Cosine dynamic push-out rate control method considering airport busy degree

Abstract

The invention relates to the technical field of airport ground management and control, in particular to a cosine dynamic push-out rate control method considering airport busyness, a cosine function is introduced to dynamically adjust the push-out rate of a multi-runway airport, and when the queuing length of a taxiway is close to a threshold value, the push-out rate is not suddenly reduced to zero, but is attenuated in a progressive mode, so that the airport busyness is reduced. The push-out rate is in a non-linear decreasing trend along with the increase of the queuing length, so that extreme congestion is avoided, and the flight push-out continuity is ensured; in addition, taxiway waiting time is converted into parking space waiting time, the airport resource utilization rate is balanced, and the taxiing waiting time of departure flights is effectively shortened; meanwhile, based on a time-phased mechanism of departure and arrival demand changes, a push-out control threshold is dynamically adjusted, taxiway capacity and push-out demands under the condition of self-adaptive matching of multiple runways can be realized through time division, extra time loss caused by strategy stiffness is reduced, and delay distribution is more uniform through a dynamic adjustment mechanism.

Description

Technical Field

[0001] The invention relates to the technical field of airport ground management and control, and in particular to a cosine dynamic push-out rate control method considering airport busyness. Background Art

[0002] With the rapid development of the civil aviation industry, the gap between the growing demand for flights and the limited available airspace is widening, resulting in frequent flight delays. Therefore, improving the operational management efficiency of existing resources has become the key to improving flight punctuality. In fact, the phenomenon of queuing during flight takeoff is one of the main reasons for low operational efficiency, high takeoff costs and large amounts of exhaust emissions.

[0003] In response to this problem, relevant scholars have conducted research on outbound flight pushback. Existing pushback control methods include pushback time slot allocation, pushback sequence optimization, and pushback rate control. For example, Chinese patents with application publication numbers CN117854331A and CN119479380A, etc. In addition, relevant research on pushback rate control has not yet been verified in a multi-runway system.

[0004] For random and dynamically complex airport environments, existing research has shown certain limitations. For example, the DPC strategy relies on a static design with a fixed threshold, which makes it difficult to dynamically adapt to complex operating conditions. When the queue length approaches the threshold, taxiway congestion may aggravate delays, which requires a more flexible dynamic adjustment mechanism to achieve multi-objective collaborative optimization of the departure process. Summary of the invention

[0005] The purpose of the present invention is to provide a cosine dynamic pushback rate control method considering the busyness of the airport, dynamically adjust the pushback rate of a multi-runway airport by introducing a cosine function, optimize the limitations of a traditional threshold control strategy, adaptively match the taxiway capacity and pushback demand in a multi-runway situation, and ensure the continuity of flight pushback.

[0006] To achieve the above object, the present invention provides a cosine dynamic push-out rate control method considering airport busyness, comprising the following steps:

[0007] Step 1: Obtain historical departure data and process it;

[0008] Step 2: Construct a cosine dynamic push-out control model;

[0009] Step 3: Divide the busy hours throughout the day;

[0010] Step 4: Obtain the optimal taxiway threshold set;

[0011] Step 5: When the termination condition is met, output the flight optimization sequence and cost value.

[0012] Optionally, in the process of constructing the cosine dynamic push-out control model in step 2, it includes formulating a cosine dynamic push-out rate strategy, confirming an objective function, and selecting constraint conditions;

[0013] The mathematical expression of the cosine dynamic push-out rate is as follows:

[0014]

[0015] Among them, when N(k) is the k-time period corresponding to the N value, the taxiway waiting queue obeys the capacity-constrained M / M / S / N queuing model, where S is the number of service stations, expressing the number of runways; and N is the taxiway queue length threshold.

[0016] Optionally, in step 2, the objective function is set to minimize the taxiway waiting cost and the parking stand occupancy penalty, and the expression is:

[0017]

[0018] Wherein, C represents the departure cost defined in the present invention; F D Refers to the departing flight collection; represents the fuel consumption cost per minute, in units of RMB per minute, and E[W] is the taxiing waiting time W of the i-th flight. i ; G i represents the flight gate waiting time caused by the introduction of restrictions; β represents the penalty coefficient.

