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Education & Research Education & Research

Volume 2 Number 1 JAAER Fall 1991 Article 5

Fall 1991

Competition for Hub Dominance: Some Implications to Airline Competition for Hub Dominance: Some Implications to Airline

Profitability and Enplanement Share Profitability and Enplanement Share

Atef Ghobrial

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COMPETITION FOR HUB DOMINANCE: SOME IMPLICATIONS TOAIRLINE PROFITABILITY AND ENPLANEMENT SHARE

Atef Ghobrial

ABSTRACT

The phenomenon ofairline competition for hub dominance in terms of frequency concentrationhas been on the rise since deregulation. Using cross-sectional time-series data, this studyexplores the impact of hub dominance on airline profitability and enplanement share at the hubairport. The regression analysis finds a significant positive relationship between airline profitabilityand hub dominance. The relationship between an airline's share ofpassenger enplanements andits hub dominance seems to follow an S-curve indicating that high frequency shares areassociated with even higher enplanement shares, and conversely.

INTRODUCTIONDeregulation has led to

radical changes in airlinenetwork planning. A main focalpoint for these changes hasbeen the greatly increasedemphasis on Ihubbing.I Allcarriers have sought to build uptheir previous hubs, and in manycases have created new ones.

The hubbing phenomenonhas been the subject of manystudies. Kanafani and Ghobrial(1982) studied the relationshipbetween the economies ofaircraft size and airline hubbing.In 1985, they expanded theiranalysis to assess the impact ofairline hubbing on airportcongestion and its implicationsto airport economics. Kanafaniand Hansen (1985) showed that,when all other variables (such asstage length, aircraft capacity,network size, etc.) are controlledairlines with strong hubbed routesystems incur roughly the samecost to provide a given amountof transportation as those withless hubbed systems. Ghobrialand Sousa (1987) investigatedsome airline strategies todominate their main connectinghubs.

Toh and Higgins (1985)attempted to test whether there

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exists a positive and strongrelationship between airlinehubbing and profitability. Theydeveloped two indices for airlinehubbing and profitability for 17airlines in 1982. The regressionof the hub index on the profit­ability index showed a very poorfit and the independent variable(hub index) seemed to be statis­tically insignificant. Toh andHiggins (1985) also commentedthat profitability is notguaranteed by hub netwrokcentrality, which is contrary topopular belief.

This paper is an attempt toextend the work of Toh andHiggins to explore further theimpact of hub dominance onairline profitability and itspassenger enplanement share.The findings of Toh and Higginstogether with the results of thisstudy will help shed some lighton the commonly held belief thathubbing leads to moresuccessful and profitableoperations (see Aviation Weekand Space Technology,November 1981). The paperbegins by discussing thephenomenon of airline hubbingand hub dominance. This isfollowed by exploring therelationship between profitability

and hub dominance usingregression analysis. The secondphase of this paper assesses theimpact of hub dominance onairline share of passengerenplanements at the hub air­port. The paper concludes withsome implications to airlinenetwork planning, congestion atmajor hubs, and the publicpolicy towards airline mergers.

TRENDS IN AIRLINENETWORK CENTRALITYAND HUB DOMINANCE

A comparison of airlinenetworks of today with those ofthe mid 1970s amplydemonstrates that hubbing hasincreased. The now familiarpattern of multiple linksemanating from a handful of hubairports has replaced theseeming hodge-podge thatcharacterized many routesystems under regulation.

One indication of a hubbednetwork is the concentration ofoperations at a few airportswhich serve as transfer points forconnecting traffic. Measures ofconcentration of an airline'soperations can therefore serveas measures of the degree ofhubbing of that airline's routenetwork. One such a measure isthe one-airport concentration

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Hub Dominance

Table 1Operational Statistics for Selected Airlines In 1980

Airline Main Hubbing hub airline profithub index * dominance ranking at index **

index * main hub %

AA ORO 0.146 26.80 2 -3.50AL PIT 0.189 63.04 1 9.47BN DFW 0.321 37.82 1 -5.70CO DEN 0.252 26.30 3 -5.28DL ATL 0.224 46.40 1 5.42EA ATL 0.208 41.19 2 0.47FL DEN 0.225 34.14 1 7.49NW MSP 0.156 41.09 1 2.12OZ STL 0.205 32.36 2 -0.34PA MIA 0.141 21.99 2 -8.97PI ROA 0.081 99.50 1 6.62RC ORO 0.066 15.39 3 1.53TW STL 0.140 41.94 1 -1.85UA ORO 0.164 43.61 1 -1.55WA LAX 0.170 25.07 2 -3.62

* Estimated using data from IAirport Activity Statistics of Certificated Route Air Carrier-, U.S. Department ofTransportation, The Federal Aviation Administration, 1980.

