation poposes an equilibiu-based beneit assessent aeok o aviation inastuctue capacity investent. This aeok takes into consideation the inteplays aong key syste coponents including light delay passenge deand light taic ailine cost and aiae and thei esponses to inastuctue capacity investent. We explicitly account o the ipact o sevice quantity changes on beneit assessent. Geate sevice quantity is associated ith to positive eedback eects: the so-called Mohing eect and econoies o link/segent density. On the othe hand geate sevice quantity esults in diseconoies o density at nodes/aipots because highe taic density at the aipot leads to geate aipot delays. The capacity-constained syste equilibiu is deived o those copeting oces. To appoaches ae developed to investigate ai tanspot syste equilibiu and its shit in esponse to inastuctue capacity expansion. In Chapte e ist vie the syste equilibiu o the ailine copetition pespective. We odel ailines' gaing behavio o aiae and equency in duopoly akets assuing that ailines have the knoledge o individuals' utility stuctue hile aking decisions and that delay negatively aects individuals' utility and inceases ailine opeating cost. The theoetical ailine copetition odel developed in Chapte povides analytical insights into the inteactions aong vaious syste coponents. Unde a syetic Nash equilibiu e ind that the pesence o light delay inceases passenge genealized cost and discouages ai tavel. Ailines ould not pass delay cost entiely onto passenges though highe ae but also account o the ipact o sevice degadation on passenge illingness-to-pay and consequently passenge deand. To avoid exobitant light delays ailines ould use lage aicat eanhile taking advantage o econoies o aicat size. The esulting unit cost eduction patially osets opeating delay cost incease. The equilibiu shit tiggeed by capacity expansion educes both schedule delay and light delay leading to loe passenge genealized cost and highe deand despite slightly inceased aiae.
Ailines ill eceive lage poit and consue elae ill incease as a esult o the expansion. Although delay eduction is less than expected because o induced deand the oveall beneit hich encopasses eduction in both schedule delay and light delay ould be uch geate than estiated o a puely delay-based standpoint. The equilibiu analysis can be altenatively appoached o a tavele-centic pespective. The peise o an ai tanspot use (i.e. tavele equilibiu is that each tavele in the ai tanspotation syste axiizes his/he utility hen aking tavel decisions. The utility depends upon aket supply and peoance chaacteistics consisting o aiae light equency and light delay. The extent o ailine copetition is iplicitly elected in the deteination o aiae and light equency. Given the liited epiical evidence o the delay eect on ai tanspotation syste supply to econoetic odels o aiae and light equency ae estiated in Chapte 3. We ind positive delay eect on ae hich should be intepeted as the net eect o ailines' tendency to pass delay cost to passenges hile also copensating o sevice quality degadation. Highe delay discouages caies o scheduling oe lights on a segent. Both delay eects hoeve ae elatively sall. The estiated ae and equency odels togethe ith passenge deand and aipot delay odels pesented in Chapte 4 ae integated to oulate the ai tanspot use equilibiu as ixed point and vaiational inequality pobles. We pove that the equilibiu existence is guaanteed; heeas equilibiu uniqueness cannot be guaanteed. We apply the use equilibiu to a ully connected hypothetical netok ith the co-existence o diect and connecting ai sevices. Using a siple heuistic algoith e ind that the equilibiu is insensitive to initial deand values suggesting that thee ay be a single equilibiu o this paticula odel instance. Hub capacity investent attacts spoke-spoke passenges o non-stop outes and geneates ne deand on hub-elated outes. At the aket level hub capacity expansion ould esult in geate total deand and consequently passenge beneits in alost all akets except o ones hee a pedoinant potion o passenges choose non-stop outes due to exteely high cicuity o one-stop tavel. In the latte set o akets ate capacity expansion passenge deand and beneits ould be both educed. This counte-intuitive esult caies ipotant iplications that capacity incease does not necessaily beneit eveyone in the syste. Siila to the indings o the ailine copetition odel ith changes in light delay schedule delay aiae and total deand the use equilibiu odel yields uch highe passenge beneits o capacity investent than the conventional ethod; heeas hub delay saving is oset by taic divesion and induced deand. With continuous capacity investent the ai tanspotation netok ill itness substantial changes in sevice supply and taic pattens.
edicated to y paents Xiong ing and Zou Huaqiao i
Table o Contents Table o Contents... ii List o Tables... iv List o Figues... v Acknoledgeents... vi. Intoduction.... Backgound and oble Stateent.... Cuent actices Existing Studies and Reseach Faeok....3 Reseach Methods and Oganization o the issetation... 6. An Analytical Ailine Copetition Equilibiu Model... 8. Intoduction... 8. Model setup... 8.. eand... 8.. Supply.....3 Copetition and equilibiu....3 Copaative static analysis... 3.3. Ipact on ai ae passenge genealized cost and deand... 3.3. Ipact on aicat size and unit opeating cost... 5.3.3 Changes in consue elae... 5.4 Nueical analysis... 7.4. Equilibiu shit hen congestion occus... 9.4. Sensitivity o equilibiu to dieent capacities... 9.4.3 Beneit assessent using equilibiu and conventional ethods... 3.5 Suay... 6 3. Epiical Investigation o Flight elay Ipact on Ai Tanspotation Supply... 8 3. Intoduction... 8 3. Liteatue evie and contibution o the eseach... 9 3.. Fae... 9 3.. Fequency... 3 3.3 Eects o delay on ae... 3 3.3. Epiical odel speciication... 3 ii