[0019] Optionally, the agreed conditions in step 2 include a gate occupancy constraint, a pushback interval constraint, and a taxiway queue length constraint. The gate occupancy constraint is set to a maximum value of 30 minutes according to operating rules. The pushback interval constraint requires that consecutive flights meet the average runway service rate when performing pushback. The taxiway queue length constraint is set to a range of N(k) in the kth time period of [1,30].

[0020] Optionally, the method process for dividing the busy hours throughout the day in step 3 includes the following steps:

[0021] Step 3.1: Data preprocessing: Process the historical data of inbound and outbound flights;

[0022] Step 3.2: Initialize parameters and define the number of clusters;

[0023] Step 3.3: Iterate and optimize to obtain the clustering result of the time period number under the above definition, that is, the time period division result; return to step 3.2 to redefine the time period number and obtain the result again until the initial setting of the time period number is met;

[0024] Step 3.4: Cluster effect evaluation. Evaluate the results obtained for each number of clusters above, determine its tightness with the input data, and obtain the optimal number of time periods.

[0025] Step 3.5: Smoothing processing. Expand and process the results obtained above, and obtain the specific time intervals corresponding to each time period.

[0026] Optionally, in the process of obtaining the optimal taxiway threshold in Step 4, use the Markov chain to optimize the genetic algorithm to obtain the departure control thresholds corresponding to different time periods under global optimization, including the following steps:

[0027] Step 4.1: Define the time period division, that is, k time periods correspond to specific time points, and initialize the genetic algorithm parameters.

[0028] Step 4.2: Randomly generate the genetic algorithm population. The initial population consists of multiple groups of threshold solutions. Each group of solutions contains the thresholds for k time periods, and each threshold is randomly selected within a predefined range and adjusted during subsequent optimization.

[0029] Step 4.3: Perform independent Markov chain iterations on the thresholds for each time period.

[0030] Step 4.4: Make a judgment based on the current queuing length n of the taxiway, and arrange flights to enter the taxiway waiting queue.

[0031] Step 4.5: Calculate the overall fitness of each group of threshold solutions according to the output of the Markov chain.

[0032] Step 4.6: Generate a new population through selection, crossover, and mutation, and gradually optimize the threshold solutions.

[0033] Step 4.7: When the stop condition is met, that is, the algorithm converges or reaches the maximum number of iterations, output the optimal multiple time period threshold solutions.

[0034] The present invention provides a cosine dynamic departure rate control method considering airport busyness, which introduces a cosine function to dynamically adjust the departure rate of a multi-runway airport. When the queuing length of the taxiway approaches the threshold, the departure rate does not suddenly drop to zero, but decays in an asymptotic manner, making the departure rate decrease non-linearly with the increase of the queuing length. This not only avoids extreme congestion but also ensures the coherence of flight departures. In addition, it converts the taxiway waiting time into the apron waiting time, balances the airport resource utilization rate, and effectively reduces the taxiing waiting time of departing flights. At the same time, based on the time period mechanism that changes with the departure and arrival demands, it dynamically adjusts the departure control threshold. Through time period division, it can achieve adaptive matching of the taxiway capacity and departure demand in the case of multiple runways, reducing the additional time loss caused by rigid strategies. The dynamic adjustment mechanism of the present invention makes the delay distribution more uniform. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0036] Figure 1 It is a schematic diagram of the step flow of a cosine dynamic push rate control method considering airport busyness according to the present invention.

[0037] Figure 2 It is a schematic diagram of the policy push rate curve of the cosine dynamic push control model according to the present invention.

[0038] Figure 3 It is a schematic diagram of the policy state transition of the cosine dynamic push control model according to the present invention.

[0039] Figure 4 It is a schematic diagram of the execution flow of the busy period division method according to the present invention.

[0040] Figure 5 It is a schematic diagram of the execution flow of the Markov chain optimized genetic algorithm used to solve the push control threshold according to the present invention.