** Estimated using data from lAir Carriers Financial Statisticsl , Civil Aeronautics Board and the U.S. Departmentof Transportation, 11980

ratio which is defined as the ratioof the airline's departures fromits main hub to the total aircraftdepartures from all airportswithin the airline's domesticsystem. This ratio will be referredto as the hubbing index. For acomplete hub-and-spokenetwork structure (i.e.; all spokecities are connected only to thehub airport) the number ofaircraft operations (i.e.; take-offsand landings) at the hub airportis equal to the number of aircraftoperations at all other airports.The hubbing index is, therefore,equal to 0.5 for a completehub-and-spoke networkstructure. The trend of thehubbing index for some selectedairlines' distributions ofscheduled departures for the

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years 1976, 1978, 1980, 1982,1984 and 1986 was estimated.

For the purpose of illustration,Table 1 depicts this trend for theselected airlines in 1980. Overall,the time-series data suggest anupward trend in the hubbingindex. The few instances ofdownward movement are likelydue to large scale networkexpansions, which naturally tendto reduce concentration.

A parallel phenomenon toairline hubbing is hubdominance. While hubbingmeasures network centralitywithin the airline's system, hubdominance measures airlineconcentration relative to otherairlines operating at the samehub. An airline's dominanceindex at a particular hub could

be estimated as the share of thatairline's departures of the totalaircraft departures by all airlinesfrom that hub. This index canalso serve as a proxy for hubmonopoly. The hub dominanceindex was calculated for all air­lines under investigation at theirmain connecting hub over theperiod 1976-1984. Only domesticoperations were considered forairlines offering both domesticand international services suchas Pan Am, TWA, Northwest, etc.Table 1 reports the hubdominance index (in percent­ages) for the airlines under in1980. Also depicted in Table 1 isthe airline's ranking at its mainconnecting hub in terms of thenumber of aircraft departures.An analysis of the time-series

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data of airline ranking at majorhubs over 1976-1984 indicatesthat airlines have exploited theopportunities of free entry andexit of deregulation andattempted to dominate the hubswhich they use as funnel andtransfer points for theirpassengers.

Hub dominance appears to behighly instrumental inestablishing a strong regionalidentification among passengerswhich is important for marketingthe airline. Examples are Delta atAtlanta, American at Dallas/FortWorth, TWA at St. Louis, andContinental at Houston. Inaddition, a dominant airline at aparticular hub can reap themonopoly profits in the markets

Equation 1

served by that hub. Since themonopolist can alter the supplyof flights and set the price (i.e.;airfare), monopoly profits in thiscase are usually larger thanthose attained· under highlycompetitive conditions.

HUB DOMINANCE ANDAIRLINE PROFITABILITY

The analysis of airlineprofitability is a complex one thatinvolves a. number of factorsincluding network structure, hubdominance, fleet type andaverage aircraft size, stagelength, average yield, routemonopoly, load factor, degree ofunionization, and managementskills. For the purpose of thisstudy, we will attempt to test thehypothesis that there exists a

positive and strong relationshipbetween airline profitability andhub dominance. The profitabilityindex is estimated by dividingoperating income (i.e., operatingrevenue-operating expense) bythe operating revenue andmultiplying it by 100 to beexpressed in percentage terms.A profitability index is calculatedfor all the airlines under consid­eration. Table 1 shows theestimated profitability index forthese airlines in 1980.The Model

The relationship between airlineprofitability and hub dominanceis expressed as a linearregression model which takesthe following form:

PROFF u+PDOMr+tFIRMI+8(Y7~+

~(Y8~+4>(Y8~+3(Y84) +a(Y86)+e (1)

Where PROFi is the profitabilityindex in percentage terms ofairline i, DOMi is its hubdominance index in percentagepoints at the main hub, andFIRMi is a firm-specific variablewhich takes on the value one forairline i and zero otherwise withPan Am (PA) as the controlcarrier. Y78, Yao, Y82, Y84 andY86 in Equation 1 are dummyvariables for the year with 1976as the control year (e.g.; Y80takes on the value one forobservations in 1980 and zerootherwise.) CI, 8, ~, 9, II, ., ~,

and a are the coefficients to beestimated and e is the errorterm. Note that the inclusion of afirm-specific variable FIRM in the

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model is intended to capture theeffects of other variablesinfluencing the carrier's profit­ability. This is useful whenanalyzing cross sectional data.

