A method for predicting the length of a queue on a ramp based on a multi-queue network model

Abstract

This invention proposes a method for predicting apron queue length based on a multi-queue network model. First, using fluid flow approximation as a theoretical foundation, queues are divided according to control positions and taxiing directions. Taxiing delay is represented by a delay differential equation, and traffic transfer patterns are described using a Jackson routing matrix, extending from a single-queue model to a multi-queue network. Simultaneously, service rate, latency, and other parameters are calibrated based on historical data. This method accurately characterizes multi-stage congestion patterns during peak apron periods, achieving minute-level all-day predictions. The performance and usability of this method in apron scenarios are verified, contributing to improved airport ground operation resilience and providing a new modeling approach for optimizing apron operations at hub airports.

Description

Technical Field

[0001] This invention belongs to the field of civil aviation airport operation status analysis technology, and in particular relates to a method for predicting apron queue length based on a multi-queue network model. Background Technology

[0002] With the continuous growth in air transport demand, the contradiction between resource constraints and efficiency in the ground operations of hub airports is becoming increasingly prominent. Currently, airport capacity planning and assessment are largely based on runway capacity, assuming that apron capacity always exceeds runway capacity, thus treating the apron as an unconstrained component within the overall operational system. However, as the core hub connecting parking positions, taxiways, and runways, queue congestion on the apron has become a key factor restricting overall ground operational efficiency. Unlike runways, apron operations exhibit significant multi-node coupling and multi-factor dynamic interference characteristics: aircraft need to complete multiple operations such as handover, taxiing, and waiting between different control positions, and must also deal with issues such as taxiway conflicts. Furthermore, they are susceptible to external disturbances such as weather conditions and adjustments to airspace departure procedures. Current apron queue control largely relies on reactive measures, adjusting control strategies only after congestion occurs, lacking proactive intervention capabilities based on prediction. This leads to excessively long ground waiting times for aircraft, increased fuel consumption, which in turn increases operating costs and reduces passenger experience.

[0003] Currently, scholars have conducted extensive research on airport ground operations. Research methods for analyzing airport ground operations can be divided into two categories: First, mathematical methods, which use mathematical equations as their core, quantify dynamic patterns through airport flow relationships, and are driven by historical data to ultimately calculate outputs. Second, simulation methods, which focus on recreating actual operational scenarios, constructing models based on topological information such as airport structure and parking position layouts, and simulating the real process through discrete-time iterations. Current research on apron queues still has limitations in both mathematical and simulation methods, which can be summarized in the following four aspects:

[0004] (1) Existing mathematical models mostly adopt the idea of ​​simplifying the modeling of the apron as a whole, which fails to effectively distinguish the heterogeneity of service processes of different control seats.

[0005] (2) For service rates and time lags generated during the process of transferring regulatory responsibilities, existing studies have simplified them into fixed parameters and included them in the model without considering the dynamic change attributes of such parameters.

[0006] (3) Although existing simulation models can restore the apron topology and basic operation process, they lack a specific dynamic mathematical modeling step for apron queues.

[0007] (4) The simulation method requires iterative calculation on an event-by-event basis, resulting in high overall computational complexity; the mathematical method is prone to large approximation errors during peak hours on the tarmac, and both have limitations in terms of real-time performance. Summary of the Invention

[0008] In view of this, the present invention aims to overcome the shortcomings of the above-mentioned problems in the prior art and proposes a method for predicting apron queue length based on a multi-queue network model.

[0009] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0010] In a first aspect, the present invention provides a method for predicting apron queue length based on a multi-queue network model, comprising the following steps:

[0011] Step 1: Construct a dynamic model of a single queue by continuously approximating the discrete queuing process;

[0012] Step 2: Extend the dynamic model of a single queue to a multi-queue system using the principle of flow conservation to obtain a multi-queue queuing network model;

[0013] Step 3: Incorporate the time delay into the queuing network model, solve the delay differential equation, and obtain the dynamic length of each queue throughout the entire time period.

[0014] Furthermore, in step 1, when constructing the dynamic model of a single queue, the dynamic evolution process of the queue is quantitatively described by continuous state variables such as instantaneous queue length, instantaneous inflow rate, and instantaneous outflow rate, combined with ordinary differential equations constructed based on the principle of flow conservation.

