Research Article Optimizing Key Parameters of Ground Delay Program with Uncertain Airport Capacity

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1 Hindawi Journal o Advanced Transportation Volume 2017, Article ID , 9 pages Research Article Optimizing Key Parameters o Ground Delay Program with Uncertain Airport Capacity Jixin Liu, 1 Kaijian Li, 1 Minjia Yin, 1 Xuehua Zhu, 1 and Ke Han 1,2 1 College o Civil Aviation, Nanjing University o Aeronautics and Astronautics, Nanjing , China 2 Department o Civil and Environmental Engineering, Imperial College London, London SW7 2BU, UK Correspondence should be addressed to Jixin Liu; larryljx66@nuaa.edu.cn Received 19 August 2016; Accepted 7 November 2016; Published 12 January 2017 Academic Editor: Andrea D Ariano Copyright 2017 Jixin Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Ground Delay Program (GDP) relies heavily on the capacity o the subject airport, which, due to its uncertainty, adds to the diiculty and suboptimality o GDP operation. This paper proposes a ramework or the joint optimization o GDP key parameters including ile time, end time, and distance. These parameters are articulated and incorporated in a GDP model, based on which an optimization problem is proposed and solved under uncertain airport capacity. Unlike existing literature, this paper explicitly calculates the optimal GDP ile time, which could signiicantly reduce the delay times as shown in our numerical study. We also propose a joint GDP end-time-and-distance model solved with genetic algorithm. The optimization problem takes into account the GDP operational eiciency, airline and light equity, and Air Traic Control (ATC) risks. A simulation study with real-world data is undertaken to demonstrate the advantage o the proposed ramework. It is shown that, in comparison with the current GDP in operation, the proposed solution reduces the total delay time, unnecessary ground delay, and unnecessary ground delay lights by 14.7%, 50.8%, and 48.3%, respectively. The proposed GDP strategy has the potential to eectively reduce the overall delay while maintaining the ATC saety risk within an acceptable level. 1. Introduction Ground Delay Program (GDP) is an important strategy in Air Traic Flow Management (ATFM), which aims at converting airborne delay into saer and more economic ground delay [1]. Eicient ATFM calls or more elaborate and eective implementation o GDP. Conventionally, the determination o GDP parameters, such as ile time, start time, and distance, relies on the experience o low managers or rule o thumb, which may be suboptimal in many circumstances. Thereore, cost-eective GDP strategies require a systematic approach basedonmodelingandoptimizationprocedures. Research on GDP and the determination o its key parameters in various operational environments (i.e., strategic, tactical) has gained increased attention only in recent years. Ball and Lulli [2] are among the irst to study the impact o GDP parameters on delays and build a distance optimization model or layered airspace in the US. Bianco et al. [3] propose a job-shop scheduling model with sequence dependent set-up times and release dates to coordinate both inbound and outbound traic lows on all the preixed routes o an airport terminal area and all aircrat operations at the runway complex. Homan et al. [4] propose an enhanced Ration by Distance (RBD) algorithm by taking into account Collaborative Decision Making (CDM) pertaining to light equity. In their model, only lights with lying distances greater than the equity threshold can be exempted rom the GDP. Cook and Wood [5] determine the GDP end time and distance based on the probability distribution o weather conditions. Bard and Mohan [6] present a new model and solution algorithm or the arrival slot reallocation problem or airlines when responding to a GDP. Mukherjee et al. [7] propose an algorithm that can assign light departure delays under probabilistic airport capacity. Their experimental results indicate an overall delay reduction by up to 20% or ground delay assignment at San Francisco, compared to the current level. Ball et al. [8] propose a constrained version o RBD as a