3.3. ata... 35 3.3.3 Estiation esults and discussion... 37 3.4 elay ipact on light equency... 4 3.4. Epiical odel speciication... 4 3.4. ata... 44 3.4.3 Estiation esults and discussion... 45 3.5 Suay... 48 4. Use Equilibiu Model... 5 4. Intoduction... 5 4. Equilibiu oulation... 5 4.. Equilibiu coponent... 5 4.. Equilibiu oulation... 55 4..3 ieences beteen ATUE and UTSUE... 64 4.3 Solution algoith... 65 4.4 Model application... 66 4.4. Netok setup... 66 4.4. Initial equilibiu... 68 4.4.3 Equilibiu shit in esponse to capacity expansion... 74 4.4.4 assenge beneits o the expansion... 76 4.4.5 Sensitivity analysis o capacity investent... 8 4.5 Suay... 83 5. Conclusions and Futue Reseach... 85 5. Conclusions... 85 5. Copaison o the to equilibiu appoaches... 86 5.3 Futhe eseach ecoendations... 88 Reeences... 9 Appendix A: A oo o (.5 based on Epiical ata... 99 Appendix B: Coespondence beteen MAS and Metopolitan Aeas... Appendix C: Investigation o the Jacobian Matix F(X... Appendix : Estiation Results o the Reduced Fo Fequency Model... 7 iii
List o Tables Table. eived paaete values.... 8 Table. Copaison o scenaios ith and ithout capacity constaint.... 9 Table 3. einition o ae odel vaiables.... 3 Table 3. esciptive statistics o vaiables in the non-stop ae odel (N=67443.... 36 Table 3.3 esciptive statistics o vaiables in the one-stop ae odel (N=68. 36 Table 3.4 Estiation esults o the non-stop oute ae odel.... 39 Table 3.5 Estiation esults o the one-stop oute ae odel.... 39 Table 3.6 einition o equency odel vaiables.... 43 Table 3.7 esciptive statistics o vaiables in the equency odel (N=6533.... 45 Table 3.8 Estiation esults o the equency odel.... 46 Table 4. Main estiation esults o the 3NL odel.... 5 Table 4. esciption o vaiables in the aipot delay odel.... 53 Table 4.3 Estiation esults o the aipot delay odel.... 54 Table 4.4 aily AAR's and nube o connections in ou analysis and eal old hub aipots (based on 7 aveage daily values.... 68 Table 4.5 Initial equilibiu values in spoke-hub akets... 69 Table 4.6 Supply-deand chaacteistics o selected segents.... 7 Table 4.7 Supply-deand chaacteistics o selected akets.... 73 Table 4.8 Aipot delay changes.... 73 Table 4.9 opotion o connecting passenges at soe ajo US hub aipots (aveaged value beteen 4 and 8.... 73 Table 4. Changes in spoke-hub akets and segents... 75 Table 4. Syste-ide tavele beneit gains ($illion/quate.... 79 Table 4. Incoe population and light taic goth copaed to the base yea.... 8 Table 4.3 Hub delay and delay saving estiates unde the conventional and equilibiu appoaches... 8 iv
List o Figues Figue.: Tavele genealized cost as a unction o syste deand... 4 Figue.: Equilibiu aeok... 5 Figue.: eand as a unction o genealized cost o ailine... 6 Figue.: eand as a unction o genealized cost o ailine... 7 Figue.3: elay and volue/capacity atio vs. aipot capacity... Figue.4: eand and aket equency vs. aipot capacity... Figue.5: Aicat size and unit opeating cost vs. aipot capacity... Figue.6: Ai ae and genealized cost vs. aipot capacity... Figue.7: Welae gain unde dieent baseline capacity levels o a ixed capacity inceent... 3 Figue.8: Welae gain using conventional and equilibiu ethods (in pesent values... 5 Figue.9: elay savings and deand ate capacity incease using conventional and equilibiu ethods... 6 Figue 3.: Non-stop aiae as a unction o delay at the destination aipot at 5th 5th and 75th pecentiles o oute O- distance (4 78 6 iles... 4 Figue 3.: One-stop aiae as a unction o delay at the destination aipot at 5th 5th and 75th pecentiles o non-stop O- distance (77 73 868 iles... 4 Figue 3.3: Segent equency as a unction o delay at the destination aipot at 5th 5th and 75th pecentiles o segent distance (45 693 8 iles... 48 Figue 4.: Nesting stuctue o the 3NL odel... 5 Figue 4.: Netok topology and cicuity o one-stop outes... 66 Figue 4.3: istibution o (Q [k] Q [] /Q []... 69 Figue 4.4: assenge deand in spoke-spoke akets... 69 Figue 4.5: Yield and ae in spoke-spoke akets... 7 Figue 4.6: Flight equency and nube o passenges pe light in spoke-spoke akets... 7 Figue 4.7: Route- (let and aket- (ight speciic deand change in spoke-spoke akets... 74 Figue 4.8: Fae and yield change in spoke-spoke akets... 74 Figue 4.9: Changes in equency and nube o passenges pe light in spoke-spoke akets... 75 Figue 4.: Aveage consue suplus change pe ai tavel decision aking in spokespoke akets... 78 Figue 4.: assenge beneit estiates (in $illion/quate unde the to appoaches... 8 Figue 4.: Sensitivity o passenge beneit estiates to baseline capacity and capacity inceent (in $illion/quate... 8 Figue 4.3: assenge deand in spoke-spoke outes ith ininite hub capacity... 8 v