[0015] Furthermore, in step 1, according to the principle of flow conservation, we can obtain:

[0016]

[0017] In the formula: for Change in queue length at any given time; for Inflow to the queue at any given time

[0018] That is The number of customers who should enter the queue at any given time; yes The outflow of the queue at any given time, that is The number of customers who leave the queue at any given time after their service is completed;

[0019] Assuming the queue has no capacity limit, then:

[0020]

[0021] In the formula: The average arrival rate is the number of customers entering the queue per unit time, which is the inflow of the queue at time t.

[0022] In queuing theory, outflow also depends on server utilization. According to the definition of single server utilization in queuing theory, outflow is the product of service rate and utilization rate, which is the average number of services actually completed by a single server.

[0023]

[0024] In the formula: for Outflow from queue at any given moment; for The service rate of the real-time service desk is an inherent parameter of the system; for The utilization rate of the service desk is a system operation status indicator that describes the busyness of the service desk and changes dynamically with the intensity of customer arrivals.

[0025] From equations (1), (2), and (3), the equation for the dynamic queue length can be obtained, as shown in equation (4):

[0026]

[0027] Establish a quantitative relationship between steady-state queue length and server utilization and service time fluctuation:

[0028] (5)

[0029] In the formula: This is the average queue length when the queue reaches a stable state after long-term operation. Steady-state service desk utilization rate represents the average number of customers being served. It is the service time variation coefficient; the second term in the formula represents the average number of customers waiting in line.

[0030] Based on equation (5), we can derive... about Explicit analytical solution:

[0031]

[0032] Equation (6) is A cubic polynomial;

[0033] The equation is approximated as a hyperbolic rational function. Replace complex explicit solutions :

[0034]

[0035] In the formula: Represents the queue length; Let be the parameters of the hyperbolic rational function;

[0036] Parameters are determined by minimizing the integral error. :

[0037]

[0038] In the formula: This represents the expected maximum queue length;

[0039] Substituting equation (7) into equation (4), we obtain the final solvable differential equation:

[0040]

[0041] In the formula: The effective outflow rate.

[0042] Furthermore, in step 2, a routing matrix is ​​introduced to describe the flow transfer relationship between queues, which is extended to a queuing network model that can represent the multi-region coupling characteristics.

[0043] Furthermore, let's assume It is a routing matrix, where elements Indicates in queue Served into queue The proportion is given by the expression:

[0044]

[0045] In the formula: Flowing out to serve themselves; The sum of inflows from other queues; For direct input from external sources.

[0046] Furthermore, in step 3, let... To the service desk arrive The glide time is given by the expression that includes the delay:

[0047]

[0048] In the formula: The input that arrives at this queue after propagation delay and proportional routing from other queue services is obtained by adding delay to term (10)b;

[0049] Equation (11) uses numerical integration to obtain the queue length at any time, as shown in Equation (12):

[0050]

[0051] In the formula: For queue exist The queue length at any given time.

[0052] Secondly, the present invention provides a tarmac queue length prediction device based on a multi-queue network model, including...

[0053] The single queue model building unit is used to construct a dynamic model of a single queue by continuously approximating the discrete queuing process.

[0054] The multi-queue network model building unit is used to extend the dynamic model of a single queue to multiple queues using the principle of flow conservation, thus obtaining a multi-queue queuing network model.

[0055] The solution unit is used to incorporate time delay into the queuing network model, solve the delay differential equation, and obtain the dynamic length of each queue throughout the entire time period.

[0056] Thirdly, the present invention provides an electronic device, including a processor and a memory communicatively connected to the processor and used to store executable instructions of the processor, wherein the processor is used to execute the above-described method for predicting apron queue length based on a multi-queue network model.

[0057] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for predicting apron queue length based on a multi-queue network model.

[0058] Compared with existing technologies, the apron queue length prediction method based on a multi-queue network model described in this invention has the following advantages:

[0059] The method of this invention enables accurate characterization of multi-stage congestion patterns during peak apron periods, achieving minute-level all-day prediction. Experiments have verified the performance and usability of the method in apron scenarios, which helps improve the resilience of airport ground operations and provides new modeling ideas for optimizing apron operations at hub airports. Attached Figure Description

[0060] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0061] Figure 1This is a schematic diagram of the queue length prediction process in Embodiment 1 of the present invention;

[0062] Figure 2 In Embodiment 1 of the present invention A diagram illustrating the comparison between approximate and true values;

[0063] Figure 3 This is a schematic diagram of the overall algorithm framework in Embodiment 1 of the present invention;

[0064] Figure 4 This is a comparison chart of the predicted queue length and the actual queue length in Embodiment 1 of the present invention;

[0065] Figure 5 This is a bubble chart showing the average absolute error distribution of queue prediction in Embodiment 1 of the present invention.