2 2 Journal o Advanced Transportation practical alternative to allocation procedures used in GDP operations. Manley and Sherry [9] develop a GDP Rationing Rule Simulator (GDP-RRS) to calculate perormance and equity metrics or all the stakeholders using six alternate rules. Delgado et al. [10] suggest that the amount o delay can be recovered by using cruise speed reduction techniques or GDP. Glover and Ball [11] describe a two-stage stochastic, multiobjective integer program or GDP planning. Kuhn [12] introduces several two-phase approaches to GDP planning, which address some issues with weighted sum methods while managing computational burdens. Delgado and Prats [13] present a case study by analyzing all the Ground Delay Programs that took place in San Francisco, Newark Liberty, andchicagoo Hareduringoneyear.Theresultsshowthat, by introducing cruise speed reduction techniques or GDP, it is possible to deine larger scopes, partially reducing the amount o unrecovered delay. Most o the aorementioned literature on GPD ocuses on the determination and optimization o GDP key parameters such as end time and distance. However, none have considered the ile time o ground holding as one o the decision variables. Conventionally, the ile time is based on either the actual capacity reduction time or the experience o low management sta. However, an appropriately selected ile time could signiicantly reduce the delay times, as shown in our numerical study (see Figure 2). Moreover, the problems o inding the optimal end time and distance are solved separately and sequentially by existing approaches, which may be suboptimal in practice. This paper makes contribution in the ollowing three aspects o GDP: (1) An optimal ile time problem is proposed to urther improvetheperormanceogdpunderuncertainties associated with airport capacity. This problem is ormulated as an integer linear program. (2) Unlike existing approaches, which solve or the end time and distance sequentially, we propose an integrated ormulation that inds the optimal end time and distance simultaneously. The resulting GDP strategy is thus expected to outperorm existing ones. (3) A case study is conducted in Guangzhou Baiyun Airport in China, where GDP is still in a preliminary state o development. The results show a signiicant reduction in total delay and unnecessary ground delay. In addition, the proposed optimization problems take into account not only GDP operation eiciency, butalsolightequity,airlineequity,andatcsaety risks. The theoretical ramework developed in this paper has the potential to underpin a systematic and widespread implementation o GDP in the Chinese air traic system. The rest o this paper is organized as ollows. Section 2 introduces the general concept o GDP as well as its mathematical model. Section 3 presents the mathematical programming ormulation or determining the key parameters, including ile time, end time, and distance. A case study o the Guangzhou Airport is conducted in Section 4. Finally, Section 5 oers some concluding remarks. 2. Ground Delay Program 2.1. GDP Parameters. When the traic demand at a destination airport is predicted to exceed its capacity, Ground Delay Program is invoked to control the dynamic traic demand. According to the GDP operational protocol, the low management department is required to release the GDP key parameters to relevant civil aviation authorities prior to the implementation o GDP. The key parameters include the ollowing: (1) File time, t, is the time when the low management department releases the start time, end time, and distance o the GDP. Flights already airborne at the ile time are to be exempted. (2) Start time, T s, is the time when traic low at the destination airport begins to exceed its capacity, minus a buer time. It marks the start o the time horizon or the ground delay, and lights whose scheduled times o arrival are later than the start time are to be aected by GDP. As the start time is very close to the time when GDP is initiated, the orecast o weather conditions and low proiles is relatively accurate, and hence the paper considers the start time as given and known. (3) End time, T e, is the oicial end time o the GDP. Flights with scheduled times o arrival later than the end time are not to be aected by ground delay and can take o according to their original schedules. (4) Distance, D, is the radius o the region centered at the destination airports that are aected by the GDP. All lights originating rom airports within this region are to be aected by GDP, while those beyond this geographic region are to be exempted and can operate as scheduled. Some o these key parameters, along with some others, are illustrated in Figure 1, where the meaning o STD, CTD, STA, andctacanbeoundinthelistoacronymsattheendo the paper Uncertain Airport Capacity. In GDP, airport capacity is quantiied based on the number o acceptable landing aircrat (A/C) per hour, namely, Airport Acceptance Rate (AAR). Generally, the airport capacity can be predicted based on inormation such as weather conditions. Hence, Predictive Airport Acceptance Rate (PAAR) is used to characterize airport capacity in GDP. For a given start time o the GDP, there is usually a desired capacity recovery time. The capacity recovery time also marks the end o the GDP and is hence also reerred to as cancellation time hereater. The actual capacityrecoverytimeisassumedtoollowcertainprobability distribution ξ that is supported in a neighborhood o the desired capacity recovery time. To simpliy our numerical analysis presented later, we consider the discretization o this probability distribution unction by introducing n time intervals, each associated with a probability p i (i = 1,...,n). The airport PAAR during the whole GDP is a ixed value. Moreover, the PAAR ollows a discrete distribution δ, with