[0041] Figure 6 It is a schematic diagram of the inbound flight demand in a specific embodiment of the present invention.

[0042] Figure 7 It is a schematic diagram of the outbound flight demand in a specific embodiment of the present invention.

[0043] Figure 8 It is a schematic diagram of the iterative process of the optimized genetic algorithm in a specific embodiment of the present invention.

[0044] Figure 9 It is a schematic diagram of the time comparison of simulating and comparing each push control method in a specific embodiment of the present invention. Detailed implementation manners

[0045] The following will describe in detail the embodiments of the present invention. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0046] The present invention provides a cosine dynamic push rate control method considering airport busyness, including the following steps:

[0047] Step 1: Obtain historical departure data and process it;

[0048] Step 2: Construct a cosine dynamic push-out control model;

[0049] Step 3: Divide the busy hours throughout the day;

[0050] Step 4: Obtain the optimal taxiway threshold set;

[0051] Step 5: When the termination condition is met, output the flight optimization sequence and cost value.

[0052] Please refer to the step flow chart Figure 1 The present invention is further described below in combination with the terms and specific steps in the steps:

[0053] Specifically, the present invention performs fitting clustering on the airport historical data, divides the airport into busy periods, and configures different push-out control thresholds for different periods through an intelligent algorithm.

[0054] In step 2, a cosine-based pushback control model is constructed, and a multi-period cosine-based pushback control (CPC) pushback rate control method is proposed to adjust the pushback probability according to the current taxiway queue status, with the goal of converting the taxiway waiting time into the parking stand waiting time. And with minimizing the taxiway waiting cost and the parking stand waiting penalty as the objective function, the optimal threshold set for implementing all-day pushback control is sought, as follows:

[0055] Step 2.1: The mathematical expression formula for the CPC strategy’s launch rate is as follows:

[0056]

[0057] Among them, N(k) corresponds to the value of N in the k-time period. The field of operations research believes that the taxiway waiting queue obeys the capacity-constrained M / M / S / N queuing model, where S is the number of service stations, which expresses the number of runways; and N is obviously the threshold of the taxiway queue length. The arrival rate of the system corresponds to the flight push-out application rate, and the service rate is the efficiency of runway processing. For the parking stand waiting queue, its arrival rate is inevitable, because the flight departure plan will not change; and its service rate depends on the situation of the taxiway waiting queue. In this regard, for the taxiway waiting queue, the arrival rate λ depends on the cosine push-out control strategy adopted.

[0058] The probability curve is as follows Figure 2 shown.

[0059] Considering the dynamics of the system, assuming that the number of runways (service stations) is S = 2, a Markov state transition diagram is constructed to simulate the behavior of the waiting queue, such asFigure 3 as shown

[0060] Using the principle of birth and death processes, probability equations for state 0 and state n can be established. Among them, the birth and death process transition equation from state 0 to state 1 is as shown in Equation (3). Among them, the system load level ρ is an index to measure the system service capacity and demand capacity, representing the overall load of the system, that is:

[0061]

[0062] π0·λ (0) = μ·π1 (3)

[0063] π1 = π0ρ (4)

[0064] Since the present invention focuses on multi-runway airports, it is assumed that the number of service desks is S≥2. For the service rate, it is assumed to be μ (n) = min(n,S)μ, which means that the derivation process from state 1 to state 2 is different from before, that is:

[0065] π1·λ (1) = Sμ·π2 (5)

[0066]

[0067] From the normal equation it can be obtained that:

[0068]

[0069] The arrival rate of flights entering the taxiway waiting system represents the weighted average arrival rate under all system states, and its expression is:

[0070]

[0071] The expected taxiway queue length, defined as the number of flights queuing on the taxiway waiting to enter the runway in the system, is expressed as:

[0072]

[0073] According to Little's law, the calculation formula for the average waiting time of aircraft in the taxiway queue is:

[0074]

[0075] Since the focus of the present invention is on the taxiway queue, the state transition process of the boarding gate queue will not be elaborated.