[0066] Figure 6 This is a schematic diagram of the control sector layout of Beijing Daxing International Airport in Embodiment 1 of the present invention;

[0067] Figure 7 This is a schematic diagram of the ground topology network structure of Beijing Daxing International Airport in Embodiment 1 of the present invention;

[0068] Figure 8 This is a sector correlation heatmap from Embodiment 1 of the present invention;

[0069] Figure 9 This is a schematic diagram showing the fitting results of the EAP eastbound queue length and westbound queue service rate in Embodiment 1 of the present invention;

[0070] Figure 10 This is a schematic diagram showing the fitting results of the EAP westbound queue length and eastbound queue service rate in Embodiment 1 of the present invention;

[0071] Figure 11 This is a schematic diagram showing the fitting results of the WAP eastbound queue length and westbound queue service rate in Embodiment 1 of the present invention;

[0072] Figure 12 This is a schematic diagram showing the fitting results of the WAP westbound queue length and eastbound queue service rate in Embodiment 1 of the present invention;

[0073] Figure 13 This is a schematic diagram showing the fitting results of the eastbound queue length and westbound queue service rate of GW1 in Embodiment 1 of the present invention;

[0074] Figure 14 This is a schematic diagram showing the fitting results of the westbound queue length and eastbound queue service rate in Embodiment 1 of the present invention;

[0075] Figure 15 This is a schematic diagram showing the fitting results of the eastbound queue length and westbound queue service rate of TW1 in Embodiment 1 of the present invention;

[0076] Figure 16 This is a schematic diagram showing the fitting results of the TW1 westbound queue length and eastbound queue service rate in Embodiment 1 of the present invention. Detailed Implementation

[0077] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0078] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0079] Example 1

[0080] This invention establishes a queuing network model based on the Fluid Flow Approximation theory. By continuously approximating the discrete queuing process, a smooth representation of discrete flight queuing behavior is achieved. First, a dynamic model of a single queue is constructed to express the characteristics of a single queue on the apron. Based on this, a routing matrix is ​​introduced to describe the flow transfer relationship between queues, ultimately extending to a queuing network model capable of representing multi-region coupling characteristics. In real-world queuing networks, another characteristic is the time delay caused by propagation; therefore, the transmission delay of customers between nodes is incorporated into the queuing network. Finally, the queue length is obtained by solving the delay differential equation, as follows: Figure 1 As shown.

[0081] Specifically, the present invention provides a method for predicting apron queue length based on a multi-queue network model, comprising the following steps:

[0082] Step 1: Construct a dynamic model of a single queue by continuously approximating the discrete queuing process;

[0083] The dynamic evolution of a queue can be quantitatively described using continuous state variables such as instantaneous queue length, instantaneous inflow rate, and instantaneous outflow rate, combined with ordinary differential equations constructed based on the principle of flow conservation. This continuous modeling approach effectively avoids the computational complexity of discrete event models in unstable scenarios, significantly simplifying the mathematical modeling process and numerical solution difficulty of unstable queuing systems. Therefore, from the principle of flow conservation, we can obtain:

[0084]

[0085] In the formula: for Change in queue length at any given time; for The inflow to the time queue, that is The number of customers who should be in the queue at any given time. yes The outflow of the queue at any given time, that is The number of customers who leave the queue at any given time after their service is completed.

[0086] Assuming the queue has no capacity limit, then:

[0087]

[0088] In the formula: The average arrival rate is the number of customers entering the queue per unit time, which is the inflow into the queue at time t. It is an external driving variable of the model and does not depend on the queue's own state.

[0089] In queuing theory, outflow also depends on server utilization. According to the definition of single server utilization in queuing theory, outflow is the product of service rate and utilization rate, that is, the number of services actually completed on average by a single server.

[0090]

[0091] In the formula: for Outflow from queue at any given moment; for The service rate of the real-time service desk is an inherent parameter of the system; for The utilization rate of the service desk is a system operation status indicator that describes the busyness of the service desk and changes dynamically with the intensity of customer arrivals. This indicates that the service desk is full. This indicates that the service desk is available.

[0092] Therefore, the dynamic queue length equation can be obtained from equations (1), (2), and (3), as shown in equation (4):

[0093]

[0094] Based on the classic queuing theory (M / G / 1 queue) and the Pollaczek-Khinchine formula, a quantitative relationship is established between steady-state queue length and server utilization and service time fluctuation.

