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Airport Gate Scheduling for Passengers, Aircraft, and Operation Sang Hyun Kim, Eric Feron∗, John-Paul Clarke School of Aerospace Engineering Georgia Institute of Technology Atlanta, GA, U.S.A. sanghyun.kim, feron, [email protected] Aude Marzuoli†, Daniel Delahaye 3 Ećole Nationale de l’Aviation Civile 1 Toulouse, France 0 2 aude.marzuoli, [email protected] n a January 17, 2013 J 6 1 Abstract ger airlines [2]. Because of the hub-and-spoke struc- ] ture of the airports network, major airports, such Y as Hartsfield-Jackson Atlanta International Airport, Passengers’ experience is becoming a key metric to S have a significant impact on the performance of the evaluatetheairtransportationsystem’sperformance. . overall system. In particular, connecting passengers s Efficient and robust tools to handle airport oper- c insuchhubsmayrepresentthelargestshareoftraffic ations are needed along with a better understand- [ ing of passengers’ interests and concerns. Among and are most vulnerable to delays that can severely 1 perturb their journeys. In worst cases scenarios, a various airport operations, this paper studies air- v single delay can ”snowball” through the entire net- port gate scheduling for improved passengers’ expe- 5 work [3]. 3 rience. Three objectives accounting for passengers, 5 aircraft, and operation are presented. Trade-offs be- Airport Collaborative Decision Making (A-CDM) 3 tween these objectives are analyzed, and a balancing aims at reducing delays and improving system pre- 1. objectivefunctionisproposed. Theresultsshowthat dictability, while optimizing the utilization of re- 0 the balanced objective can improve the efficiency of sources and reducing environmental impact. This 3 traffic flow in passenger terminals and on ramps, as effort is currently one of the five priority measures 1 well as the robustness of gate operations. in the Flight Efficiency Plan published by IATA, : v CANSO and Eurocontrol [4]. In the U.S., the CDM- i basedgrounddelayprogramplanningandcontrolap- X peared in 1998; the stakeholders are the Joint Gov- r a 1 Introduction ernment Industry program, airlines, the Federal Avi- ation Administration including Air Traffic Control andAirTrafficFlowManagement,andairports. The Flight delays do not accurately reflect the delays im- mechanisms involve the provision of accurate data posed upon passengers’ full itineraries. The growing (estimates of arrival and departure times) to stake- interest to measure the Air Transportation System’s holders, the share of information, the airline deci- performance calls for new metrics, reflecting passen- sion to cancel or delay flights, and the rescheduling gers’experience[1]. Thecostofcongestionanddelays withpriorityconstraints. Severalimprovementshave insuchacomplexsystemishuge. In2011, according been reported resulting from the CDM initiative, toAirlinesforAmerica,103millionsystemdelaymin- such as the Collaborative Departure Queue Manage- utes have cost $7.7 billions to scheduled U.S. passen- ment strategy at Memphis International Airport [5] or the Surface Congestion Management scheme at New York’s John F. Kennedy International Airport ∗EricFeronisalsowithEćoleNationaledel’AviationCivile. †Aude Marzuoli is also with Georgia Institute of Technol- [6]. However,therestillisagrowingneedformoreef- ogy. ficient and more robust tools to handle operations at 1 The last objective of this study is to minimize dis- turbances in gate operations or equivalently to maximize the robustness of gate assignment [10, 11]. Ro- bust means that the gate assignment is less sensitive to uncertain delays. Severe delays perturb gate operations by forcing arriving aircraft to wait for gates, or air traffic controllers to reassign gates. The dis- turbances can be reduced if the gate assignment is robust against uncertain delays. In addition, a robust gate assignment allows air traffic controllers to utilizegate-holdingdeparturecontrolmoreefficiently [12]. Thegate-holdingdeparturecontroldelayspush- backsinordertoreducetaxitimesandemissionwhen the airport surface is congested. As a result, aircraft occupy gates longer than scheduled and it can nega- tivelyimpactgateoperations. Ifthegateassignment