[0076] Step 2.2: Objective function:

[0077] In the present invention, it is assumed that the influence of weather and unexpected factors is not considered; the flights launched by the application adopt the first-come, first-served (FCFS) rule, and the launch process is completed by a tractor, without fuel consumption, and the time consumed for launching is ignored; a fixed runway service time is adopted, that is, the influence of the takeoff wake interval of different aircraft types is not considered; and the influence of inbound flights is not considered. To improve the runway utilization rate, the influence of the boarding gate occupancy rate on the apron turnover rate is considered, and the objective function is set to minimize the taxiway waiting cost and the boarding gate occupancy penalty, so as to find the optimal threshold set for implementing the launch control, that is

[0078]

[0079] where C represents the departure cost defined in the present invention; F D refers to the set of departing flights; represents the fuel consumption cost per minute, with the unit of yuan per minute; during the simulation process, E[W] is the taxi waiting time W of the i-th flight i ; Gi represents the boarding gate waiting time of the flight due to the launch restriction; in particular, β represents the penalty coefficient, which is introduced to prevent the boarding gate waiting time from being too long. Research shows that when the boarding gate waiting time reaches t = 30 minutes, the fuel cost and the penalty cost are equal, and when it exceeds, the penalty cost increases exponentially. When the boarding gate waiting time is less than 30 minutes, the penalty cost is lower than the equivalent fuel consumption cost during the same period, but once the boarding gate waiting time exceeds 30 minutes, the penalty cost will increase rapidly due to the delay and exceed the fuel consumption cost during the same period, that is:

[0080]

[0081] Step 2.3: Constraint conditions:

[0082] G i ≤G max (14)

[0083] t i +μ i,i+1 ≤t i+1 (15)

[0084] N min ≤N (k) ≤N max (16)

[0085] Among them, equation (14) represents the boarding gate occupancy constraint. According to the operation rules, G max is set to 30 minutes; equation (15) represents the launch interval constraint, requiring that consecutive flights meet the average runway service rate when performing push-back; equation (16) represents the taxiway queue length constraint, and the range of N(k) in the k-th time period is set to [1, 30].

[0086] The method for dividing peak hours in Step 3 is as follows:

[0087] The first step: Data preprocessing. Obtain the historical data of airport situation characterization indicators

[0088] The second step: Initialize parameters. First, determine the initial number of segments k, that is, the number of clusters in the clustering process, that is, how many groups the data will be divided into. Secondly, initialize the membership matrix. Randomly initialize the membership matrix [u ij , where [u ij represents the membership degree of the data point x i belonging to the clustering center c j . Thirdly, set the fuzzy index m>1, usually taking the value of 2. Among them, the data point x i is a combined data point of multiple indicators.

[0089]

[0090] The third step: Iterative optimization. Calculate the clustering center c j , and update the expression formula of the membership matrix U as shown in Equations (18) and (19), and judge convergence. If the change in the membership matrix is less than the preset threshold ∈, stop the iteration and obtain the period division result; otherwise, return to the previous step.

[0091]

[0092]

[0093] The fourth step: Evaluate the clustering effect. Use the silhouette coefficient to evaluate the clustering quality and verify the rationality of the period division, and adjust the period k. Then return to Step 2, and compare the silhouette coefficients under different k values to obtain the optimal number of periods. Among them, the silhouette coefficient takes into account the compactness and separation degree between samples. For each sample i in the clustering, its silhouette coefficient is:

[0094]

[0095] Among them, a(i) represents the average distance from sample i to other samples in the same cluster, that is, the within-cluster compactness. b(i) represents the average distance from sample i to the samples in the other cluster closest to it, representing the between-cluster separation degree of sample i. The value range of s(i) is between [-1,1]. The overall silhouette coefficient is the average of the silhouette coefficients of all samples, as shown in Equation (23).

[0096]

[0097] Step 5: Smoothing processing. According to the membership matrix U, each time point is divided into the category with the largest membership degree. And combined with the division requirements of the airport's busy periods (such as the minimum period length), the division results are smoothed.

[0098] For the schematic diagram of the whole process, please refer to Figure 4 .