3 Journal o Advanced Transportation 3 Flights already airborne at the ile time are not to be delayed File time Ground delay Start time GDP time o duration End time STD CTD STA CTA Figure 1: Illustration o key GDP time parameters. Objective unction w 1 : w 2 =α α = 0.2 α=1 α=5 0 α=10 11:45 11:00 11:30 12:00 12:30 13:00 13:30 14:00 File time Figure 2: Objective unction values corresponding to dierent ile times. m possible values A i (i=1,2,...,m), each with a probability p j (j=1,2,...,m). 3. Optimal GDP Key Parameter Model 3.1. Model Description. In a simpliied and ideal situation, each ground delay time slot receives maximum utilization, and hence the total delay time experienced by all lights is a ixed value; this is known as the principle o conservation o total delay time. Thereore, in the determination o GDP parameters, the minimum total delay time is not taken as the objective; instead, this paper considers the weighting o various delay indices and equity or delay allocation in the ormulation o the objective unctions. The announcement o GDP at the ile time takes place beore its implementation. This paper considers an optimal ile time model and proposes an integer linear programming approach. On the other hand, the end time and distance are simultaneously optimized in a single problem, instead o sequentially, in order to maximize the eectiveness o the resulting GDP strategy. The overall optimization problem or the GDP key parameters consists o two parts: the optimal ile time problem and the joint end-time-and-distance problem. The procedures proposed in this paper can be illustrated as ollows: (I) With the GDP start time known, based on the probability distribution o the airport capacity recovery time,wecalculatethelyingdistancesoallrelevant lights and select the largest distance as the GDP distance and the latest airport capacity recovery time asthegdpendtime.thesetemporaryvalueswillbe optimized in Step (III). (II) The optimal GDP ile time is computed according to the model presented in Section 3.2, with the GDP end timeanddistanceromstep(i)astheinputvariables. (III) With the optimal GDP ile time rom Step (II), compute the optimal GDP end time and GDP distance based on the joint optimization model presented in Section 3.3. Ourmodelisbasedontheollowingassumptions: (i) The uncertainty in airport capacity is expressed by the AAR uncertainty and AAR recovery time uncertainty, with the corresponding probability distribution known. (ii) The processes o AAR reduction and AAR recovery are instantaneous. (iii) The aircrat s light time rom the departure airport to the destination airport is certain and known GDP File Time Model. The optimal GDP ile time problem is conceived by weighing the total airborne delays and the total unnecessary delays Variable Deinition. We outline the main variables and their notations as ollows: t :GDPiletime T c : GDP cancellation time ξ: probability distribution o GDP cancellation time δ: probability distribution o airport PAAR values

4 4 Journal o Advanced Transportation E ξδ : the expectation over the joint probability distribution o GPD cancellation time and PAAR T ξ : the duration o GDP, which is a random variable that depends on ξ and consists o several time intervals with the length o ΔT, that is, T ξ = t(ξ) 1, t(ξ) 2,...,t(ξ) N }, the irst time interval beyond T ξ being T N+1, with ininite capacity (The ininitecapacity assumption is widely adopted in the literature o GDP.) C δ : the airport PAAR value, which is a random variable with distribution δ w i : the weights assigned to various objective unctions in the optimization problem In addition, ive auxiliary variables c t(ξ),e t(ξ),d t(ξ),g t(ξ),and a t(ξ) are deined to express constraints associated with light controls: t(ξ) = 1 i light arrives at the airport within t (ξ) duetogdp 0 otherwise, c t(ξ) = 1 i light is exempted and arrives at the airport within t (ξ) 0 otherwise, e t(ξ) = 1 i light is not exempted and arrives at the airport within t (ξ) 0 otherwise, d (1) t(ξ) = 1 i light executes ground holding within t (ξ) 0 otherwise, g t(ξ) = 1 i light executes airborne holding within t (ξ) 0 otherwise. a Objective Function. The multiobjective o the optimization problem is expressed as the weighted sum o the expectation o the