Figure 1: Airport operations and the focus of this is robust, aircraft are able to stay longer at gates study. without disturbing gate operations and gate-holding departure control performs better. Allthreeobjectivescannotbesatisfiedatthesame airports. This effort should be combined with a nec- time. Hence, this study presents trade-offs between essary shift towards a better understanding of pas- objectivesusingflightschedulesinaU.S.hubairport. sengers’ interests and concerns. Most air travelers have experienced walking long distances in a passenger terminal to catch a flight 2 Gate Assignment Problem or waiting on board their aircraft while it is waiting for a gate or is delayed by the movement of another 2.1 Data Source aircraft. Many of such situations can be resolved or reduced by proper gate scheduling or assignment. Previous studies on gate assignment generated ficti- Airport operations range from landing to take-off tiouspassengerdata(e.g.,numberoftransferpassen- of an aircraft as shown in Fig. 1. When an aircraft gers) because such data are not published. Thanks lands, it taxies into a ramp area and parks at a gate. to a major U.S. carrier, this study is able to assign While the aircraft is docking at the gate, passengers airport gates and analyze gate assignments with the disembark and board the plane. When the aircraft actual number of transfer passengers at a U.S. major is ready to depart, it pushes back and taxies out to hub airport. Flight schedules and transfer passenger a runway. Then, the aircraft takes off the airport. dataonMay1st,2011atthehubairportareobtained Among these operations, this study focuses on the fromthecarrier. Alltheflightsareassumedtobefull optimization of ramp operations and the accommo- with passengers. Passengers who check in at the air- dation of passengers. port (origin passengers) and whose final destination The first objective of this study is to minimize istheairport(destinationpassengers)movefromthe the transit time of passengers in a passenger termi- passenger terminal to a gate. Passengers who have nal. The transit time of passengers consists of the connectingflightsattheairport(transferpassengers) time from the security checkpoint to a gate, from a move from a gate to another gate. Because only the gate to baggage claim, and from one gate to another data on the number of transfer passengers of a sin- gate. This is the most common objective of tradi- gle carrier are available, passengers except transfer tional studies focusing on gate assignment [7, 8]. passengers among the carrier’s flights are dealt with The second objective of this study is to minimize origin and destination (O&D) passengers. taxitimeonramps[9]. Thetaxitimedependsonthe length of taxi route. However, interfering taxi routes 2.2 Objective 1: Minimize Passenger causetaxidelay. Iftwoaircrafttaxiinoppositedirec- Transit Time tions on the same taxi lane, which does not happen ontaxiway,itresultsintaxidelays. Becausethetaxi The first objective is to minimize the transit time route of an aircraft is determined by the locations of of passengers. Passengers in an airport are catego- assigned runway and gate, gate assignment is critical rizedintothreegroups. Originpassengersbegintheir to reduce taxi time and taxi delays on ramps. itinerary from the airport. Destination passengers 2 finish their itinerary at the airport. Transfer passen- certain amount of time, which is called buffer time gerschangefromoneflighttoanotherattheairport. (tbuff). Equation (3) is meaningful only if flights i The transit time of origin passengers depends on and k are assigned to gate j (x = x = 1) be- ij kj the distance from a security checkpoint to a gate in cause M is an arbitrarily large number. t indicates s m i (d ). Letv denotetheaveragemovingspeed,which the scheduled gate-in time (arrival time) of flight i, varies with the configuration of passenger terminal: out t indicatesthescheduledgate-outtime(departure vm is higher where passengers can move faster by i time). F and G denote the sets of flights and gates. taking moving sidewalk, underground people mover, etc. Assume that flight i is assigned to gate j and o 2.3 Objective 2: Minimize Aircraft thenumberoforiginpassengersofflightiisn , then i the total transit time of origin passengers of flight Taxi Time o s m i is n d /v . Similarly, the total transit time of i j The second objective is to minimize unimpeded taxi d b m destination passengers of flight i is n d /v , where i j time and taxi delay. The unimpeded taxi time for d n is the number of destination passengers of flight an arrival measures from when an aircraft enters a i i, and db is the distance from gate j to a baggage spot to when the aircraft parks at a gate without j claim. Therefore, the transit time of O&D passen- any taxi delay. The taxi time from a spot to a gate gers is determined by the location of a single gate is calculated by dividing the distance from a spot because the locations of the security checkpoint and to a gate by the taxi speed. The unimpeded taxi baggage claim are fixed. time for a departure measures from when an aircraft Contrarily, the transit time of transfer passengers pushesbacktowhentheaircraftleavestheramparea dependsonthedistancebetweentwogates(d ). Let without any taxi delay. It contains the duration to jl n denotethenumberoftransferpassengersbetween push back. A taxi delay happens in either of the ik flight i and flight k. Then, the total transit time of following cases. 1) A taxiing aircraft blocks the push passengers who transfer between flight i and flight k backrouteofanotheraircraft. 2)Twoaircrafttaxiin is n d /vm. opposite directions on the same taxi lane. The first ik jl Consequently,thetransittimesofO&Dpassengers caseiscalledapushbackblockingandthepushback areexpressedbylineartermsandthetransittimesof is delayed until the taxiing aircraft passes through transfer passengers are expressed by quadratic terms the push back route. The second case is called a taxi in the objective function (1), where x is a decision blocking and one of the aircraft must shift its taxi ij variable that indicates whether flight i is assigned to lane to another taxi lane. Therefore, the taxi routes gatej. Theformulationofthefirstobjectiveisgiven of two aircraft condition taxi delays. in below. Let n denote the number of arrival passengers i in of flight i and u denote the unimpeded arrival taxi j s b time of gate j. Note that arrival passengers include Obj =minimize(cid:88)(cid:88)(no dj +nd dj ) x both destination passengers and transfer passengers pax i vm i vm ij of arriving flight i. Let nout denote the number of i∈Fj∈G i out +(cid:88)(cid:88) (cid:88) (cid:88)n djl x x (1) departure passengers of flight i and uj denote the ikvm ij kl unimpeded departure taxi time of gate j. Then, the i∈Fj∈Gk∈F,k>il∈G weighted unimpeded taxi time of flight i, which is subject to weighted by the number of passengers on board, is (cid:88) ninuin + noutuout. Similar to the transit time of x =1, ∀i∈F (2) i j i j ij O&D passengers of objective 1, the weighted unim- j∈G peded taxi time is expressed by a linear term in the out in buff out in buff (ti −tk +t )(tk −ti +t ) objective function (5). ≤M(2−xij −xkj), i(cid:54)=k, ∀i,k ∈F, ∀j ∈G (3) Taxi delay (tdly) involves a pair of aircraft and it x ∈{0,1}, ∀i∈F, ∀j ∈G (4) is weighted by the sum of the number of passengers ij (cid:26) on board of both aircraft. For instance, if the taxi 1 if f is assigned to g where x = i j delay occurs between two arrivals, the total number ij 0 otherwise. in in of passengers is n +n . The quadratic terms of i k Two constraints are given in (2)-(3). Equation (2) the objective function (5) are weighted by a general makes sure that every flight is assigned to a single form, n +n . i k gate. Equation (3) constrains two successive gate Theformulationofthesecondobjectiveisgivenbe- schedules, so that they are separated more than a low. Theconstraintsofthefirstobjectiveareapplied 3 Figure 2: Gate conflict and its duration. Figure 3: Expected duration of gate conflict. equally. in out t > t . Details of the calculation are given in k i [11]. (cid:88)(cid:88) in in out out Obj =minimize (n u +n u ) x The expected duration of a gate conflict is known taxi i j i j ij to rely on gate separation [11]. Using the delay data i∈Fj∈G (cid:88)(cid:88) (cid:88) (cid:88) dly of a U.S. carrier at a hub airport in May 2011, the + (n +n )t x x (5) i k ij kl expected duration is