[0099] In the process of Step 4 to obtain the optimal threshold set of the taxiway, the Markov chain optimization genetic algorithm is adopted, and the queue length of the current taxiway is adjusted in real time based on the queuing threshold and variable service rate corresponding to each period.

[0100] The specific implementation is as follows:

[0101] Step 1: Initialize parameters. Define the period division, that is, k periods correspond to specific time points, and initialize the genetic algorithm parameters (population size, crossover rate, mutation rate, etc.). Based on the first-come-first-served (FCFS) principle, all flight push requests are sorted according to their push request times to generate a push request sequence, ensuring that the flight order is processed according to the time priority principle. And initialize the initial value of the queue length, the mean value μ ave , key parameters such as the taxiway capacity in the iterative algorithm.

[0102] Step 2: Randomly generate the genetic algorithm population. The initial population consists of multiple groups of threshold solutions. Each group of solutions contains the thresholds of k periods, and each threshold is randomly selected within a predefined range and adjusted in the subsequent optimization process to maximize the operation efficiency of the airport.

[0103] Step 3: Markov chain loop. Independent Markov chain iterations are performed on the thresholds of each period to evaluate their performance. In each iteration, the Markov chain will update the threshold of the current period and calculate the push control effect of this period according to the push request sequence. When the last flight in the k-1 period cannot be pushed out in this period due to the delay of the previous flight, the system needs to move this flight into the taxiway queue of the next period until the queue length of this period meets the push requirements. This process ensures that the push control strategy can adapt to the dynamically changing flight flow and can cope with emergencies within a certain range. For the taxiway, the flight always enters the overall taxiway waiting queue with a probability of [0.5cosπ(n / N)+0.5], that is, with a probability of 1 - [0.5cosπ(n / N)+0.5] it loses the opportunity to enter the taxiway, resulting in the behavior of waiting at the parking position; for the service rate μ(n), the present invention believes that it should specifically be the minimum safety distance between two consecutive flights. To reflect the effectiveness of the push control strategy, the difference in the wake vortex safety intervals between different aircraft types is set as the mean value of the wake vortex safety intervals under the aircraft type ratio in the example data in this stage, that is, for an airport with r runways, the fixed service rate is set as μ(n) = μave ·r。

[0104] Step 4: Flight sequence loop. For each flight waiting to push back, the system will make a judgment based on the current queuing length n of the taxiway. When the queuing length of the taxiway is less than N, the system uses the CPC method to control flight i. During this process, the setting of the service rate μ(n) is used to calculate the queuing status of the taxiway at each moment, and whether to allow a new flight to enter the queue is determined according to the current queuing situation. When the allowable push-back time interval is greater than or equal to μ(n) and meets the input requirements, then (i + 1) flights are allowed to enter the taxiway waiting queue. Through simulation, the mutual influence between the taxiway capacity and different flight push-backs is evaluated. During the evaluation process, if the calculated G i value exceeds G max , it is directly pushed back.

[0105] Step 5: Fitness calculation. According to the output of the Markov chain, the overall fitness of each set of threshold solutions is calculated, corresponding to the objective function of the model of the present invention. Among them, for each flight push-back request, the optimal taxiway queuing length W, its corresponding taxiway waiting time G, and other parameter values are marked, the cost index CTi is recorded, and the cumulative cost CT under all thresholds is statistically calculated.

[0106] Step 6: Genetic operations. New populations are generated through selection, crossover, and mutation to gradually optimize the threshold solutions. Among them, the goal of the selection operation is to select the threshold solution set with the strongest fitness from the current population. The stronger the fitness of an individual, the more it represents that the solution can meet the optimization goal, so it is more likely to be selected for crossover and mutation. In the crossover operation, two threshold solution sets will exchange part of the gene information to generate a new threshold solution set. Specifically, for each pair of selected parents, the algorithm will randomly select a crossover point, divide the threshold solutions of both into two parts, and then exchange the two parts to generate two new offspring. The mutation operation generates new solutions by randomly changing the threshold of a certain period in the threshold solution set. This operation is usually carried out at a certain mutation rate

[0107] Step 7: When the stopping condition is met, that is, the algorithm converges or reaches the maximum number of iterations, the optimal threshold solutions for multiple periods are output. These solutions represent the threshold parameters that can most effectively control the queuing and push-back requests of the airport taxiway during the optimization process. The finally output threshold solution set is used to guide the runway assignment in the next departure plan to ensure the shortest taxiway queuing time and an efficient flight push process, thereby improving the overall departure efficiency.