[0095]

[0096] In the formula: This is the average queue length when the queue reaches a stable state after long-term operation. Steady-state service desk utilization rate represents the average number of customers being served. It is the service time variation coefficient, which is the ratio of the standard deviation of service time to the mean, and is used to describe the degree of fluctuation in service time; the second term in the formula is the average number of customers waiting in line.

[0097] Based on equation (5), we can derive... about Explicit analytical solution:

[0098]

[0099] Equation (6) is The cubic polynomial has high computational complexity and poor model coupling. To balance accuracy and practicality, the equation is approximated as a hyperbolic rational function. Alternatives to complex explicit solutions:

[0100]

[0101] In the formula: Represents the queue length; Let be the parameters of the hyperbolic rational function;

[0102] Equation (7) is an approximate form of the complex solution, which satisfies the boundary conditions: the service rate is 0 when the queue is empty and 1 when the queue is saturated. Furthermore, the monotonicity is consistent; the longer the queue, the busier the service station.

[0103] Parameters are determined by minimizing the integral error. :

[0104]

[0105] In the formula: This represents the expected maximum queue length.

[0106] Figure 2 This is an approximate value for the service desk utilization rate. Compared with theoretical value The comparison between them proves the effectiveness of the approximation.

[0107] Substituting equation (7) into equation (4), we obtain the final solvable differential equation:

[0108]

[0109] In the formula: the first term on the right side of the equal sign is the effective outflow rate, which is constrained by the maximum service capacity of the service desk and the queue length; The external input rate drives queue growth.

[0110] Step 2: Extend the dynamic model of a single queue to a multi-queue system using the principle of flow conservation to obtain a multi-queue queuing network model;

[0111] The single-queue model is extended to multiple queues using the principle of flow conservation: if the queues are interconnected, the output of one queue becomes the input of another. Jackson networks are classic open-loop networks in queuing theory. Borrowing the routing matrix concept from Jackson networks, let... It is a routing matrix, where elements Indicates in queue Served into queue The ratio. Therefore, the expression can be obtained:

[0112]

[0113] In the formula: Flowing out to serve themselves; The sum of inflows from other queues; For direct external input (such as landing flights and outgoing flights initially entering the system).

[0114] Step 3: Incorporate the time delay into the queuing network model, solve the delay differential equation, and obtain the dynamic length of each queue throughout the entire time period.

[0115] In real-world queuing networks, another characteristic is the time delay caused by propagation, which does not include the waiting time within the queue. This means incorporating the transmission delay between nodes into the queuing network.

[0116] set up To the service desk arrive Given the glide time, we can obtain an expression that includes the delay:

[0117]

[0118] In the formula: This is the output of the service provided by this queue through its own service desk; For direct external input; The input to this queue is obtained by adding the delay to the term of equation (10)b, which is the input that is served by other queues, after propagation delay and proportional routing.

[0119] Equation (11) can be used to obtain the queue length at any time by numerical integration, as shown in Equation (12):

[0120]

[0121] In the formula: For queue exist The queue length at any given time.

[0122] This invention uses Delayed Differential Equations (DDE) as its core algorithm architecture and employs a fixed five-part statistical window to balance temporal resolution and data stability. This window size avoids drastic data fluctuations caused by excessively short intervals while preventing excessively long windows from obscuring dynamic characteristics (longer windows can lead to increased queue lengths due to multiple queuing events rather than continuous queuing), thus making it suitable for capturing the temporal variation characteristics of airport ground queuing.

[0123] The key operational metrics in this window-based calculation model include the average number of queued and arriving aircraft in each time period. To ensure consistent metric dimensions and calculation logic, the service rate is also calculated based on the same five-minute window. The number of outbound and landing flights within the time window is used as the external traffic driver; then, a traffic flow topology is constructed based on the queue set of the queue network layer; on this basis, the routing matrix clarifies the seat traffic flow direction, the delay mapping module quantifies the transfer time delay between queues, and the service rate module dynamically adjusts the traffic processing speed of the queues—these three elements together provide core parameter support for DDE (Data Demand Analysis); subsequently, the equations are solved using a numerical integration method adapted to the characteristics of DDE, ultimately obtaining the dynamic length of each queue throughout the entire time period. The algorithm architecture is as follows: Figure 3 As shown.

[0124] The effectiveness of this invention will be verified through experiments below.