The model in Equation 1 wasestimated twice (i.e.; with andwithout the firm-specific variableFIRM) using the cross sectional,time series data over 1976-84.The results of estimating bothmodels along with t-statistics areshown in Table 2. For thepurpose of simplicity andcomparison, the variable FIRM isreplaced by its correspondingairline code in Table 2. Note thatthe Durbin-Watson value inTable 2 indicates that the hypo­thesis that there exists no first

order serial correlation cannot berejected. No correction was,therefore, preformed on theresults obtained.Analysis

The coefficient B in both modelestimations is positive andstatistically significant at the 0.05level. The hypothesis that thereexists a positive and strongassociation between profitabilityand hub dominance cannot,therefore, be rejected. The valueof coefficient B in the secondmodel estimation indicates that aone percent increase in anairline's hub dominance indexwill likely be associated with anincrease of 0.178 percentagepoints in its profitability index.

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The results suggest that adominant airline at a particularhub reaps the monopoly profitsby charging higher fares.

The inclusion of the firm­specific variable increased theregression fit as the value of the

multiple correlation coefficient(R2) improved from 0.326 to0.543. The yearly dummyvariables suggest increasinglosses between 1980 and 1982,with 1984 marking a period offinancial recovery for the

Hub Dominance

industry. This pattern seems toaccord with the trends in fuelprices as well as the intensecompetition among airlines in thefirst few years of deregulationwhich may have led to destruct­ive airfare competition.

Table 2:Results of Model Estimating Equation 1

MODEL 1 MODEL 2VARIABLEI Estimated T- Estimated T-COEFFICIENT Value Statistics Value Statistics

CONSTANT -1.535 -0.60 -11.239 -3.23DOM 0.205 4.74 0.178 2.58Y78 -3.041 -1.04 -2.865 -1.06Y80 -6.529 -2.28 -7.631 -2.79Y82 -10.964 -3.86 -11.324 -2.70Y84 -6.953 -2.36 -6.899 -2.39Y86 -6.713 -2.22 -8.247 -2.86AA 12.658 3.02AL 11.882 2.34BN 10.468 2.03CO 14.351 3.43DL 14.422 3.35EA 12.435 2.85FL 10.662 2.66NW 12.888 2.91OZ 13.662 3.04PI 9.361 1.61RC 18.112 3.99TW 7.089 1.65UA 10.593 2.76WA 10.123 2.33

R-8quared = 0.33 R-8quared = 0.54Durbin-Watson = 2.18 Durbin-Watson = 2.41

The above results coupled withthose obtained by Toh andHiggins suggest that increasedemphasis on hUbbing cannot, byitself, contribute to airline profit­ability unless it is associated withairline dominance of the mainhub (or the few hUbs) it uses forits operations. To elaborate

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further, we provide twoexamples. The first is the case ofUSAir which, in 1980, establisheda hub in Pittsburgh wherecompetition was generallyabsent. While most airlinesexperienced losses in 1980 and1982, USAir posted impressiveprofits, and, overall, USAir was

the most profitable airlinebetween 1980 and 1984. Thesecond example is Pride Airwhich, in late 1985, adopted acomplete hub-and-spoke systemwith New Orleans as the mainhub (i.e., hubbing index equals0.5). Pride Air could not with­stand competition at New

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Hub Dominance

Orleans from other dominantairlines (such as Delta, Eastern,Continental, Southwest, etc.) andhad to declare bankruptcy by theend of 1986.

In light of the above, one canconclude that the commonlyheld belief that hubbing leads tomore successful operations isattributed mainly to the fact thatmost airlines tend to dominatethe main connecting hubs withintheir systems. This is apparentby examining individual airline'sranking at the major hub asshown in Table 1.