[0108] The flowchart is shown in Figure 5 .

[0109] Furthermore, the present invention also proposes simulation embodiments for auxiliary explanation, specifically as follows:

[0110] (1) Data processing and time period division

[0111] The present invention uses MATLAB R2023a for simulation research. Based on the consistency of flight schedules within three months, the flight data of Beijing Capital International Airport from August to October 2013 is analyzed, including flight numbers, scheduled departure times, actual departure times, pushback request times, and actual pushback times. To better divide the peak passenger flow periods at the airport, each day is divided into 96 time windows, each with a length of 15 minutes, and the daily average value of each time window within three months is calculated. As Figure 6 and Figure 7 shown, there is a continuous peak in inbound flights after 8:00 am, with regular fluctuations throughout the day. Similarly, the demand for outbound flights peaks around 8:00 am, decreases between 9 - 11 am, and then remains at a relatively high level. The demand for outbound flights is generally equal to that of inbound flights.

[0112] The fuzzy C-Means (FCM) clustering method is used to divide the airport resource allocation time periods. The present invention determines the optimal number of time periods based on the evaluation of the silhouette coefficient. Referring to relevant research, the range of k is set to [2, 10], and the corresponding silhouette coefficient results are as follows:

[0113] Table 1 Silhouette coefficient values for different k values

[0114] k 2 3 4 5 6 Silhouette coefficient 0.597 0.668 0.643 0.687 0.703 k 7 8 9 10 Silhouette coefficient 0.769 0.878 0.851 0.788

[0115] Among them, the k value shows an overall trend of first increasing and then decreasing. Although there are fluctuations, the optimal value is reached when k = 8. Then, smoothing processing is adopted to determine the corresponding specific time periods as follows: (1) 0:00 - 4:00; (2) 4:00 - 7:00; (3) 7:00 - 9:00; (4) 9:00 - 11:00; (5) 11:00 - 13:00; (6) 13:00 - 17:00; (7) 17:00 - 19:00; (8) 19:00 - 24:00.

[0116] (2) Pushback strategy simulation

[0117] The simulation is carried out with 775 flights throughout the day on November 1, 2013. The present invention focuses on two main takeoff runways at Beijing Capital International Airport: 36L / 18R and 36R / 18L. In the case of dual runways, the service time is determined according to the aircraft type statistics, that is, the single runway service time is 1.43 min. According to the aviation fuel price in the year of data collection, the taxiing fuel cost per unit time for each aircraft is 51.87 yuan / min. The boarding gate queuing waiting penalty coefficient is set to β = 0.245. The population size is set to 100, and the number of iterations is set to 50. The iterative process of the optimized genetic algorithm of the present invention is as Figure 8 .

[0118] The optimal solution is reached at the 25th iteration. The thresholds corresponding to the 8 time periods are N = [14, 18, 4, 9, 10, 9, 10, 11], and the cost is minimized at this time. Then, the departure process is simulated using the uncontrolled method, N-control method, DPC method, and CPC method respectively. Among them, the CPC-01 strategy refers to a single threshold applied throughout the day, while the CPC-02 strategy is the ultimate research focus of the present invention.

