In actual operation, the daily flow rate for the route segments are extremely high in China which are presented in Fig 3. However, this rate in Europe and America is limited to If traffic surpasses the threshold value, the responsible air navigation service provider will activate alternate parallel routes or divert air traffic [ 1 ]. This extremely congested route network brings huge uncertainty to arrival management.
Particularly the congestion often appears in the terminal areas, which makes air carrier always focus on the earliest takeoff time due to flight punctuality consideration. It means even though there are two ways to achieve flight punctuality, which are departure on schedule and arrival on schedule. The former is more preferred than the latter. Through the above analysis, a model has been developed in order to deal with changes in the operating factors caused by restricted time period. This will be covered in detail in Section of Formulation.
In this section, a mathematical model is developed to deal with the DSP with newly changes illustrated in Section of Problem description. For facilitating the statement, as well as helping readers to understand the context better, the notations used throughout this paper are listed as follows in prior. The objectives of the current problem are stated as follows. Objective O 1 focuses on efficiency which aims to reduce the total departure flight delay for the entire time span. However, during the restricted time periods, objective O 1 may lead to huge delay in certain departure flows due to their combination and sharing a common accepting rate.
It is indispensable to maintain a reasonable equity level among them. Thus, objective O 2 is designed to minimize the delay differences among diverse directions for restricted time periods.
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The constraints of the problem are as follows. Constraint 3 ensures that no flight should take off before it is ready. Constraint 4 prevents the aircraft from being moved further in the schedule and received a patch of huge delay, the latest acceptable CTOT is limited within 2 times of predefined delay statistical standard. The first flight is assumed to take off at its requested take-off time by Eq 5. Employing a pre-setting number k represents the Maximum Position Shifting MPS , Constraint 6 ensures some degree of fairness by restricting the final schedule to deviate significantly from the FCFS schedule.
Constraints 7 and 8 ensure flights pair satisfy the wake turbulence separation minima and Minutes-In-Trail separation which form different and same departure flows respectively.
To deal with the accepting rate combination of direction flows analyzed in Section of Problem description, besides Constraints 3 to 8 , two additional constraints are needed. Constraints 9 and 10 ensure the flights from restricted departure flows meet pre-setting takeoff separation requirement between the later and former aircraft in the departure sequence during restricted time period. When the restricted time period is finished, flight j is the first flight after it. Constraint 11 ensures flight j has opportunity to use the first time after the end of the restricted time period.
Since flight punctuality is a performance evaluation index for air traffic management, it is treated as Constraint 12 which aims to ensure the proportion of non-delayed flights no less than a pre-setting value. Beside MIP, dynamic programming DP serves as another alternative to formulate air traffic scheduling problem, e. For ASP, such a triangle inequality holds readily since a landing aircraft is only restricted by the wake turbulence separation of consecutive aircraft.
In Balakrishnan and Chandran [ 22 ], and Rathinam et al. Actually, for DSP, such a triangle inequality does not hold since, beside the wake turbulence separation, a departing aircraft is additionally restricted by the Minutes-In-Trail separation which depends on all previous departed aircrafts. TS is a metaheuristic approach designed to find a satisfactory solution of combinatorial optimization problem which is first introduced in Glover [ 29 ]. Since then it has been applied to various problems. Different from heuristics which are known to be too problem dependant, metaheuristics are more generalized approaches able to solve larger problems better and faster [ 30 ].
Previous work Atkin et al. According to the model and the problems in the Section of Problem description, the following algorithm procedure is designed. Get an initial solution X now as described in Section of Input data and parameters. In this section, we apply our model and algorithm to an actual operation scenario in order to explore the potential benefits.
It is necessary to note that PEK is surrounded and thus partly interfered by three airports, i. During the peak hours of PEK, these three airports are restricted in varying degrees. In accordance with Section of Problem description and without loss of generality, this section still chooses TJN as the low-priority counterpart of high-priority PEK to perform the case study.
This paper adopts a sequence in order of ascending Revised Estimate Time of Departure RETD which includes starting and inbound delay as initial solution.
The motivation is to fully capture the impact of pre-departure delays. The main reasons for flight delay in China in are airline itself, air traffic flow control and weather impact, accounting for In addition, aircraft mechanical failures and inbound delay are the main reasons of airline delay. In spite of recovery measures, very limited actions can be taken in the event of a shortage of airlines transport capacity.
Therefore, airline itself has a significant impact on flight delay in China which can not be ignored. The procedure for generating RETD is described as follow. There are a total of flights that are scheduled to depart from TJN during that day. The flights from to are selected, altogether flights as the input in experiment. There are two kinds of departure in our schedule, one is the starting departure flight which conducts the first flight segment on the flight cycle and no preceding flight before.
The other is the connection departure flight which situates in the middle of flight segment rotation, the inbound delay of preceding flight may influence the departure of succeeding flight. If there is no starting delay for starting departure flight i , it will depart according to their original schedule time, thus For those connection departures, the different inbound delay of preceding flights will result in ground service duration change, thus 14 Fricke and Schultz [ 31 ] use 24, flight operations of A data from DLH to explore the relationship between inbound delay and turnaround duration time.
The statistical results indicate that the mean value of turnaround time decreases with inbound delay increases. The detail results are introduced as follow:.
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The detail requirement is presented in Table 2. The average taxi out time of Tianjin airport is In our experiment, we assume that taxi out time equals to taxi in time. Thus, the revised estimate time of departure is generated which can represent the departure demand shifting. Table 3 shows the statistical data of departure flights for each departure flow during the period. According to Civil Aviation Air Traffic Management Rules of China, the minimum time separation between two consecutive departure flights shall comply with wake turbulence separation minima.
The detail requirement is shown in Table 4.
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The operation log records 3 restricted time periods which are , and on that day. During those restricted time periods, D5, D6 and D7 will be combined and share a common accepting rate for Beijing area control center.
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The detailed required time separations for different departure flows according to flight destination are listed in Table 5. The predetermined number of MPS is denoted as k. In contrast to the problems faced by Atkin et al. Fig 4 shows that the hourly number of departures are even less than 10 in some time periods. In addition, Minutes-In-Trail separations in busy traffic direction flows are relatively large. Therefore, moves the flight far away from its RETD position will exceed the delay adjustment range and k is set to 3 in our experiment. The weight of each direction is determined by traffic volume.
A day operation data of October is adopted. The statistics of the proportion of traffic flow in each direction is presented in Table 6. The experiment result on the RETD schedule generating shows that the demand shifting has occurred. Fig 4 presents the detail departure demand distributed for each hour, blue column and red column represent departure demand based on ETD and RETD respectively. Fig 5 displays the trend of individual optimal solutions for the flight delay and the direction average delay difference in restricted time periods corresponding to different iterative steps.
As the iterative step continues to increase, the individual feasible solution approaches the optimal direction and searches for the Pareto optimal solution in the decision space.
The two objective values from the initial minutes and The overall flight delay is minutes reveals that the preflight delays have a great impact on the result of inefficient slot utilization. Our selected case data of TJN exist an average of The mitigation practice on the one hand lies in airline to improve transportation capacity and flight supportability. On the other hand, air traffic management unit schedule arrangement should be based on the operation characteristics of close located airports with different priority to collaboratively reduce scheduled delay.
As observed in Fig 6 , the algorithm has searched the Pareto optimal solution when the stop condition is reached. The frontier curve is decreasing, meaning that as delay-saving reaches a higher level, more equity needs to be given up in order to achieve equal improvement in efficiency. Therefore, Air traffic managers can make a comprehensive trade-off between efficiency and equity based on the performance characteristics of the Pareto optimal solution set.
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