HUB DOMINANCE ANDAIRLINE ENPLANEMENT

SHAREThe second phase of this study

is to assess the impact of hubdominance on airlineenplanement share at the hubairport. Route monopoly andmarket dominance have beenthe subject of many studieswhich attempted to relate anairline's passenger share in agiven market to its frequencyshare of the total flights in themarket. Renald (1970), Fruhan(1972), and Miller (1979) showedthat the relationship between anairline's market share and itsfrequency share follows anS-curve; meaning that high

Equation 3

frequency shares are associatedwith even higher market sharesand conversely. Following thesame approach, we will test thehypothesis that there exists apositive and strong relationshipbetween an airline's enplane­ment share at a given airportand its hub dominance. Anairline's enplanement share at ahub is estimated as the ratiobetween the airline's passengerenplanements to the totalpassenger enplanements by allairlines at that hub.The Model

In developing an enplanementshare model for an airline at agiven hub, it will be assumedthat passengers exhibit utilitymaximization behavior in theirchoice of a carrier. It can bereadily shown that by maximizingthe passenger's utility function,the standard multinomial logitprobabilistic choice model canbe obtained, such that:

Equation 2

elJ(im)

p1m .E eIJ{Jn1J (2)

J

where Pim is the probability thata passenger at hub m will selectan airline i, or simply thepassenger enplanements shareof airline i at hub m; and U{im) isthe utility of airline i topassengers at hub m. The logitmodel has widely been used insimilar applications, primarilybecause of its advantagesrelative to other probabilisticchoice model forms. For adiscussion and derivation of thelogit model, the reader can referto Kanafani (1985, Chi 5).

The passenger utility's functionconsists of a vector (i.e.; array)of the carrier's service attributesat a particular hub. Theseattributes include flightfrequency, aircraft size, airfare,departure schedule, and airlineimage. For the purpose of thisstudy, the utility function willconsist of the carrier's flightfrequency at the hub. Othervariables influencing an airline'sshare of passenger enplane­ments will be accounted for byincorporating a firm-specificvariable in the utility function.Based upon the abovediscussion, the utility functionUOm) is given as:

U(jm) =a. LOG(FREQ) jm+P flRMr- e (3)

where FRE.Qjm is the flightfrequency of airline j at hub m,FIRMj is a firm-specific variablewhich takes on the value one forcarrier j and zero otherwise. CI

and B are the coefficients to beestimated, and c is the error

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term. A PRIORI sign of CI isexpected to be positive since anincrease in flight frequency willyield better levels of service.Levels of service include suchmeasures as frequency of flights,aircraft size, on-time

performance, in-cabin service,and flight itinerary (e.g.; non-stopflights versus multi-stop orconnecting flights). Note that theflight frequency variable (FREQ)is expressed in a logarithmicform in order to examine, in

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Table 3Input Data for the Enplanement Share Model for 1980

Hub Dominance

Hub Airline Enplanements Aircraft(millions) Departures

ORO AA 3745.3 47344DL 1975.2 25286UA 6217.5 77356

PIT AL 3022.6 54291TW 978.2 15068UA 619.5 9651

DFW BN 3645.7 57352AA 3079.5 45658DL 1677.5 23257

ATL DL 10342.7 119472EA 7620.1 105170RC 789.1 21620

DEN FL 2230.6 41880CO 2107.1 31711UA 2670.3 39002

MSP NW 1787.1 25618RC 1023.3 24060WA 532.2 8481

MIA PA 1078.4 14030

EA 2289.9 27881DL 819.7 12116

STL TW 2333.1 34127OZ 1042.4 24705

AA 661.9 14637

LAX WA 1953.7 23380AA 1673.3 17337UA 3033.6 34989

Source: IAirport Activity Statistics of Certificated Route Air Carriers.1

U.S. Department of Transportation. The Federal Aviation Administration. 1980

relative terms, the relationship frequency share as explained a multiple airport region, Harveybetween an airline's enplane- earlier. In his investigation of (1986) showed that using aments share and its flight passenger choice of an airport in nonlinear specification for

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Hub Dominance

yielded a better estimate than alinear one.

In order to test thehypothesisthat there exists apositive and strong relationshipbetween airline enplanementshare and its hub dominance,the logit model in Equation 2 isestimated. In their survey ofairline strategies to dominatetheir main hubs, Ghobrial andSousa (1987)showed that mostpassenger enplanements at agiven hub are carried by the top

Table 4:ResuRs ofEstimating Equation 3

three airlines. The logit modelwas, therefore, estimated usingdata for the top three airlines agiven hub. The hubs selected forestimating the model are thoselisted in Table 1 over the periodfrom 1976 to 1984. For thepurpose of illustration, Table 3shows the 1980 data for aircraftdepartures and passengerenplanements for the top threeairlines dominating particularhubs.