Acknoledgeents Coing to Bekeley is one o the ost ipotant landaks in y lie. I eel vey blessed ith the help and copany o any people because o ho y acadeic pusuit and pesonal adventue have been a tuly eniching and eading expeience. The coplete list o people to ho y thanks should be deliveed ay equie a e exta pages. Hee I ould like to convey y special gatitude to soe o the. Fist and oeost I a deeply indebted to oesso Mak Hansen ho has been y adviso eve since I began y gaduate studies at Cal. I as attacted to Bekeley lagely by an ealie seies o his papes but have only elt oe otunate to have the chance to take y h jouney unde his supevision. I eel iensely gateul to hi o leading e to the old o tanspotation econoics exposing e to a vaiety o eseach topics and alays standing ith e to cope ith diicult situations and shae joyul oents in his unique jocula anne. I a totally ipessed by the idth and depth o his knoledge and insights about tanspotation his citical thinking ceativity and inspiation in identiying and shaping eseach pobles. This is not to ention a copehensive inteactive ive-yea long elective couse on the philosophies o eseach huo and lie that I have taken ith hi inside and beyond McLaughlin 7. Mak no atte hethe I get an A o B+ upon gaduation you special couse has aleady been caved into y unogettable Cal eoy. The inluence o you special class is deeed poound and ill peeate though the est o y acadeic lie. Much alike one o the ipotant indings in y dissetation any conventional vie o such inluence ould only lead to substantial undeestiation o its value. I ould like to thank the othe to ebes in y dissetation coittee oessos Sae Madanat and Jaes oell. Sae is not only an excellent teache but a thoughtul eseach ento. His Inastuctue Systes Manageent couse is one o y all-tie avoite classes. Thank you Sae o encouaging e to deepen y eseach and oeing e valuable suggestions on caee developent. Special thanks to oesso Jaes oell o his Econoetic class o hich I have beneited geatly in building y ethodological oundation o conducting epiical eseach. I a also gateul to hi o being alays consideate. My gatitude uthe extends to othe aculty ebes ithin and outside o Bekeley. My eseach ideas ee shaped by seveal consevations ith oesso Adib Kanaani in the ealy stage o y h study. The advice o oesso Calos aganzo is vey helpul in claiying soe ethodological issues. I eel vey otunate to have oked ith Joan Walke as a gaduate student instucto o he CE 93 class. I alays enjoyed chatting ith he and appeciate he enthusiastic suppot in the latte pat o y h study. I ould also like to thank oesso Kenneth Tain o his excellent ECON 44 class and the enlightening discussion on the discete choice odel issues I encounteed in y dissetation. I eel otunate to have knon oesso Michael Ball. Collaboation vi
ith hi has eally been a pleasant expeience. oessos Nicole Adle Jan Bueckne avid Gillen and Yaeng Yin all oeed e vey helpul suggestions and insights in vaious pats o y eseach. My dissetation ould not have been in the cuent o ithout the beneicial discussions ith the. And cetainly I eel otunate to be pat o the Bekeley NEXTOR eseach tea. Thanks to Jing Xiong o taking good cae o e especially duing y ealy days in Albany. Jing hile you HONA Civic ay no longe exist in the old I still vividly eebe the ee ides hoe you oeed e ate the end o any oking days hich saved e tons o coute tie o taking the 5L bus hich had pseudo-ando opeations duing the evening peak. My h eseach stated ith collaboation ith Megan Ryeson. Thank you Megan o you nueous helps acadeically and beyond thoughout y h. Those days oking togethe ae tuly pat o y ondeul Cal eoies. I a vey gateul to Ay Ki o the shaing o he expeiences and o he consideation and encouageent even ate she let Bekeley. Ay thank you o being alays on y side. I ould also like to thank Yoonjin Yoon o kindly oeing e helpul advice as a then senio ello student and no aculty ebe. It has been such a pleasue to have Gukaan Buxi and Tasos Nikoleis as dea iends and labates ith ho I had any inteesting discussions in oice and outside the Noth Gate. I deeply appeciate y iendship ith ebes in the "younge" geneation o the NEXTOR tea: Michael Seelhost Yi Liu Lu Hao Elaine Kan Iene Kan and Matthe Elke. The tie spent ith you has only ade y NEXTOR expeience iche and to a ulle extent. Sincee thanks go uthe to NEXTOR pedecessos Wenbin Wei Avijit Mukhejee and Chieh- Yu Hsiao o shaing ith e thei acadeic expetise and insights. I ould like to expess y appeciation to y othe Bekeley ello tanspotation students and aluni in paticula Kenneth Kuhn Edad Huang Weihua Gu Yiguang Xuan Kathik Sivakuaan and Jeey Lidicke. Thanks ae also due to e Saoop o his a accoodation evey tie I visited the Univesity o Mayland. I teasue the iendship ith Nguyen Tuong and Zhen Sun that e stated o ou vey ist seeste at Bekeley. Ou unscheduled eals and outdoo activities ceated lots o intedisciplinay intellectual talks and divesion in each o ou h lives. I ould additionally like to thank Zhen Qian o alays being thee anseing y questions. Zhen thank you o goading e into uthe investigation o tanspotation netoks. I a gateul to Noine Shia and Helen Bassha in the ITS oice o being vey helpul ith nueous logistical issues and to Shelly Okioto in the CEE ain oice o patiently helping gaduate students in vaious aspects. He invaiable a sile akes the day sunnie heneve I get out o he oice. My h eseach as unded by the Univesity o Calionia Tanspotation Cente the Fedeal Aviation Adinistation the NASA Aes Reseach Cente and the Intenational Council on Clean Tanspotation. Financial suppot o the above agencies is geatly appeciated. Additional thanks ae due to Joseph ost avid Chin Thea Gaha Michael Wells Banava Sidha Neil Chen Hok Ng and Mazya Zeinali o the constuctive discussions about y eseach. vii
Thank you Mo and ad o you poound love and etenal encouageent. Without the any yeas that you unconditionally spent aising educating and suppoting e nothing ould have been possible. I hope this dissetation can be dedicated to you as both a git and copensation o being aay o you ove the yeas. Last but not least it is so lucky to have et y best iend Buyun Chen. Thank you Buyun o co-piloting ou plane ith you love suppot it and kindness. It is also because o you that I have gained a consideable aount o isthand expeience and oe thoough undestanding o the US ai tanspotation syste. viii