[0125] The queuing dynamic equation is numerically integrated forward from the start time of each day, with a time step discretized in 1-minute increments. To visually demonstrate the model's performance, the queue lengths of typical days from the test dataset are selected for predictive analysis. Time is in UTC format, and the presented queue lengths are the average values ​​within a 5-minute window. Interpolation smoothing is applied to both the actual and predicted values ​​to improve visualization.

[0126] Figure 4 The prediction results for some queues are given. Figure 4 (a) Figure 4 (b) Figure 4 (c) The predicted lengths of the ground seats GW1 eastward queue, the apron seats EAP westward queue, and the tower seats TW1 eastward queue are presented visually. All three figures show that the model predictions and actual values ​​match the tidal fluctuations throughout the day in UTC. The queue length changes during off-peak (0:00 to 8:00 Beijing time) and peak periods are consistent. The actual values ​​and predictions show a high degree of matching, demonstrating cross-sector and all-time applicability.

[0127] Figure 5A bubble chart of the mean absolute error of the prediction results for different control seat queues is presented. First, the prediction errors for TW1 (eastbound and westbound) are 0.40 and 0.38 respectively, representing the lowest overall error level, indicating that the control seat queues have relative regularity and predictability. Runway 35R, as the main departure runway, exhibits strong traffic regularity, which is closely related to the control seats being primarily constrained by runway release strategies and takeoff sequencing, resulting in a relatively concentrated and consistent operational rhythm, allowing the prediction model to capture its dynamic characteristics well. In contrast, runway 11L is located further north, with a relatively long taxiway path, leading to complex routing delays and intersection conflicts, increasing prediction uncertainty. Its TN prediction error is as high as 0.49, slightly higher than other control seat queues.

[0128] Secondly, among the ground control units, the MAE (Modular Error) for GW1 in the east and west directions were 0.37 and 0.47 respectively, showing a significant difference. The lower error in the east direction indicates a more stable operating rhythm for the arrival queue in the ground control sector, while the west direction may have increased prediction errors for the departure queue due to the complex distribution of taxiways and diverse handover points. The prediction error for GE (Gross Execution) was 0.43, which is at a moderate level, indicating that the model's predictive ability in this area is relatively balanced.

[0129] Finally, in the apron control area, the prediction errors for WAP and EAP were 0.50 / 0.45 and 0.42 / 0.46 (east / west directions), respectively. The prediction error for the apron control sector was generally slightly higher than that for the tower sector, with WAP showing the highest value of 0.5 in the east direction. This result reflects the operational complexity of the apron control sector: complex taxiways and dense intersections within the apron often lead to sudden conflict avoidance and waiting during departure. Furthermore, compared to the east apron, the west apron handles a higher proportion of domestic flights (high-frequency short-haul), resulting in more significant queue fluctuations during peak flight periods and a larger prediction residual. The east apron connects more international long-haul routes, exhibiting stronger scheduling cycles and lower variability, thus resulting in a slightly lower prediction error.

[0130] Overall, the prediction error of the control tower area is smaller than that of the apron and ground areas, indicating that the prediction model has higher reliability in areas with relatively stable operating patterns, while the prediction accuracy decreases in apron areas with more operational disturbances and frequent taxiing conflicts. This phenomenon suggests that future model improvements need to introduce more feature variables reflecting operational uncertainties in apron and complex taxiing path areas to enhance the model's predictive capabilities.

[0131] Overall, the prediction results demonstrate that the proposed seat-based delayed queue network model can accurately characterize the queue dynamics of different regions on a minute-level scale. The prediction error is within an acceptable range and can reflect the differences in operational complexity among different control seats. These results not only validate the model's applicability in real-world scenarios but also provide quantitative evidence for further optimizing coordination strategies between the control tower, ground control, and apron.

[0132] In the specific implementation of this invention, Beijing Daxing International Airport (ZBAD) was selected as the case study object. Figure 6 The exhibition showcases the actual layout of Beijing Daxing International Airport, featuring three parallel runways (35L, 35R, and 01L) and one angled runway (11L). The control sectors are clearly marked: Tower positions: TW1 (West Tower Position 1), TW2 (West Tower Position 2), TE (East Tower Position), TN (North Tower Position); Ground control positions: GW1 (West Ground Position 1), GW2 (West Ground Position 2), GE (East Ground Position); Apron control positions: WAP (West Apron Position), EAP (East Apron Position). The airport primarily operates under two modes: northbound and southbound. The choice of operating mode depends on several key factors, including air traffic flow, meteorological conditions (such as wind direction and visibility), and airspace capacity constraints. The northbound normal operation mode is the dominant mode for daily operations, where runways 11L and 35R handle takeoffs, and runways 01L and 35L handle landings. This model boasts significant advantages such as high flight flow stability, complete historical operational data, and low frequency of mode switching interference, providing ample and reliable data support for model validation and result analysis. Given the dominant operational position and data advantages of this model, this invention will focus on in-depth analysis of the northbound normal operation mode. Therefore, the queuing network model established in step 1 will be applied to the airport surface, and a ground multi-queue network model for Beijing's large international airport will be proposed based on the northbound regular operation mode.