total airborne delays and the total unnecessary delays: min Z(t,ξ,δ)=w 1 E ξδ F (ξ, δ)} } +w 2 E ξδ U t (ξ, δ)} } }}. (2) F } }} A t In (2), E ξδ F A t (ξ, δ)} and E ξδ F U t (ξ, δ)}, respectively, represent the total airborne delay time and the total unnecessary delay time o all the lights when the GDP ile time is t, the probability distribution o cancellation time is ξ, and the probability distribution o airport PAAR is δ. Here the unnecessary delay U may be expressed in terms o the ground delays or lights executing ground holding. In case o early cancellation o GDP, the part o the ground delay that cannot be recovered is called unnecessary delay: U min ( = T c ETD, CTD ETD, CTA T c ) i ETD <T c < CTA 0 otherwise. (3) Here, ETD,CTD,andCTA denote the quantities corresponding to the light (see the list o Acronyms) Constraints c t(ξ) g t 1(ξ) + g t(ξ) = d t(ξ), (4) F F F F c t(ξ) + e t(ξ) + a t 1(ξ) a t(ξ) =C δ, F F F F t T s, F, (5) (6) A t (ξ, δ),ut (ξ, δ) 0, (7)

5 Journal o Advanced Transportation 5 2 i=1 w i =1, w i (0, 1). Constraint (4) states that each light can perorm exactly one landing within the possible GDP cancellation time; (5) represents airport capacity constraint; (6) means that the GDP ile time is earlier than the GDP start time; (7) is simply the nonnegativity constraint or the objectives; and (8) speciies conditions to be satisied by the weights. This problem is ormulated as a single-objective integer linear program, which is a widely considered mathematical optimization ormulation in ATFM [14]. The integer linear program can be readily solved by standard solvers such as CPLEX Joint GDP End-Time-and-Distance Model. The joint endtime-and-distance model incorporates unnecessary delay, total airborne delay, and average ground delay to measure the eiciency o GDP and, meanwhile, takes airline equity and Air Traic Control (ATC) risks into consideration Deinition o Variables. The ollowing additional notations are deined based on those presented in Section 3.2.1: (8) t e :GDPendtime s: distance that deines the range o exemption V A : the variance o light delays used to measure light equity V F : the variance o average ground delay o airlines, which measures airline equity k: ATC risk control coeicient p: ATC risk penalty actor used to control ATC risks during the operation o GDP c i : regulatory actor used to balance the weights o GDP eiciency term, equity term, and ATC risk term F m : maximum number o airborne holding aircrat ater the GDP end time B: capability parameter or ATC to tackle GDP extension, which can be expressed as 1 i the number o exempted A/C exceeds ATC capacity threshold within extended GDP time rame and 0 otherwise Objective Function min E ξδ c 1 (w 1 F A t e,s (ξ, δ) +w 2 ( F U t e,s (ξ, δ) +Mt e,s F (ξ, δ))) +c 2 (V t e,s F (ξ, δ) +Vt e,s A (ξ, δ)) +c 3 (e k Fte,s M (ξ,δ) +pb(ξ, δ)) } } }. (9) In (9), E ξ,δ F A t e,s (ξ, δ), E ξδ F U t e,s (ξ, δ), E ξδm t e,s F (ξ, δ)}, E ξδ V t e,s F (ξ, δ)}, E ξδv t e,s A (ξ, δ)}, and Ft e,s M (ξ, δ), respectively, represent total airborne delay o all lights, total ground delay time, average ground delay, standard deviation o ground delays o all nonexempt lights, standard deviation o total ground delays o the airlines, and maximum number o airborne holding aircrat ater GDP end time, given that the GDP end time is t e,distanceiss,and probability distributions o the cancellation time and airport PAAR are ξ and δ, respectively. The three main terms in the objective unction, respectively, represent eiciency, equity, and ATC risk Constraints c t(ξ) g t 1(ξ) + g t(ξ) = d t(ξ), (10) F F F F c t(ξ) + e t(ξ) + a t 1(ξ) a t(ξ) =C δ, F F F F (11) t e T s, (12) 0 s S max, (13) A t e,s 3 i=1 2 i=1 (ξ, δ),ut e,s (ξ, δ),mt e,s F (ξ, δ),vt e,s F (ξ, δ),vt e,s A (ξ, δ), F t e,s M (ξ, δ) 0, (14) c i =1, c i (0, 1), (15) w i =1, w i (0, 1), (16) k 0; pis arbitrarily large, (17) where (10) expresses that each light can perorm exactly one landing within the possible GDP cancellation time, (11) denotes airport capacity constraint, (12) and (13) describe constraint on the scope o decision variables, (14) expresses the nonnegativity constraints or the objectives, (15)-(16) speciy the constraints or the weights, and (17) expresses constraints on the risk control coeicient and assigns higher penalty coeicient to ATC s capability o dealing with extended ground delay. Compared to the optimization problem (2), (4) (8), the joint end-time-and-distance problem described above is ar more complex due to its nonlinear objective and constraints. Driven by the need or ast computation or near-real-time operation, metaheuristic methods (e.g., genetic algorithm) are employed below to allow a lexible trade-o between optimality and computational eiciency [15 19].