. Intoduction. Backgound and oble Stateent Flight delay is a seious and idespead poble in the United States. Beteen and 7 light taic inceased by about % but the nube o late-aiving lights oe than doubled. One in evey ou lights as delayed o oe than 5 inutes in 7 in the National Aispace Syste (NAS (BTS. The total econoic ipact o light delays accuing to passenges ailines and the eaining o the econoic syste aounted to $3 billion in 7 (Ball et al.. Although taic and delay have declined soehat ove the past e yeas due to the econoic ecession the Fedeal Aviation Adinistation (FAA expects deand goth to esue ith total Revenue assenge Miles (RMs oecast to incease at an aveage annual ate o 3.% o 84.6 billion in to.57 tillion in 3 (FAA a. This ill ipose unpecedented challenges on opeational punctuality in the utue NAS. A ajo cause o light delay is deand-capacity ibalance in the ai tanspotation syste paticulaly in the aipot teinal aea. At any ajo US aipots ai taic is oten scheduled close (soeties even above the axiu aiield capacity. Capacity constaints can esult o pesistent shotalls in physical aviation inastuctue such as unays o as the esult o a capacity dop unde incleent eathe conditions. The ibalance beteen deand and capacity iplies that the light delay poble can be appoached o the pespective o eithe deand o capacity. Classic deand-side solutions include intoducing congestion ees and liiting the nube o slots at congested aipots. The othe solution is to add oe capacity to the existing aviation inastuctue eithe though deploying ne technologies o building ne physical inastuctue. In the US the ajo poga o technology deployent is FAA's $6 billion-dolla Next Geneation Ai Tanspotation Syste (NextGen (GAO hich ais to tanso the NAS o a gound-based into a satellite-based syste though the deployent o seven ajo technology eleents (FAA b. hysical inastuctue ipoveent ees to the econstuction and extension o unays hich ay involve concuent taxiay and aispace econiguation. Accoding to FAA (7a ou ajo aipots in the US cuently need oe capacity. The nube ill go to oe than to dozen by 5. Beteen and 5 the epoted investent needs o aipot capacity expansion aounts to $9 billion (Hansen. In ode to estiate the etun on this investent appopiate beneit assessent ethodologies ae o citical ipotance. This eseach poposes a novel equilibiu-based aeok to assess beneits o aviation inastuctue capacity investent. ieent o the conventional appoach hich oten ocuses exclusively on light delay eduction ou ok takes a oe holistic vie o aviation syste esponse to capacity investent. We ecognize delay as one o
the seveal integal coponents in the ai tanspot supply-deand equilibiu and that capacity investent tigges uthe inteactions aong syste coponents leading to an equilibiu shit. Syste equilibiu equilibiu shit and the associated beneits ae odeled o both ailine copetition and use behavio pespectives. Ou eseach ills an ipotant gap in the liteatue and can lead to ipoveents o the cuent beneit assessent ethodologies o aviation capacity investent.. Cuent actices Existing Studies and Reseach Faeok While conventional aviation capacity investent analysis ae conducted at the aipot level (FAA 999 ove the yeas the ability to assess the econoic value o aviation inastuctue investent has becoe inceasingly sophisticated. Consideable stides have been ade in NAS-ide siulation tools such as NASAC ACES and LMINET to incopoate light tajectoies eathe en-oute and aipot capacity constaints to peo capacity investent analysis at the syste level (ost 6; ost et al. 8. On the othe hand the easueent o beneits is still lagely delay based ith delay eduction beneits taking the o o passenge tavel tie and ailine cost savings (e.g. Steinbach and Giles 5. The undelying assuption is that the only changes aising o a capacity investent that need to be consideed ae the incease in capacity and consequent eduction in delay. Vey liited attention has been paid to the echaniss though hich ailines and ai taveles espond to light delay eduction. This delaycentic appoach soeties causes pobles. In pactice delays pedicted by the siulation odels can appea too high to be ealistic. To cope ith this analysts esot to ad hoc eedies such as soothing the light schedule o siply tuncating delay estiates. Thus despite the added capability to siulate opeations the lack o copehensive undestanding o the syste esponse ay lead to a biased and incoplete epesentation o the investent beneits. Ai tanspot syste esponse to capacity investent has been consideed oe in the acadeic aena but ith the ajoity o the studies conducted at the aipot level. Thee is a long tadition in theoetical studies to odel passenge deand as a unction o eithe delay alone (Moison and Winston 983 o one pat o the passenge genealized cost (Moison and Winston 989 7; Ou et al. 4; els and Vehoe 4; Zhang and Zhang 6. But the systeic ipacts o light delay ipact cetainly extend beyond that. Joge and de Rus (4 highlight the inclusion o delay savings o both existing and diveted passenge taic in aipot investent beneit analysis. With delays aicat have to spend oe tie eithe on the gound o in the ai inceasing ailine opeating expenses. The ipact o delay on ailine cost has been epiically tested and quantiied in Hansen et al. ( and Zou and Hansen (. at o these delayinduced expenses ill be passed onto passenges though highe ae hich in tun leads to loe deand as odeled in Mille and Clake (8. Hoeve theoetical and epiical knoledge about the extent o delay cost passage is still lacking. As a esult odeling o the pecentage o delay cost tanse in Mille and Clake (8 has to ely on siulation techniques.