shown in Fig. 3 and it is fit to i∈Fj∈Gk∈F,k>il∈G a×bsep(i,k),whereaandbareconstantsandsep(i,k) subject to (2)-(4). denotes the gate separation between flights i and k. The formulation of the third objective is given be- 2.4 Objective 3: Maximize the Ro- low. Note that the expected duration of a gate con- bustness of Gate Assignments flict is weighted by the number of arrival passengers. The third objective is to maximize the robustness of gate assignments. Equivalently, the objective is to minimize the duration of gate conflicts. If a gate is Obj =minimize(cid:88) (cid:88) nina×bsep(i,k)(cid:88) x x robust ij kj still occupied by an aircraft when another aircraft i∈Fk∈F,k>i j∈G requests the gate, the latter should wait until the as- (6) signed gate or another gate is available, which cor- subject to (2)-(4). responds to a gate conflict. Fig. 2 illustrates a gate conflict, where act (i) and act (i) denote the actual a d arrival and departure times of flight i, and the gate separation is the time gap between the scheduled de- 2.5 Trade-offs of Multiple Objectives out parture time of flight i (t ) and the scheduled ar- i in rival time of flight k (t ). In Fig. 2, flight i is sched- It is known that there are trade-offs between objec- k uled to leave the gate before flight k arrives, but the tives that are presented in this study [9, 13]. In or- departure time of flight i is delayed and flight k ar- dertoanalyzethetrade-offsbetweenthreeobjectives, rives earlier than schedule. So, when flight k arrives, five scenarios are presented in Table 1. Scenarios 1-3 the gate is not released yet and flight k has to wait optimize each objective. Scenario 4 weighs equally for a gate. on objective 1 and 2. So, it optimizes two objectives Because the actual arrival and departure times are concurrently. Scenario 5 takes all the objectives into unknown when gates are assigned, the duration of account: 40% on the first and second objectives and a gate conflict is estimated based on the probabil- 20% on the third objective. These percentages are ity distributions of arrival delay and departure de- chosen arbitrarily: the proportion of three objectives lay. Theexpecteddurationofagateconflictiscalcu- depends on the policy of airport gate managers and lated by E[act (i)−act (k)|act (i) > act (k)] when airlines. d a d a 4 Table 1: Scenarios Scenario Objective Function Explanation Scenario 1 Obj =Obj Optimize objective 1 only. pax Scenario 2 Obj =Obj Optimize objective 2 only. taxi Scenario 3 Obj =Obj Optimize objective 3 only. robust Scenario 4 Obj =0.5Obj +0.5Obj Balance objective 1 and 2. pax taxi Scenario 5 Obj =0.4Obj +0.4Obj +0.2Obj Balance all the objectives. pax taxi robust Figure 4: Insert move. Figure 6: Transit time per passenger in minute. reaches the maximum iteration or there is no im- Figure 5: Exchange move. provementoftheobjectivevalueaftersomeiterations pastthelastbestscore. Theinsertmoveisevaluated 2.6 Optimization Method at every iteration in order to intensify a local search around a narrow neighborhood of the current solu- The Tabu Search (TS) is a meta-heuristic algorithm tion. The interval exchange move is evaluated peri- known to efficiently deal with combinatorial opti- odically in order to diversify the search: the interval mizationproblemssuchasthegateassignmentprob- exchangemovebringsarelativelylargechangeinthe lem [14, 15]. Because the gate assignment problem is current solution. More details of the implementation complex, it is hard to find the optimal solution in a of the TS on the gate assignment problem are given reasonable time. The TS can outperform the Branch in [9]. and Bound and Genetic Algorithm in terms of solution time and solution accuracy for the gate assignment problem [9]. The TS is a local search so the al- 3 Results gorithmcanconvergetoalocaloptimum,whichisnot the global optimum. In order to help the TS escape Fig.6illustratestheaveragetransittimeofeachpas- from a local optimum, a tabu memory restricts the senger. As expected, scenario 1 (Pax 100%) results TS from utilizing recently used search moves for cer- in the shortest passenger transit time. In scenarios 4 tain iterations. However, if a restricted search move and 5, passengers walk longer than in scenario 1 but improves theobjective value, thesearchmovecanbe less than in the original (current) gate assignment usedregardlessofthetabumemory,knownastheas- and scenarios 2 and 3. pirationcriterion. Twotypesofneighborhoodsearch Fig. 7 shows the average taxi time of each passen- moves of TS are shown in Fig. 4 and Fig. 5. The in- ger. Undoubtedly, scenario 2 (Taxi 100%) produces sertmovechangesaflight’sgateassignmentfromone the shortest taxi time with zero taxi delay. From toanother,andtheintervalexchangemoveswapsthe Fig. 6 and Fig. 7, it is inferred that scenarios 4 and gate assignments of two groups of flights. 