Using the cross sectional,

MODEL 1

time-series data for the selectedairlines over 1976-84, passengerenplanements for each airline ata given hub were converted toproportions and the logit modelin Equation 2 was estimatedtwice (i.e.; with and without thefirm-specific variable FIRM).Because of the logarithmicspecification of the model, twoobservations were omitted fromthe data, that is, Piedmont'soperations at ROA in 1976 and1978. The results of estimating

MODEL 2VARIABLE!COEFFICIENT

FREQAAALBNCODLEAFLNWOZPAPIRCTWUAWA

LOG LIKELIHOODAt Zero Slope:At Convergance:R-Squared:

EstimatedValue

1.0505

T­Statistics

57.79

-263.62-44.74

0.94

EstimatedValue

1.07900.0928

-0.33600.00220.07990.0453

-0.1899-0.19280.0482

-0.18120.2029-0.20~

0.55610.14590.10100.1313

T­Statistics

63.451.27

-3.33-0.030.820.60

-2.88-1.860.53

-1.882.06

-2.22-6.871.731.410.17

-262.6213.59

0.97

both models along with t-statis­tics are shown in Table 4. Forthe purpose of comparison, the

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variable FIRM is replaced by itscorresponding airline code inTable 4.

AnalysisThe sign of CI agrees with its APRIORI sign and the FREQ

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variable seems to be highlysignificant. Moreover, using thestatistical hypothesis testing, onecannot reject the hypothesis thatthe coefficient u is greater thanone in both model specifications.The relationship betweenenplanement share and hubdominance seems, therefore, tofollow an S-curve meaning thathigh frequency shares at a givenairport are associated with evenhigher enplanement shares, andconversely.

For the purpose of illustration,we consider the case of DeltaAirlines' operations at AtlantaHartsfield Airport between 1976and 1986. Figure 1 depicts thetrends in Delta's share of thetotal aircraft departures at Atlanta

(i.e., hub dominance index)along with its share of pass·engerenplanements (in percentagepoints). The observed patternDelta's dominance of Atlantathrough frequency concentrationis evident. Because Delta is thedominant airline at Atlanta itsshare of passenger enplane­ments is consistently higher thanits corresponding aircraftdeparture share as depicted inFigure 1.

The disproportionalityphenomenon between anairline's enplanement shar.e andits frequency share is attributedto passenger identification withthe dominant carrier in theregion. For instance, localtravelers originating in the

Hub Dominance

Atlanta area learn which carrieroffers the greatest flightfrequency (Delta in this case)and given the existence ofinformation costs, passengerstend to contact that carrier first.Information costs include thetime and communicationexpenses of calling severalairlines and/or travel agencies.Passengers flying Delta viaAtlanta can enhance theirchances of enjoying single-planeservice. Furthermore, throughincreased frequency concen­tration at Atlanta and a propertiming of flight arrivals anddepartures, Delta Airlines canoffer connecting passengers asingle-airline service (i.e., on-lineconnection,) thus reducing the

• Delta's AircraftDeparture Share

• Delta's EnplanementShare

60

50

40

tc 30Bisa.

20

10

0

1976 1978 1980

Year

1982 1984 1986

Figure 1: Aircraft Departure Share and Enplanement Share for Delta Airlines at Atlanta Hartsfield Airport

passengers chances of missinga connection or losing baggage.

CONCLUSIONSThis paper attempts to shed

light on the phenomenon of air-

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line frequency competition as ameans to dominate its majorconnecting hubs. It is concludedthat airline network centralization(hubbing) cannot by itself contri-

bute to airline profitability unlessit is associated with airlinedominance of the main hub (orthe few hubs) it uses for itsoperations. By dominating its

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Hub Dominance

main hubs, airlines can reap themonopoly profits from themarkets served by these hubsand realize higher enplanementshares than departure shares.

Several conclusions emergefrom the above discussion. First,in establishing a hub, airlinesseem to follow a number ofstrategies including: 1) stayingaway from competition bymonopolizing the hub such asUSAir operations at Pittsburgh,and Piedmont at Charlotte; and2) engaging in frequencycompetition to dominate the hub,and establishing regional identi­fication with passengers topromote airline services.Examples are Delta at Atlanta,American at Dallas/Fort Worth,and TWA at St. Louis. Second, totake advantage of the nonlinearrelationship between passengerenplanements share andfrequency share, airlines mayelect to operate higher flightfrequency with relatively smallersize planes. Agarwal and Tally(1985) showed that passengersare more sensitive to changes infrequency delay (i.e., changes inflight frequency) than to changes