In addition to deand and ae esponses an ipotant piece that has not been adequately captued in aviation capacity investent analysis is sevice quality. The aviation syste like uban tansit systes oes scheduled tanspotation sevices. Flight delay is cetainly one diension in the sevice quality. Anothe is the quantity o sevices povided hich has been extensively studied in the uban tansit context (e.g. Mayo et al. 98; Fankena 983; Else 985. In ai tanspotation eseach etics o syste-ide sevice quantity include Available Seat Miles (ASM Available lane Miles (AM and Revenue assenge Miles (RM; at the oe disaggegate light segent level sevice quantity is easued in light equency. Flight equency deteines passenge schedule delay (anza 979; Abahas 983; Hansen 99; Ghobial and Kanaani 995 hich easues the dieence beteen a passenge's peeed depatue tie and the neaest light depatue tie and is theeoe pat o an individual's total tip tie. Most studies assue that light taic is invaiably popotional to passenge deand beoe and ate investent ith only a e exceptions. Joge and de Rus (4 ague that ne capacity ould enable incease in depatue equency and encouage the use o salle aicat. Hansen and Wei (6 peo an epiical investigation on the ipact o a ajo capacity expansion at allas- Fot Woth aipot. They ind that the delay eduction beneit ay be patially oset by light deand induceent and ailine schedule adaptations. Nonetheless neithe o the gives explicit calculation o passenge schedule delay change. Associated ith light equency adjustent is a eedback loop beteen equency and passenge deand ist ound and coonly knon in public tansit as the Mohing eect (Mohing 97 hich ees to the act that equency incease educes schedule delay and taveles' genealized cost. As a consequence oe deand ill be geneated leading to an even highe equency. This positive eedback eect has been genealized to othe scheduled tanspotation sevices including ai tanspot (Hansen 995; els and Vehoe. Hoeve only liited attention to this eect has been paid in aviation inastuctue investent eseach (Matin and Socoo 7. The Mohing eect becoes even oe ipotant in hub-and-spoke ai tanspot netoks hee equency incease on a hub-spoke segent ill beneit passenges on any outes that shae the sae segent. The esulting deand incease on these any outes then leads to highe segent passenge taic and uthe equency incease. The enhanceent o Mohing eect in hub-and-spoke netoks has been aely ecognized in the liteatue. ehaps equally ipotant to the Mohing eect is econoies o density anothe intinsic eatue that has not been ully consideed in the aviation inastuctue investent analysis. Econoies o density ees to ailines' declining aveage cost o dense taic ithin a given netok. The existence o the econoies o density has been epiically identiied at both ailine (Cave et al. 984; Gillen et al. 985 99 and oute (Bueckne and Spille 994; Bueckne et al. levels. As pointed out above aviation inastuctue investent educes delay and invites oe taic. This esults in educed ailine aveage cost. Loe unit cost allos ailines to oe passenge less expensive aes. As a esult oe passenges ill be induced. Like the Mohing eect the econoies o density induces positive eedback loop. 3
While educed light delay and schedule delay ipove the quality o the ai sevice poduct plausibly esulting in highe aiae it is ou belie that the oveall eect o light delay eduction schedule delay decease and the econoies o density is loe tavele genealized cost. We illustate this in Figue. hee taveles genealized cost easued in $/ile is plotted against total deand in the syste quantiied as passenge-iles. With no congestion the tavele supply cuve ill be a donad slopping cuve S because o the Mohing eect and the econoies o density intesecting ith the deand cuve at point G. When congestion occus the ne constained tavele supply cuve S ill tack the unconstained one S until delay appeas in the syste ate hich S stats to vee upads intesecting the deand cuve at point B. The pupose o investing in inastuctue capacity is to shit the point at hich this deviation occus to the ight and hence donad such that the ne constained tavele supply cuve ill intesect ith the deand cuves at point C. Inastuctue investent then leads to a eduction in tavele genealized cost and highe syste deand denoted espectively by the distance A and CE. The aea ABC epesents passenge elae gains o the investent. Hoeve because poit change involves changes in passenge deand aiae light equency and unit opeating cost it is diicult to discen gaphically ailines' (poduces' suplus. Tavele genealized cost ($/ile eand S S : Unconstained supply (congestion ee S : Constained supply (beoe investent S : Constained supply (ate investent S A B F E C G S eand (passenge-iles Figue.: Tavele genealized cost as a unction o syste deand To explicate the vaious causal elationships entioned above e popose the olloing equilibiu-based aeok to odel syste esponse to aviation inastuctue investent as shon in Figue.. We conside light delay passenge deand aiae light taic and ailine cost as ive endogenous syste coponents. An equilibiu is chaacteized by a set o consistent values o the syste coponents. We hypothesize that once inastuctue investent is ade inceased capacity leads to loe light 4
delay hich induces oe taveles to use the ai tanspotation syste encouages ailines to schedule oe lights and educes ailine unit opeating cost. With unit cost eduction ailines ill ake necessay ae adjustent in thei poit axiization pocess hich also depends upon the aket stuctue. Ne aiae and light taic aect tavele genealized cost and theeoe passenge deand. Othe deandinluencing actos including socio-econoic chaacteistics copetition o othe odes can be easonably egaded as exogenous to syste esponses. Change in deand in tun aects aiae again though ailines' poit axiization and the aount o light taic. Like aiae the deteination o light taic depends uthe upon the aket stuctue. Ne light taic suggests a ne level o light delay in the syste. The changes in light taic and delay ente ailines' poduction pocess in hich input pices ae assued exogenous esulting in an updated ailine cost. It is clea that once capacity investent is ade it ill tigge a coplicated set o inteactions aong the syste coponents the inal outcoe o hich is chaacteized by an equilibiu shit. We use a dashed line to epesent the potential eedback o delay to investent decisions in that the esponse o capacity investent is on a uch longe tie scale than those o the boxed syste coponents. Fo this eason investent decisions ae assued exogenous in the dissetation. Investent Socio-econoic chaacteistics Modal copetition Inastuctue Capacity assenge eand Maket stuctue Flight Taic Flight elay Ai Fae Maket stuctue Maxiizing oit Ailine Cost oduction output Input pices Figue.: Equilibiu aeok 5
.3 Reseach Methods and Oganization o the issetation Based upon the dual elationship beteen supply and deand e can odel the ai tanspot syste equilibiu o to copleentay pespectives. On the one hand the syste equilibiu is the esult o ailines' poit axiization. Ailines seek thei best picing and scheduling stategies taking into account the eaction o passenge deand hich is deteined by the utility stuctue o taveles. In paticula e assue that ailines in axiizing poit explicitly ecognize the delay ipact on passenge utility stuctue as ell as thei on opeating cost. Since it is likely that ultiple ailines copete in an ai tanspotation syste the achieveent o the equilibiu ill involve gaing behavio. Folloing this logic in the ist appoach an analytical odel ill be developed to study the ai tanspot equilibiu o the ailine copetition pespective. While aipot capacity constaints have been consideed in soe ecent ailine gaetheoetic odeling (e.g. Evans ; Li et al. ; Vaze and Banhat ou ailine copetition odel deals ith siultaneous pice and equency copetition speciically in the context o capacity investent. The analytical natue o ou odel also povides soe useul theoetical insights into the inteplays aong the syste coponents. Altenatively the