[0133] To address the issue of congestion at multiple ground resource points, the queuing situation in each ground control sector is analyzed and assessed. For example... Figure 7 As shown, based on actual operational conditions, the ground control sector is divided into east-west queues, with queues in the same direction linked in a chain. If an aircraft's travel time into a control sector exceeds the normal taxiing time for that area, it is determined that the aircraft has not left the control sector and is still in the taxiing queue for that area. Additionally, entering Q11 or Q12 is considered as taxiing into a parking position and leaving the system.

[0134] In the construction of the airport ground traffic queue network model, the routing matrix and queue delay are two core elements characterizing the network coupling relationship and timing response characteristics. Together, they support the model's ability to dynamically simulate actual ground traffic flow. To accurately capture the real characteristics of airport ground operations, the model is driven by historical data, and the required basic data are all taken from the Airport Collaborative Decision Making System (A-CDM) and the Advanced Surface Activity Guidance and Control System (A-SMGCS).

[0135] Routing matrix medium elements Defined in the preorder queue After completing the service, enter the queue. The proportion. It should be noted that this allocated traffic will incur a certain propagation delay. Only after that will the traffic flow reach the target queue. Based on the traffic flow distribution obtained from historical operation data statistics, the routing matrix that can be determined is shown in Equation (13), and the rows and columns of its elements follow a fixed order.

[0136] (13)

[0137] The routing matrix has two functions: first, it undertakes the connection of the apron topology and quantifies the directed connectivity between queues, as shown in equation (14).

[0138]

[0139] Second, it reflects the flow allocation rules, determining how the queue output is split in the downstream parallel path. For example, all outputs from Q1 flow to Q3; while 24% of the outputs from Q5 flow to Q7, and 76% flow to Q11.

[0140] In airport ground traffic queuing networks, delay is defined as the travel time required for an aircraft to move from one controlled area to another, including only travel time under normal operating conditions and excluding queuing time in departure or destination queues. This type of propagation delay is a key factor in inter-queue coupling, as it determines the time difference between the output traffic of one queue and the traffic becoming the input of another queue.

[0141] Based on statistical analysis of historical taxiing data, the median taxiing time within the controlled area was identified as the normal taxiing time. Choosing the median better reflects the time it takes for aircraft to taxi in most cases, and this time was used as the propagation delay between queues associated with this sector.

[0142] In a ground-based queue network model based on control seat allocation, the routing matrix and propagation delay are two core elements determining the network's coupled structure and temporal response. The routing matrix provides the rules for distributing traffic across paths, while the propagation delay specifies the time delay at which traffic reaches the target queue. The combination of these two elements transforms the static network topology into a dynamic system with explicit time-delay coupling characteristics, ultimately constructing a multi-queue network model that incorporates delays.

[0143] To ensure the model's practicality, the service rate was determined from actual operational data, and the service time at the service counter was defined as the time difference between consecutive aircraft exiting the queue while the queue was in place. The dataset contains 12,976 arrival data points and 12,995 departure data points; approximately 70% of the data was used to train the model parameters, and the remainder was used for testing.

[0144] Based on the actual operation of Beijing Daxing International Airport, assuming that the congestion in a control sector is due to the same sector directing inbound and outbound flights in different directions, the service rates of queues in different directions within the same control sector will affect each other. By generating a Spearman correlation coefficient heatmap of queue length and service rate, the interaction between queues can be observed. Figure 8 As shown.

[0145] from Figure 8 It is evident that there is a general negative correlation between east-west queues within the same sector. For example, there is a correlation between the length of the EAP west-bound queue and the EAP east-bound service rate, the length of the WAP east-bound queue and the WAP west-bound service rate, and the length of the GW1 east-bound queue and the GW1 west-bound service rate. Spearman's coefficient shows that when queues are congested in one direction, it may lead to a decrease in the service efficiency of queues in another direction, indicating resource competition and service bottlenecks. Between queues in different sectors, the heatmap shows a mixed relationship of positive and negative correlations. For example, the EAP east-bound queue and the GE west-bound queue show a negative correlation, while the TN1 east-bound queue and the TW1 west-bound queue show a certain positive correlation. This indicates that the service and queuing processes between certain control areas (such as the East Tower and West Tower areas) are relatively independent with less interference between them, while other areas (such as the apron and ground seating) exhibit a stronger negative correlation due to the interconnected taxiways.