5balancewellbetweentwodifferentobjectives: min- The TS iterates until the number of iteration imizing passenger transit time and minimizing taxi 5 4 Conclusion This study presented several simulations of gate assignments according to different objectives. These objectives are minimizing transit time of passengers in passenger terminals; minimizing aircraft taxi time on ramps; and minimizing the duration of gate conflicts. It is known that there are trade-offs between these objectives so an objective function that bal- ancesthreeobjectivesatthesametimewasproposed. Thebalancingobjectivefunctionsatisfiesallthethree objectiveswhileotherobjectivefunctionsonlysatisfy one or two objectives. Moreover, the balancing objective function outperforms the current gate assignment in every objective. Therefore, the gate assign- Figure 7: Aircraft taxi time per passenger in minute. ment of the airport has a potential to be improved regarding the efficiency of traffic flow in passenger terminals and on ramps, as well as on the robustness of gate operations. Futureworkwillaccountforgate-holdingstrategies generated by Airport CDM. Although this study in- cludes the robustness of gate assignment, which was shown to help gate-holding strategies perform better, a comprehensive analysis of gate-holding strategies and passengers’ experience at the airport is still needed. Hence, future work will address the impact of gate-holding strategies on passengers. References [1] A.Cook,G.Tanner,S.Cristóbal,andM.Zanin. Figure 8: Expected duration of gate conflict per pas- Passenger-Oriented Enhanced Metrics. In Sec- senger in minute. ond SESAR Innovation Days, 2012. [2] Airlines for America. Annual and Per- Minute Cost of Delays to U.S. Air- time. lines. http://www.airlines.org/Pages/ Annual-and-Per-Minute-Cost-of-Delays-to-U. Fig. 8 shows the average gate conflict duration of S.-Airlines.aspx. each passenger. Scenario 3 (Robust 100%) induces the shortest duration of gate conflict. Note that sce- [3] S. AhmadBeygi, A. Cohn, Y. Guan, and P. Be- nario 5 (Pax 40%, Taxi 40%, Robust 20%) gives the lobaba. AnalysisofthePotentialforDelayProp- second best result of the robustness of gate assign- agation in Passenger Airline Networks. Journal ment while scenario 4 (Pax 50%, Taxi 50%) gives of Air Transport Management, 14(5):221–236, less robust gate assignment. Consequently, scenario 2008. 5 balances three objectives at the same time better than other scenarios. [4] Eurocontrol. Airport CDM Implementation. 2006. From the results, scenarios 1, 2, and 3 give the best results for each objective but lead to poor per- [5] C. Brinton, C. Provan, S. Lent, T. Prevost, formance with respect to other objectives. Also, sce- and S. Passmore. Collaborative Departure nario4performswelljustforobjective1and2. Only Queue Management: An Example of Collabo- scenario 5 succeeds at satisfying all the objectives. rative Decision Making in the United States. In Theoriginalgateassignment,however,doesnotshow 9th USA/Europe ATM Research & Development satisfactory performance for the given objectives. Seminar, 2011. 