equilibiu poble can be vieed o taveles' vantage point. It is easonable to assue that evey tavele ties to axiize he/his utility hen aking tavel decisions ith ull knoledge about the aket supply (i.e. ae and equency and peoance (i.e. light delay chaacteistics hich change ith the passenge deand patten. An equilibiu is achieved hen no tavele can ipove he/his utility by unilateally changing the deand choice. This chaacteizes the use equilibiu condition. In the second appoach e exaine the ai tanspot use equilibiu ith syste coponents all based upon epiical odels. We ill deonstate that the ai tanspot use equilibiu cobines eatues o both classic supply-deand equilibiu and deand-peoance equilibiu the latte o hich idely applied to the uban taic context. To ou knoledge it is the ist tie to intoduce use equilibiu in the ai tanspot context. We ill sho that ou key indings o both appoaches ae lagely consistent. The eainde o this dissetation is oganized as ollos. In Chapte e ist pesent the oulation o an analytical ailine copetition equilibiu odel. Copaative static and nueical analyses o equilibiu shit in esponse to capacity change ae then discussed. We estiate the associated beneit gains and copae the ith those o the conventional appoach. The discussions then sitch to the odeling o ai tanspot use equilibiu. In Chapte 3 e peo an epiical investigation o the delay ipact on aiae and light equency the to ost ipotant supply-side chaacteistics. Chapte 4 then poceeds to the ull investigation o the ai tanspotation use equilibiu. Equilibiu coponents the oulation o the equilibiu and solution algoith ae discussed in ode. We apply the use equilibiu concept to a hypothetical ai tanspot netok in hich siila to Chapte e exaine the initial equilibiu and equilibiu shit and copae beneit gains o the equilibiu appoach ith 6
estiates using the conventional ethod. We oe conclusions and point out diections o utue eseach in Chapte 5. 7
. An Analytical Ailine Copetition Equilibiu Model. Intoduction In this chapte e ist apply the eseach aeok poposed in Section. to an ailine copetition odel to exploe the capacity-elated ai tanspot supply-deand equilibiu and ho the equilibiu shits in esponse to capacity expansion. We assue that ailines deteine thei ae and equency in a copetitive envionent taking into account individuals' utility stuctue. Flight delay aects both tavel utility o individuals and opeating cost o ailines. espite the existence o a lage body o theoetical liteatue analyzing the econoics o ailine copetition behavio so a elative e eots have been devoted to ailine behavio vis-à-vis inastuctue capacity constaints and investent. The olloing analytical odel intends to povide soe helpul insights into the inteplays aong passenge deand ai ae ailine cost light taic and delay o a icoscopic ailine copetitive point o vie.. Model setup.. eand We conside a duopoly city-pai ailine aket a special case o oligopolistic akets. To caies ae engaged in pice and equency copetition. Folloing ost theoetical and applied liteatue o this kind (e.g. Schippe et al. 3; Bueckne and Givin 8; Bueckne and Zhang e estict ou attention to the syetic equilibiu i.e. the to ailines ae identical to peseve analytical tactability. As peviously discussed taveles conside both ae and sevice quality hen aking tavel decisions. In the absence o capacity constaints the piay sevice quality diension is schedule delay deined as the dieence beteen a tavele s desied depatue tie and the closest scheduled depatue tie o all lights. Although individual passenges ae concened about thei speciic depatue tie it is easonable to use equency to captue the oveall schedule delay eect hen aket deand is concened. Epiical studies oten use the invese o equency (Eiksen 978; Abahas 983 hich is intuitive i e conside a situation hee light depatues and passenge deand ae unioly distibuted along a tie cicle o length T. Then the expected schedule delay equals T/4 ith light equency being (lights. The schedule delay cost is the expected schedule delay ultiplied by soe cost paaete. This kind o teatent is adopted by any siila studies (e.g. Richad 3; Bueckne and Floes-Fillol 7; Bueckne and Givin 8. 8
In the absence o taic delay a epesentative consue ill ace to genealized costs (pices coesponding to the sevices povided by to ailines: i i o i=. We i assue the epesentative consue has the olloing utility unction: U( q q q q ( q q ( q qq q (. hee q epesents the nueaie good. ae positive paaetes. The concavity condition equies. The epesentative consue axiizes U q q subject to the olloing incoe (budget constaint: ( q q q q I (. hee I denotes incoe. The ist-ode conditions o the coesponding Lagangian L U q q q ( q q q ith being the Lagange ultiplie ae ( I L q L q q q (.3. (.3. L q q q (.3.3 L ( q q q I (.3.4 The second-ode conditions ae guaanteed since the Hessian is negative sei-deinite given the concavity o the utility unction. Substituting (.3. into (.3. and (.3.3 yields the olloing syste o linea invese deand unctions: i q i q i i (.4 hee the subscipt i denotes the copeting ailine. Incopoating the genealized cost expession and solving (.4 o i= lead to the olloing syetic deand unction q i i i i (.5 i i The aket-level ailine deand unctions Q i (i= ae obtained by aggegating q i s ove all consues 9
Q i i i i (.6 i i hee n n n ith n being the nube o consues in the aket. Obviously suggesting that the sevices povided by the to ailines ae ipeect substitutes. The above deand unction pesents a geneal caie-level deand unctional o hich dies o a ecent pape studying aipot congestion by Floes- Fill ( hee a ixed total deand is assued. Fo one pespective the assuption o ixed total deand is a nice popety o analytical tactability since the ocus o thei study is on congestion. On the othe hand unde ou deand setup an incease in ticket pice o ailine ill divet soe passenges to ailine. Ou speciication uthe allos soe passenges ho ould have chosen ailine i pice ee not inceased to not tavel by eithe ailine they ay choose altenative odes o not taveling at all. Likeise i ailine inceases its equency then it can not only da passenges o i but also geneate additional deand. In eect this aket-level deand esponse pesents anothe ipotant phenoenon caused by congestion. When congestion eeges due to liited capacity passenges ill sue diectly o light delay because they value the exta tip tie. This adds a ne coponent into the genealized cost. We assue the congestion cost to passenges is identical acoss passenges egadless o hich ailine as chosen. We use the aveage light delay L and ultiply it by a cost acto k to epesent the contibution o delay to passenge genealized cost. Folloing the sae deivations as above the ne deand unction can be itten as Q i i i L i (.7 i i hee k n ( k ( is the coeicient indicating the unit ipact o delay on deand. evious studies odel L at the aipot level and to be a unction o total taic volue and capacity (e.g. Moison and Winston 8; Zhang. As one city pai is consideed hee e assue L to be a unction o the lage o the taic volue/capacity atios o the to aipots in the city pai. The aipot ith the lage atio is deined as the ocal aipot. In the subsequent analysis e assue the aival end o the city pai pesents the ocal aipot hich is the teinus o N identical akets and is the only aipot ith a signiicant capacity liitation. We uthe assue that the decision-aking o each aket is independent. Then the total taic volue o aiving lights at the ocal aipot is N( +. The taic volue/capacity atio is N( + /K Since at an aipot depatue and aival taic volues ae alost equivalent it ould suice to only conside the aival taic volue in odeling aipot delay. In eect Moison and Winston (8 ind that no signiicant dieence ould esult o consideing total light opeations and depatues/aivals sepaately. Fo othe aipot delay studies the piay concen is oten light aival delays (e.g. Hansen ; Hansen et al.. Theeoe in this study e ocus on the aival taic volue at the ocal aipot and the te taic volue in the est o the chapte ees speciically to taic volue o aivals.