in stochastic delay (i.e., changesin aircraft size). Pacific South­west Airlines appeared to haveadopted this strategy byreplacing many of its B-727 withthe smaller Bae 146-100 and Bae146-200 aircraft in many routesin the California corridor. Third,since there has been a trend inmergers between two airlinesdominating the same hub.Examples are Northwest andRepublic at Minneapolis, TWAand Ozark at St. Louis, andSouthwest and Transtar atHouston. One can view thesemergers as a means to create amonopoly power and chargehigher airfares. From theperspective of policy making, theissue of monopoly power oughtto be considered whenapproving mergers betweenairlines hubbing at the sameairport.

Finally, while hub dominancethrough frequency competitionoffers opportunities both forairlines and passengers, it maypose problems as well.Excessive frequency concentra­tion at airports may result insome negative economic

impacts such as congestion,pollution, and noise. Congestiondelay may outweigh some of thebenefits of aircraft concentrationby increasing flying costs forairlines and travel time forpassengers.LIMITATIONS OF THE STUDYIn attempting to assess the

impact of hub dominance onairline profitability andenplanement share, it wasassumed that flight frequency isthe only explanatory variable inthe econometric models. Othervariables contributing to airlineprofitability and enplanementshare were accounted for byincorporating a firm-specificvariable in the models. While theresults showed a positive strongrelationship between profitabilityand enplanement share on onehand and hub dominance on theother, further research is neededto incorporate other hubdominance strategies in themodels. These include airfarestructure at the main hubs,aircraft size, arrangements fortraffic feeding through a subsid­iary, and frequency concentra­tion during peak periods.

Atef Ghobrial holds a Ph.D. in Transportation, a Master of Business Administration, and aMaster of Science in Civil Engineering from the University of California at Berkeley. He ispresently an Associate Professor at Georgia State University where he directs the aviationadministration program. He has published several papers in the area of air transportation, andis a transportation consultant in the U.S. and abroad.

REFERENCES

Aviation Week and Space Technology, November 9, 1981, p. 49.Agarwal, V. and Talley, W. (1985) The Demand for International Air Passenger Services Provided

by U.S. Carriers. 11 International Journal of Transport Economics, pp. 63-70.Douglas, G. and Miller III J. (1974). Economic Regulation of Domestic Air Transport: Theory and

Practice, Brookings Institution, Washington, D.C.

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Hub Dominance

Fruhan Jr, W. (1972). The Fight for Competitive Advantage-A Study of the United States DomesticTrunk Carriers, Division of Research, Graduate School of Business Administration, HarvardUniversity, Boston, Massachusetts.

Ghobrial, A. and Sousa, J. (1987). Airline Strategies for Hub Dominance: A Statistical Analysis.Journal of Transportation Research Forum.

Harvey G. (1986). Airport Choice in a Multiple Airport Region. Department of Civil Engineering,Stanford University.

Kanafani, A. (1985). Transportation Demand Analysis, McGraw Hill, New York.Kanafani, A. and Ghobrial A. (1982). Aircraft Evaluation in Air Network Planning.1I TransportationEngineering Journal of the American Society ofCivil Engineering, vol. 108, no. TE3, pp. 282-300.

Kanafani, A. and Ghobrial, A. (1985). Airline Hubbing-Some Implications for Airport Economics.Transportation Research, Vol. 19A, No.1, pp. 15-27.

Kanafani, A. and Hansen, M. (1985) Hubbing and Airline Costs. Research Report, Institute ofTransportation Studies, Berkeley, UCB-ITS-RR-85-12.

Miller, James. (1979). Airline Market Shares Versus Capacity Shares and The Possibility ofShort-Run Loss Equilibria. Research in Law and Economics, Vol. 1, pp. 81-96.

Renal, G. (1970). Competition in Air Transportation: An Econometric Approach. UnpublishedMS thesis, Department of Aeronautics and Astronautics, MIT, Massachusetts.

Toh, R. and Higgins, R. (1985). The Impact of Hub and Spoke Network Centralization and RouteMonopoly on Domestic Airline Profitability. Transportation Journal. vol. 24, no. 4, pp. 16-27.

U.S. Department of Transportation. The Federal Aviation Administration, Airport Activity Statisticsof Certificated Route Air Carriers. Published Annually.

U.S. Department of Transportation. Air Carriers Financial Statistics. Published Quarterly.

+ + +

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