6 6 Journal o Advanced Transportation Solution Algorithm. In order to meet the requirement o real-time operation, a highly eicient solution algorithm is needed to balance between computational burden and solution quality. In this paper we employ the genetic algorithm tocomputeoptimalsolutionsorthegdpendtimeand distance. (a) Coding Strategy. According to constraints (12) and (13), mapping-based binary coding is selected or this model [20]. The coding is designed as ollows: the combination o GDP end time and distance makes up each chromosome, or example, X 1,X 2,...,X n,owhichx i =(x i1,x i2 ). The chromosome genic value x i1 represents time to airport capacity recovery (in minutes), and x i2 denotes the distance (in km), that is, the radius o the geographical area. The coding mode is X=(x 1,x 2 ) (18) B 11 B 12 B 1p1 B 21 B 22 B 2p2 in which B ij (j = 1,2,...,n i ) is a sequence o binary string codes associated with integer x i (i = 1, 2), andregionp i o each x i is coded as ollows. Let integer x i (i = 1, 2) [0, M i ],wherem i is actorized according to the ollowing pseudocode: do while n 0 =0; x=m k ; p = 0 p=p+1 n p = int [log 2 (x+1)] x=x 2 n p +1 x>0 The p i integers generated rom the algorithm above satisy (19) M i = (2 n 1 1) + (2 n 2 1) + +(2 n p 1), (20) which means that M i is the sum o p i integers. This coding mode can eectively resolve common issues, such as invalid codes and low accessibility to coding space o integer decision variables, and improve the perormance o the genetic algorithm. (b) Fitness Function. With a given itness unction, the genetic algorithm may evaluate the strength and weakness in the solutionprocess,basedonwhichchoicesontheindividuals can be made. Since the objective unction o the problem is to be minimized, the itness unction is adopted as ollows: F((t)) = c max (t) (t) <c max, 0 (t) c max, where c max is the estimated maximum value o ( ). (21) (c) Selection o Crossover and Mutation. Theselectionoperation adopts optimal conservation strategy. Survival o the ittest applies to the remaining individuals with roulette wheel Table 1: Probability distribution o airport capacity recovery time ξ. Airport capacity recovery time Probability o occurrence 17: : : : : : : : : Table 2: Probability distribution o airport PAAR δ. Airport PAAR Probability selection in light o their itness. The model depends on a two-point crossover mode or the crossover o chromosomes; speciically, we randomly select two chromosomes and two crossover points according to the crossover probability. We then interchange the binary codes o the chromosome between the two crossover points. Based on the coding mode o this algorithm, the algorithm or mutation operation is to employ two-point basic bit mutation or chromosome genes, namely, to select the positions o two genes at random and conduct nonoperation to the value. 4. Simulation Study In this section we conduct a case study o the proposed GDP strategy and its key parameters. Real data rom a certain day o operation at Guangzhou Baiyun International Airport were used or the simulation o GDP, and these include actual light schedule. A hypothetical weather condition is assumed and causes the meteorological department to predict airport capacity reduction rom 14:00 to 18:00, and 104 lights in total are aected. According to the route segment data in National Aeronautical Inormation Publication (NAIP), the light distance is the sum o distances traveled along each route segment in the planned route in the iled light plan (FPL) and the route distance o arrival and departure. Airport capacity is uncertain during the implementation o GDP. The desired airport capacity recovery time is 18:00 based on the weather orecast, and we assume that the airport capacity recovery time ollows a normal distribution centered at the desired recovery time 18:00, with a standard deviation o 20 minutes [21]. The discrete probability distribution o airport capacity recovery time or a 15-minute time resolution isobtainedasshownintable1.theprobabilitydistribution o airport PAAR during airport capacity reduction period is shown in Table 2. We note that both o these distributions are only illustrative and may not represent the real-world