6 Author Biography [6] A.Nakahara,T.G.Reynolds,T.White,C.Mac- carone, and R. Dunsky. Analysis of a Surface CongestionManagementTechniqueatNewYork Sang Hyun KimisaPh.D.candidateintheSchool JFK Airport. In 11th AIAA Aviation Technol- of Aerospace Engineering at the Georgia Institute of ogy, Integration, and Operations (ATIO) Con- Technology. He holds his B.S. degree in mechanical ference, 2011. and aerospace engineering from Seoul National Uni- versity, South Korea. His research interests are op- [7] R. Mangoubi and D. Mathaisel. Optimizing timization, transportation, airport operations, ramp Gate Assignments at Airport Terminals. Trans- management, and general aerospace engineering. portation Science, 19(2):173–188, 1985. Aude Marzuoli is currently pursuing a PhD in Aerospace Engineering at the Georgia Institute of [8] A. Haghani and M.C. Chen. Optimizing Gate Technology, with a focus on air traffic management, Assignments at Airport Terminals. Transporta- optimization and control. In 2012, she obtained her tion Research Part A, 32(6):437–454, 1998. Master in Aerospace Engineering from Georgia Tech andherEngineeringDiplomafromSupelecinFrance. [9] S. Kim, E. Feron, and J.-P. Clarke. Gate As- She previously attended the Lycee Henri IV in Paris signment to Minimize Passenger Transit Time for her preparatory classes. and Aircraft Taxi Time. Journal of Guidance, Eric Feron is received the B.S. degree from Ecole Control, and Dynamics, in Press. Polytechnique, Palaiseau, France, the M.S. degree fromtheEcoleNormaleSuprieure,Paris,France,and thePh.D.degreefromStanfordUniversity, Stanford, [10] A.Bolat. ProceduresforProvidingRobustGate CA. He is the DuttonDucoffe Professor of Aerospace Assignments for Arriving Aircrafts. European Software Engineering, Georgia Institute of Technol- Journal of Operational Research, 120(1):63–80, ogy, Atlanta, GA. Prior to that, he was with the 2000. faculty of the Department of Aeronautics and Astro- nautics,MassachusettsInstituteofTechnology,Cam- [11] S. Kim and E. Feron. Robust Gate Assignment. bridge,for12years. Hisformerresearchstudentsare In Proceedings of AIAA Guidance, Navigation, distributed throughout academia, government, and and Control Conference, Portland, OR, 2011. industry. He has published two books and several AIAA. research papers. His research interests include using fundamental concepts of control systems, opti- [12] S. Kim and E. Feron. Impact of Gate Assign- mization, and computer science to address impor- mentonGate-holdingDepartureControlStrate- tant problems in aerospace engineering such as aer- gies. In IEEE/AIAA 31st Digital Avionics Sys- obatic control of unmanned aerial vehicles and mul- tems Conference (DASC). IEEE, 2012. tiagent operations such as air traffic control systems and aerospace software system certification. [13] S. Kim and E. Feron. Robust Gate Assignment. John-Paul Clarke is an Associate Professor in unpublished. the Daniel Guggenheim School of Aerospace Engi- neering with a courtesy appointment in the H. Mil- [14] F. Glover and M. Laguna. Tabu Search, vol- ton Stewart School of Industrial and Systems Engi- ume 1. Kluwer Academic Publishers, 1998. neering, and Director of the Air Transportation Lab- oratory at the Georgia Institute of Technology. He [15] J. Xu and G. Bailey. The Airport Gate Assign- received S.B. (1991), S.M. (1992), and Sc.D. (1997) mentProblem: MathematicalModelandaTabu degreesinaeronauticsandastronauticsfromtheMas- SearchAlgorithm.InProceedingsofthe34thAn- sachusetts Institute of Technology. His research and nualHawaiiInternationalConferenceonSystem teaching in the areas of control, optimization, and Sciences, pages 77–77. IEEE, 2001. system analysis, architecture, and design are moti- vated by his desire to simultaneously maximize the efficiency and minimize the societal costs (especially Acknowledgment on the environment) of the global air transportation system. This work was supported in part by the Euro- Daniel DelahayeisdoingresearchfortheFrench peanCommunityFrameworkProgramme7underthe Air Navigation Research Center since 1995 and is META-CDM project. memberoftheartificialevolutionteamoftheapplied 7 mathematics research center (CMAP from Ecole Polytechnique, France). Delahaye graduated with an Engineer degree from ENAC, a Master of Sci- ence in signal processing from the national polytech- nic institute of Toulouse in 1991, the PhD D in au- tomatic control from Ecole Nationale Supérieure de l’Aronautique et de l’Espace (SUPAERO) in 1995. Following a Post-Doc in the Department of Aero- nautics and Astronautics at MIT in 1996, he has been working continuously in the Applied Mathe- matic Laboratory of ENAC, where he is conducting researchonstochasticoptimizationforlargescaleair traffic management. 8