[0146] This heatmap validates the hypothesis regarding the service rates of queues in different directions within the same sector: queues in different directions within the same sector significantly influence each other. Furthermore, in some controlled sectors where only one direction's queue is either arriving or departing, their service rates are directly fitted using historical data.

[0147] Therefore, a fitting relationship is established between queue length and average service rate of opposite queues. In the fitting results, the slopes of the service rates in the east-west direction are different. Figures 9 to 16These are fitting plots of the EAP eastbound queue length versus westbound queue service rate, the EAP westbound queue length versus eastbound queue service rate, the WAP eastbound queue length versus westbound queue service rate, the WAP westbound queue length versus eastbound queue service rate, the GW1 eastbound queue length versus westbound queue service rate, the GW1 westbound queue length versus eastbound queue service rate, the TW1 eastbound queue length versus westbound queue service rate, and the TW1 westbound queue length versus eastbound queue service rate.

[0148] like Figure 9 , 10 As shown, the absolute value of the service rate slope of the eastbound queue in the EAP East Apron control sector is significantly greater than that of the westbound queue, indicating that the eastbound queue in this sector is more significantly affected by the westbound queue. Considering that the eastbound queue mainly consists of flights departing from runway 11L, with only a small number flowing to the WAP West Apron, this data characteristic reflects the priority given to inbound flights in the EAP East Apron control strategy.

[0149] like Figure 11 , 12 As shown, the WAP West Apron control sector exhibits a pattern consistent with the EAP East Apron: the absolute value of the service rate slope for the eastbound queue is also greater than that for the westbound queue, indicating that the eastbound queue is more significantly influenced by the westbound queue. The core flow direction of the eastbound queue in this sector is departure from runway 11L, echoing the eastbound queue flow characteristics of the EAP apron. For the TN1 eastbound queue and the TE westbound queue, only unidirectional queues exist within their control sectors, so there is no influence from opposing queues, allowing for direct fitting of the service rate.

[0150] like Figure 13 , 14 As shown, the GW1 West Ground Sector, as the core node connecting the West Apron and the Tower Sector, has an eastward queue mainly corresponding to the traffic flow of arriving flights taxiing to the West Apron (WAP), while the westward queue corresponds to the traffic flow of departing flights taxiing to the 35R main runway. This data characteristic reflects the priority given to the connection of arriving flights in the GW1 ground control strategy. When the queues in the arriving direction are congested, the service efficiency in the departing direction will be more significantly squeezed. This echoes the pattern that the "eastward queues have a more prominent impact" in the EAP and WAP apron control sectors. The strong negative correlation also verifies the operational nature of the GW1 sector's two-way queues sharing taxiing resources and mutually restricting each other.

[0151] like Figure 15 , 16As shown, the westbound queues in sector TW1 correspond to departure traffic on runway 35R, while the eastbound queues primarily represent arrival traffic on runway 35L. The slope of the data characteristics reflects the priority given to flights departing from runway 35R in the TW1 control strategy: the backlog in the westbound departure queues has a stronger suppressive effect on the eastbound arrival service rate, and the high fit also reflects the stable operational pattern of the tower sector, which is centered on runway release rhythm. Compared to ground and apron sectors, the fitting relationship between queue service rate and length is more reliable.

[0152] Example 2

[0153] A device for predicting apron queue length based on a multi-queue network model, comprising:

[0154] The single queue model building unit is used to construct a dynamic model of a single queue by continuously approximating the discrete queuing process.

[0155] The multi-queue network model building unit is used to extend the dynamic model of a single queue to multiple queues using the principle of flow conservation, thus obtaining a multi-queue queuing network model.

[0156] The solution unit is used to incorporate time delay into the queuing network model, solve the delay differential equation, and obtain the dynamic length of each queue throughout the entire time period.

[0157] Example 3

[0158] An electronic device includes a processor and a memory communicatively connected to the processor for storing processor-executable instructions, the processor being used to execute the aforementioned apron queue length prediction method based on a multi-queue network model.

[0159] Example 4

[0160] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for predicting apron queue length based on a multi-queue network model.