7 Journal o Advanced Transportation 7 situation. However, they are used here simply to demonstrate the solution procedure and can be easily adjusted with speciication rom real-world dataset. Slot allocation is conducted with Ration by Distance (RBD) algorithm [22] to simulate GDP operation Result o File Time Optimization. In the simulation, the latest possible cancellation time or GDP end time is set to be 19:00 with a distance o 4000 km. The easible ile time is between0and180minutesaheadothegdpstarttime.the objective unction values o the optimal ile time problem are calculated or dierent choices o the ile time; the results are shown in Figure 2. α in Figure 2 is the ratio o the two weights in the objective unction, that is, w 1 /w 2 ; see (2). It relects the tradeo between partial airborne delays and unnecessary delays. Larger values o α conorm to the actual operation when saety is o top priority. As can be seen rom the igure, all the curves attain their minimum values when the GDP ile time is 11:45, namely, 135 minutes beore the GDP start time Result o Joint End-Time-and-Distance Optimization (1) Weighting Parameters. The paper adopts multiscenario analysis to assess the optimal solution with a range o choices o the weighting parameters. The parameter setting or the objective unction in each scenario is shown in Table 3 (see (9) or the deinition o these parameters). Here, we make note o the act that experience indicates that the total airborne delay ranges between 0 and 1200 minutes and unnecessary delay time between 0 and 700 minutes, with average delay between 0 and 120 minutes. Moreover, ater the GDP end time, the maximum number o aircrat held in the air ranges between 0 and 14, and the binary parameter or ATC to handle delay is 0 or 1. Given this background inormation, we select the relative weights in Table 3, the ATC risk control coeicient k = 0.5, and the risk penalty coeicient p = 1000, such that the individual weighted objectives in (9) are on the same numerical scale to represent them with balance in the weighted sum, while allowing a range o tweaks to interpret the sensitivity o the overall objective. (2) Solution and Comparison. The optimal GDP end time and distance in the 16 scenarios are obtained by solving the optimization model rom Section 3.3 and presented in Table 4. Among all the solutions in Table 4, the earliest end time is 18:16, corresponding to Scenarios #10 and #14, which are balance scenarios with high weight (c 1 )giventotheeiciency terms (i.e., delays) and low weight (c 2,c 3 )ortheequity terms and the ATC risk terms. Thus, the balance scenarios emphasizing eiciency can yield relatively early GDP end times.amongallthesolutions,theourlatestendtimesare rom Scenarios #1, #2, #3, and #4. In these our scenarios, it is consistent that the airborne delay receives higher priority (weight) than the ground delays. In the rest o the solutions, balance scenarios with later end times correspond to #8, #12, and #16, which are scenarios with the highest weight or the Table 3: Weighting parameters. The numerical values shown are relative weights or the ease o presentation and interpretation. The actual weights used in the model satisy (13) and (14). Scenario number Parameter setting 1 w 1 : w 2 =10: 1 c 1 : c 2 : c 3 =1: 1 : 1 2 w 1 : w 2 =10: 1 c 1 : c 2 : c 3 =5: 1 : 1 3 w 1 : w 2 =10: 1 c 1 : c 2 : c 3 =1: 5 : 1 4 w 1 : w 2 =10: 1 c 1 : c 2 : c 3 =1: 1 : 5 5 w 1 : w 2 =5: 1 c 1 : c 2 : c 3 =1: 1 : 1 6 w 1 : w 2 =5: 1 c 1 : c 2 : c 3 =5: 1 : 1 7 w 1 : w 2 =5: 1 c 1 : c 2 : c 3 =1: 5 : 1 8 w 1 : w 2 =5: 1 c 1 : c 2 : c 3 =1: 1 : 5 9 w 1 : w 2 =1: 1 c 1 : c 2 : c 3 =1: 1 : 1 10 w 1 : w 2 =1: 1 c 1 : c 2 : c 3 =5: 1 : 1 11 w 1 : w 2 =1: 1 c 1 : c 2 : c 3 =1: 5 : 1 12 w 1 : w 2 =1: 1 c 1 : c 2 : c 3 =1: 1 : 5 13 w 1 : w 2 = 0.2 : 1 c 1 : c 2 : c 3 =1: 1 : 1 14 w 1 : w 2 = 0.2 : 1 c 1 : c 2 : c 3 =5: 1 : 1 15 w 1 : w 2 = 0.2 : 1 c 1 : c 2 : c 3 =1: 5 : 1 16 w 1 : w 2 = 0.2 : 1 c 1 : c 2 : c 3 =1: 1 : 5 Table 4: Optimal solutions under various balance scenarios. Scenario number End time Distance 1 18: : : : : : : : : : : : : : : : ATCriskterm.ItcanbeseenthatthepursuitolowerATC riskmayleadtomorelightsinvolvedinthegdp,which tends to postpone the GDP end time. The minimum optimal distance in the table is 2146, corresponding to the balance Scenario #14, which is also the scenario with the earliest optimal end time. The distances in the rest o the scenarios do not exhibit discernible pattern with dierent weights. For a more detailed comparison, we ocus on three dierent GDP scenarios/strategies. The irst one is the actual implementation corresponding to the real-world operation.