[0119] Figure 9 The changing trends of the average taxiway waiting time, gate waiting time, and target cost for each departure control method are shown. The key to the departure control strategy lies in its ability to convert taxiway queue time into gate waiting time. The effectiveness of the departure strategy can be most directly evaluated through time conversion. After implementing the departure strategy, the taxiway waiting time is greatly reduced. Among these strategies, the effects of the DPC and CPC-01 strategies are almost the same because they both feature using a single critical value throughout the day. In both cases, the departure probability gradually decreases from 1 to 0, and the probability is 0.5 when it reaches N / 2. However, the difference between the two is that compared with DPC, when the taxiway queue length is less than or equal to half of the control threshold [0, N / 2][0, N / 2][0, N / 2], the CPC strategy increases the possibility of departure, accelerates the departure process, and reduces the gate waiting time. On the other hand, in the range of [N / 2, N][N / 2, N][N / 2, N], the CPC strategy adopts a more stringent departure strategy. The purpose of doing this is to accelerate the dissipation of the taxiway queue, which helps to effectively reduce the taxiway waiting time. From the perspective of the goal, the CPC strategy is significantly better than the DPC strategy, but from the data perspective, since the averages are compared, the difference is not obvious. In practice, the performance of the CPC strategy is slightly better than that of the DPC. The specific values are shown in Table 2.

[0120] Table 2 Results of each departure control method

[0121]

[0122] Among them, R c represents the percentage of cost reduction, and R w represents the percentage of reduction in taxiway waiting time. Compared with other departure control methods, the CPC method can reduce the departure cost and effectively reduce the waiting time on the taxiway. The Markov chain optimization genetic algorithm proposed in the present invention is used to obtain the N value for each time period under global optimization. At the same time, it is observed that in the 3rd time period, the flight demand increases sharply, resulting in a smaller N value, indicating that the airport ground operation control is more stringent. The difference between the 2nd time period and this time period is that the demands for both inbound and outbound flights are relatively low. In this case, the departure control can be looser, so the result of N is 18.

[0123] Compared with the uncontrolled state, the CPC-02 method reduces the cost by 41.97%, and compared with the DPC method, it reduces the cost by 8.73%. In addition, although CPC-01 and CPC-02 are consistent in terms of the launch rate, their focuses are different. CPC-02 takes into account the ground traffic at the airport on the basis of CPC-01. The ground taxiing volume shows a time peak-valley pattern during the day. Therefore, corresponding launch control thresholds should be set for different busy periods to reflect the flexibility of the strategy. In the time dimension and the target cost dimension, the single-threshold method is 9.1% and 8.59% higher than the multi-threshold method respectively.

[0124] In summary, a cosine dynamic launch rate control method considering airport busyness proposed by the present invention shows unique advantages compared with the current traditional launch methods, specifically including:

[0125] 1. The present invention adopts a time-division mechanism based on the changes in departure and arrival demands to dynamically adjust the launch control threshold, enhancing the flexibility of the launch rate strategy to better adapt to the actual airport traffic changes. Through time division, it is possible to achieve an adaptive match between the taxiway capacity and the launch demand in the case of multiple runways, reducing the additional time loss caused by rigid strategies. This dynamic adjustment mechanism makes the delay distribution more uniform.

[0126] 2. The present invention extends the research on launch rate control to multiple runways, providing theoretical derivation and mathematical simulation for multi-runway scenarios. In addition, a cosine curve is innovatively introduced into the launch probability curve, making the launch rate decrease non-linearly as the queue length increases. When the taxiway queue length approaches the threshold, the launch rate does not suddenly drop to zero but decays in an asymptotic manner, making the launch rate decrease non-linearly with the increase in the queue length, avoiding extreme congestion and ensuring the coherence of flight launches.

[0127] 3. The goal of the cosine launch control strategy is to convert the taxiway waiting time into the apron waiting time, balance the airport resource utilization rate, effectively reduce the taxiing waiting time of departing flights, and achieve better cost-effectiveness and environmental protection effects. Compared with the unoptimized scheme, the average taxiing waiting time of flights is reduced by 42.92%; considering the airport busyness at different times, compared with the all-day single-threshold launch, it reduces by 9.1% and 8.59% in the time dimension and the target cost dimension respectively. It effectively controls exhaust emissions and conforms to the current trend of green aviation development.

[0128] The above-disclosed are only one or more preferred embodiments of the present invention. Of course, the scope of the rights of the present invention cannot be limited thereby. Those of ordinary skill in the art can understand all or part of the processes of implementing the above embodiments, and the equivalent changes made according to the claims of the present invention still fall within the scope covered by the invention.