ith K denoting the aival capacity at the ocal aipot. Given a ixed capacity and the nube o akets L is siply a unction o + i.e. L L... Supply ( We ollo Bueckne and Floes-Fillol (7 by assuing that an ailine opeates aicat ith size s and a load acto o (in act o the latte all e equie is a constant load acto. A light s opeating cost is given by c s hee c is a positive ixed cost independent o aicat size and the aginal cost pe seat. This speciication elects in pat the econoies o density on the supply side as cost pe passenge is deceasing ith aicat size. Fo ailine i (i= light equency ( i aicat size (s i and deand (Q i ae elated by the equation Qi i si. Additional expenses ill be geneated hen light delay occus as it is associated ith oe uel bun additional ce cost etc. These ae incopoated in a thid te in the light opeating cost: C i c s s L (.8 i i hee is a cost acto associated ith a unit tie o delay pe seat. The delay cost pe light is assued to be a unction o aicat size (s i and the length o delay (L. Given L a lage plane equies oe exta uel consuption and highe ce cost than a salle one...3 Copetition and equilibiu In this duopoly aket ailines copete on ae and equency to axiize poits. The poit unction o each ailine is: Q i i C ( ( L( i i i i i i i i i L L i i i i c i ( c i s o i i s L i (.9 epending on the assuptions ade the copetition beteen the to ailines can ollo dieent gae odels. We conside the case that light equency and ae can be adjusted siultaneously in a Nash ashion. The easoning ests on the act that typically ailines adjust schedules evey 3 onth (Radas and Willias 8 and taveles ay also puchase tickets onths in advance. The ist ode conditions (FOC o ailine ae: Fo caies pespective the econoies o density includes ou aspects: the use o lage and oe eicient aicat highe load actos oe intensive use o ixed gound acilities and oe eicient aicat utilization (Bueckne and Spille 994. In this chapte as load acto is assued to be econoies o density on the supply side ae piaily ebodied in the ist aspect.
( ( L L (.. ( ( ( L L c L L (.. Note that L Q. The act that ailines should ake a positive poit iplies ( L. Since L inceases ith equency /( ( L Q L c L accoding to (.. and (... Fo the delay unction L e uthe expect aginal delay incease is geate hen taic is at a highe level i.e. L.Then the second-ode deivatives (.. ( ( ( ( 3 L L L L L L (.. ae easily seen to be negative. The eaining o the second-ode condition (i.e. negative deinitiveness o the Hessian atix o is assued to hold. 3 The ist and second ode optiality conditions also apply to ailine. The FOCs ae obtained by intechanging subscipts and in (.. and (... Given the syety set-up unde equilibiu = = = =. Replacing ae and equency by and in the FOC o the ae equation (. e have ( ( L L (. Substituting the above into the FOC equency equation (.. yields 3 In ou case this equieent educes to ( L L. These nd ode conditions ae alays satisied in the olloing nueical analyses.
( ( c ( L ( ( L L [ ( ] L ( (.3 In ode to discen potential equency changes hen delay occus Equation (.3 needs to be sipliied. The last te on the ight hand side (RHS o (.3 is positive as. So is the second-to-last te on the RHS since substituting (. into this te yields ( ( L( L hich is geate than zeo olloing the FOC discussion. Then the RHS o (.3 is positive. Note that all tes except c on the RHS ae due to the pesence o congestion. Fo siplicity e denote the by. The RHS then becoes c +. The let hand side (LHS is only a unction o. The incease on the RHS due to congestion leads to an equivalent incease on the LHS though changing the value o. To study the onotonicity o the LHS e deine a ne ( unction F [ ( ]/. Taking its ist ode deivative ith espect to e obtain F { 3( [ ( ]}/ 4 (.4 Ou a pioi expectation is that ailines tend to schedule ee lights hen delay occus. This suggests that F be onotonically deceasing o F hich is equivalent to: ( [ ( ] 3 (.5 Epiical evidence suggests that it is plausible o (.5 to hold. Moe details ae povided in appendix A. Theeoe F / and the LHS o (.3 is a onotonic deceasing unction. When taic delay occus the RHS o (.3 is inceased by. ~ Consequently the equilibiu equency should adjust donads. Let and denote ~ the optial equency ith and ithout delay. We have. This act ill seve as the stating point to deive a set o othe esults in the ensuing copaative static analysis section..3 Copaative static analysis.3. Ipact on ai ae passenge genealized cost and deand The piay objective o this section is to uthe ou qualitative insight into the ipact o capacity constaint on ai tanspotation sevice by copaing the equilibiu values 3
ith and ithout congestion. When congestion occus accoding to (. ai ae ill espond in to dieent ays: educed equency (epesented by ( /[ ( ] and light delay (epesented by L /( degade the sevice quality and theeoe educe the illingness-to-pay (out o thei pocket o taveles. Theeoe the ne equilibiu ae tends to be loe. On the othe hand congestion iposes L on ailine opeating cost o each passenge caied. The te L /( in (. shos that ailines ould pass /( potion o thei delay-induced opeating cost to passenges. This te also iplies that hen the substitution eect beteen the to ailines is stonge (that is as ailines tend to pass a lage potion o thei delay cost to passenges. In noal cases the potion should be geate than ½ since. Oveall the to opposing tendencies o pice esponse blu the changes in ticket pice. The changes in ae ill be exploed nueically in the next section. Recall that the genealized cost to each passenge consists o ai ae equency and taic delay. The deand can be itten as a unction o a single genealized cost. At equilibiu deand o each caie is Q i L ( [ ] ( i (.6 Recall in section 3. that the contibution o delay to each passenge s genealized cost is kl and is deined as k (. Substituting (. into above the genealized cost unde equilibiu becoes ( L L (.7 ( ( ( When thee is no delay genealized cost equals ~ ~ ( (.8 Copaing (.7 ith (.8 to delay-elated tes ae added in (.7 hen congestion occus: L ( and L ( (. The ist te coesponds to the aoeentioned delay cost tanse o caies; the second te denotes the passenge delay cost hich is the net o diect passenge delay cost ( L ( and the pice dop due to delay ( L ( descibed beoe. Consideing uthe that ~ ~ it is easy to sho i.e. genealized cost ill incease. 4