8 8 Journal o Advanced Transportation Actual 50.8% 14.7% Proposed model 27.8% 96.1% Ideal condition Actual 48.3% 11.5% Proposed model 100% 23.8% Ideal condition % o unnecessary delay reduction % o total ground delay reduction Total ground delay Figure 3: Beneits o the proposed model in terms o delay reduction. % o A/C number reduction or unnecessary delay % o A/C number reduction or ground delay Number o aircrat or ground delay Figure 4: Beneits o the proposed model in terms o ground delay lights. The guidelines o US ATFM suggest GDP end time to be 2 hours ater the predicted airport capacity recovery time [23]. Due to the lack o proper GDP data analysis conducted in China, the latest capacity recovery time 19:00 and the maximum light distance are taken as the reerence value or the actual GDP implementation parameters. The second scenario is related to our proposed optimal GDP model, and we select the optimal strategy under Scenario #8 (see Table 4) because o the high weight o airborne delay and ATC risk, which better relects the balance choice o low management unit in the actual GDP implementation. As the third scenario, we consider the ideal condition, under which the predicted airport capacity recovery time is the actual recovery time, so the desired GDP end time is the predicted airport capacity recovery time. The results o the simulation runs involving GDP with parameters rom actual reerence, the proposed model, and ideal conditions are shown in Figures 3 and 4. Compared with the real-world deployment o GDP, the GDP with the optimized parameters obtained rom this paper reduces unnecessary delay and ground delay by 50.8% and14.7%,respectively,thenumberoaircratthatneedto execute ground delay by 11.5%, and the number o aircrat exempted rom unnecessary delay by 48.3%. The case with the idealized situation makes these reductions even more pronounced, but this is under the restrictive assumption that the realization o the uncertain parameters coincides with their predictions. It is clear that the model described in this paper can eectively reduce unnecessary ground delay time, decrease the overall ground delay, reduce the number o lights with unnecessary delays, and improve the GDP airport capacity and eiciency o ATFM, while at the same time conining risk within an acceptable level. 5. Conclusion This paper proposes a model and optimization procedure or the optimal GDP key parameters under uncertain airport capacity. The key parameters o interest are ile time, end time, and distance. Unlike existing studies on GDP, this paper explicitly computes the optimal GDP ile time, which could signiicantly reduce the delay times. We also propose a joint GDP end-time-and-distance model and solve it using genetic algorithm. The proposed models, eatured by their lexibility and autonomy, take into account not only GDP operation eiciency, but also light equity, airline equity, and ATC saety risks. Simulation study o the proposed GDP strategy with real light data has validated the eectiveness o the model. As uture research, we will conduct more detailed sensitivity analysis to understand the trade-os among various objectives in the optimization problem. This also includes the sensitivity o the solution to the AAR at the airport. In addition, data-driven robust optimization techniques [24, 25] will be considered to treat situations where the a priori distributions o the capacities are unknown. Finally, we will ocus on uniied collaborative optimization procedure with multiple decision variables. Acronyms ATFM: AirTraicFlowManagement CDM: Collaborative Decision Making CTA: Controlled Time o Arrival CTD: Controlled Time o Departure ETD: Estimated Time o Departure GDP: Ground Delay Program STA: ScheduledTimeoArrival STD: ScheduledTimeoDeparture. Competing Interests The authors declare that there is no conlict o interests regarding the publication o this manuscript. Reerences [1] M. Hu and X. Xu, Ground-holding strategies o ATC low control, Journal o Nanjing University o Aeronautics & Astronautics,vol.26,supplement,pp.26 29,1994.

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