Claims

1. A cosine dynamic launch rate control method considering airport busyness, characterized in that, The following steps are involved: Step 1: Obtain historical departure data and process it; Step 2: Construct a cosine dynamic push-out control model; Step 3: Divide the busy hours throughout the day; Step 4: Obtain the optimal taxiway threshold set; Step 5: When the termination condition is met, output the flight optimization sequence and cost value.

2. The cosine dynamic push-out rate control method considering airport busyness as claimed in claim 1, characterized in that: In step 2, the process of constructing the cosine dynamic pushout control model includes formulating the cosine dynamic pushout rate strategy, confirming the objective function, and selecting the constraint conditions; The mathematical expression of the cosine dynamic push-out rate is as follows: Among them, when N(k) is the k-time period corresponding to the N value, the taxiway waiting queue obeys the capacity-constrained M / M / S / N queuing model, where S is the number of service stations, expressing the number of runways; and N is the taxiway queue length threshold.

3. The cosine dynamic push-out rate control method considering airport busyness as claimed in claim 2, characterized in that: In step 2, the objective function is set to minimize the taxiway waiting cost and parking stand occupancy penalty, expressed as: Among them, C represents the departure cost defined by the present invention; F D refers to the set of departing flights; C t fuel represents the fuel consumption cost per minute, with the unit of yuan per minute, and E[W] is the taxi waiting time of the i-th flight W i ; G i represents the boarding gate waiting time of the flight due to pushback restrictions; β represents the penalty coefficient.

4. The cosine dynamic push-out rate control method considering airport busyness as claimed in claim 3, characterized in that: The agreed conditions in step 2 include gate occupancy constraint, pushback interval constraint and taxiway queue length constraint. The gate occupancy constraint is set to a maximum value of 30 minutes according to the operating rules. The pushback interval constraint requires that consecutive flights meet the average runway service rate when performing pushback. The taxiway queue length constraint is set to a range of N(k) in the kth time period of [1,30].

5. The cosine dynamic push-out rate control method considering airport busyness as claimed in claim 4, characterized in that: The method process of dividing the busy hours throughout the day in step 3 includes the following steps: Step 3.1: Data preprocessing: Process the historical data of inbound and outbound flights; Step 3.2: Initialize parameters and define the number of clusters; Step 3.3: Iterate and optimize to obtain the clustering result of the time period number under the above definition, that is, the time period division result; Go back to step 3.2 to redefine the number of time periods and re-obtain the results until the initial setting of the number of time periods is met; Step 3.4: Clustering effect evaluation: evaluate the results of each cluster number obtained above, determine its closeness with the input data, and obtain the optimal number of time periods; Step 3.5: Smoothing processing, expand and process the above results, and obtain the specific time interval corresponding to each time period.

6. The cosine dynamic push-out rate control method considering airport busyness as claimed in claim 5, characterized in that: In the process of obtaining the optimal threshold of the taxiway in step 4, the push-out control threshold corresponding to different time periods under global optimization is obtained using the Markov chain optimization genetic algorithm, including the following steps: Step 4.1: Define the time period division, that is, k time periods correspond to specific time points, and initialize the genetic algorithm parameters; Step 4.2: Randomly generate a genetic algorithm population. The initial population consists of multiple groups of threshold solutions. Each group of solutions contains the thresholds for k time periods. Each threshold is randomly selected within a predefined range and adjusted during the subsequent optimization process; Step 4.3: Conduct independent Markov chain iterations for the thresholds of each time period; Step 4.4: Make a judgment based on the current queuing length n of the taxiway and arrange flights to enter the taxiway waiting queue; Step 4.5: Calculate the overall fitness of each group of threshold solutions according to the output of the Markov chain; Step 4.6: Generate a new population through selection, crossover, and mutation to gradually optimize the threshold solutions; Step 4.7: When the stop condition is met, that is, the algorithm converges or reaches the maximum number of iterations, output the optimal threshold solutions for multiple time periods.

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