5 A diect consequence o passenge genealized cost incease is suppessed deand o each ailine and in the aket. Altenatively ailine deand can be expessed as only a unction o equency by substituting (. o into the deand unction (.6 ] ( [ ] ( ( [ i L Q i (.9 When thee is no delay the coesponding i Q ~ equals ] ~ ( ( [ ~ i Q i (. Given ~ and the additional delay eect te ( L ] ( [ ( in (.9 deand o each ailine becoes less hen delay occus i.e. ~ i Q Q i i..3. Ipact on aicat size and unit opeating cost Although aicat size is not consideed as a decision vaiable in ou odel context it is iplicitly deteined by passenge deand and the nube o lights scheduled. Since light load acto is assued to be the aicat size is obtained by dividing (.9 by : ] ( [ ] ( ( [ L s (. Fo the ist te on the RHS both the denoinato and nueato becoe salle hen taic delay is consideed. Nonetheless it is plausible o the ist ode deivative to be negative. 4 This just conis that deand is inelastic ith espect to equency. Hoeve the second te pesents an opposite eect the eect o delay on suppessing deand. Theeoe the changing diection o aicat size is inconclusive. The change in the unit opeating cost L s c is also let indeteinate as a consequence..3.3 Changes in consue elae The incease in passenges genealized cost and the eduction in deand that esult o delay ae shon in Figues. and. o ailines and espectively hee the abscissa and odinate denote ailine passenge deand and genealized cost. Because deand o one ailine also depends upon the genealized cost o the othe ailine both 4 / ]} ( [ {( }/ ]/ ( ( {[. Focusing on the nueato as e have ] ( [ ( ] ( [ ( Q / (. Since in geneal is less than the RHS o the above is negative. Theeoe it is plausible that the ist te on the RHS o (8 is a deceasing unction o.
deand cuves ove outad hen delay takes place. The oveall outcoes ae equilibiu shits o B to A and o F to E o ailines and. To easue changes in consue elae the classical tool is consue suplus. Since the utility unction is speciied as quasi-linea consue suplus is also an exact easue o consue elae (Vaian 99. When delay occus CS loss aises o incease in both ailines genealized cost. espite the any potential paths ealizing this genealized q cost change the act that q guaantees the calculation o CS to be path p p independent (Mishan 977; Tunovsky 98. Hee e choose the olloing to-step path as indicated in Figues. and.. In the ist step e incease the genealized cost ~ o ailine o to ith the genealized cost o ailine being povisionally ~ unchanged. The coesponding CS loss is the aea B in Figue.. As a diect esult o the ise in ailine s genealized cost the deand cuve o ailine no oves outad o to. Folloing the adjustent in the second step the genealized ~ cost o ailine ises o to ith the uthe loss o CS given by the aea ~ EH in Figue.. Concuent ith this is the hoizontal ove o ailine s deand cuve o to A (Figue.. The total CS loss is calculated by adding ~ ~ togethe the to aeas: B and EH in hich loss o oegone deand consists o to tiangula aeas: BJ and EHG. I this is consideed as an inastuctue investent poble ith educed delay ate capacity enhanceent then the su o ~ ~ B and EH is the oveall CS gain and the aeas BJ plus EHG epesent ~ the CS gain o induced deand. Given the syety setup the su o B and ~ ~ ~ EH is equal to tice the aea o the tapezoid AB (o tapezoid EF and the to tiangles BJ and EHG ae o equal size. A ~ J C B Q ~ Q Q Figue.: eand as a unction o genealized cost o ailine 6
E ~ G F H ~ Q Q Q Figue.: eand as a unction o genealized cost o ailine The elae changes on the supply side eains analytically indeteinate due to the opposing eects o delay on ticket pice aicat size and light opeating cost. The ensuing section extends the copaative static analysis by nueically exploing the esponse o both deand and supply sides unde a nube o capacity scenaios..4 Nueical analysis To gain uthe insights into the supply-deand equilibiu especially those eleents that ae let indeteinate in the peceding copaative static analysis this section peos a set o nueical analyses. The diection and to soe extent agnitude as ell o the delay eects on the vaious eleents in the equilibiu ae exained. We ist look at ho the congestion-ee equilibiu ill shit hen aipot capacity constaint appeas. We also investigate the sensitivity o the equilibiu to dieent capacity levels including changes in both the supply-deand chaacteistics and elae. Futheoe since the equilibiu appoach is not incopoated in the cuent pactice o investent analysis the dieences in beneit assessent o using the conventional and equilibiu ethods ae copaed hich shos that the equilibiu ethod yields oe ealistic and plausible estiates. In conducting nueical analyses the ist step is to deteine the paaete values o the odel. Many paaete values ae based on liteatue; soe assuptions ae ade hen epiical nubes ae not available. In this section e conside a aket o oughly passenges pe day in each diection ith daily lights seving the aket. Theeoe each ailine schedules appoxiately 5 lights pe day. One-ay ae is set to be $. In light o the estiated elasticity values in liteatue (Ou et al. 993; Joge-Caldeón 997; Gillen et al. ; Hsiao 8 pice elasticities ae set to be -.5 and -.5 at aket and ailine level espectively. The aket equency elasticities 7