[0161] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting apron queue length based on a multi-queue network model, characterized in that: Includes the following steps: Step 1: Construct a dynamic model of a single queue by continuously approximating the discrete queuing process; when constructing the dynamic model of a single queue, the dynamic evolution process of the queue is quantitatively described by continuous state variables such as instantaneous queue length, instantaneous inflow rate, and instantaneous outflow rate, combined with ordinary differential equations constructed based on the principle of flow conservation. According to the principle of flow conservation: In the formula: for Change in queue length at any given time; for The inflow to the time queue, that is The number of customers entering the queue at any given time. yes The outflow of the queue at any given time, that is The number of customers who leave the queue at any given time after their service is completed; Assuming the queue has no capacity limit, then: In the formula: The average arrival rate is the number of customers entering the queue per unit time, which is the inflow of the queue at time t. In queuing theory, outflow also depends on server utilization. According to the definition of single server utilization in queuing theory, outflow is the product of service rate and utilization rate, which is the average number of services actually completed by a single server. In the formula: for Outflow from queue at any given moment; for The service rate of the real-time service desk is an inherent parameter of the system; for The utilization rate of the service desk is a system operation status indicator that describes the busyness of the service desk and changes dynamically with the intensity of customer arrivals. From equations (1), (2), and (3), the equation for the dynamic queue length can be obtained, as shown in equation (4): Establish a quantitative relationship between steady-state queue length and server utilization and service time fluctuation: （5） In the formula: This is the average queue length when the queue reaches a stable state after long-term operation. Steady-state service desk utilization rate represents the average number of customers being served. It is the service time variation coefficient; the second term in the formula represents the average number of customers waiting in line. Based on equation (5), we can derive... about Explicit analytical solution: Equation (6) is A cubic polynomial; The equation is approximated as a hyperbolic rational function. Replace complex explicit solutions : In the formula: Represents the queue length; Let be the parameters of the hyperbolic rational function; Parameters are determined by minimizing the integral error. : In the formula: This represents the expected maximum queue length; Substituting equation (7) into equation (4), we obtain the final solvable differential equation: In the formula: Effective outflow rate; Step 2: Extend the dynamic model of a single queue to a multi-queue system using the principle of flow conservation to obtain a multi-queue queuing network model; Step 3: Incorporate the time delay into the queuing network model, solve the delay differential equation, and obtain the dynamic length of each queue throughout the entire time period.

2. The method for predicting apron queue length based on a multi-queue network model according to claim 1, characterized in that: In step 2, a routing matrix is ​​introduced to describe the flow transfer relationship between queues, which is then extended to a queuing network model that can represent the coupling characteristics of multiple regions.

3. The method for predicting apron queue length based on a multi-queue network model according to claim 2, characterized in that: set up It is a routing matrix, where elements Indicates in queue Served into queue The proportion is given by the expression: In the formula: Flowing out to serve themselves; The sum of inflows from other queues; For direct input from external sources.

4. The method for predicting apron queue length based on a multi-queue network model according to claim 3, characterized in that: In step 3, let To the service desk arrive The glide time is given by the expression that includes the delay: In the formula: The input that arrives at this queue after propagation delay and proportional routing from other queue services is obtained by adding delay to term (10)b; Equation (11) uses numerical integration to obtain the queue length at any time, as shown in Equation (12): In the formula: For queue exist The queue length at any given time.

5. A device for predicting the length of apron queues based on a multi-queue network model, characterized in that: include The single queue model building unit is used to construct a dynamic model of a single queue by continuously approximating the discrete queuing process. When constructing the dynamic model of a single queue, the dynamic evolution process of the queue is quantitatively described by continuous state variables such as instantaneous queue length, instantaneous inflow rate, and instantaneous outflow rate, combined with ordinary differential equations constructed based on the principle of flow conservation. According to the principle of flow conservation: In the formula: for Change in queue length at any given time; for The inflow of the time queue, that is The number of customers entering the queue at any given time. yes The outflow of the queue at any given time, that is The number of customers who leave the queue at any given time after their service is completed; Assuming the queue has no capacity limit, then: In the formula: The average arrival rate is the number of customers entering the queue per unit time, which is the inflow of the queue at time t. In queuing theory, outflow also depends on server utilization. According to the definition of single server utilization in queuing theory, outflow is the product of service rate and utilization rate, which is the average number of services actually completed by a single server. In the formula: for Outflow from queue at any given moment; for The service rate of the real-time service desk is an inherent parameter of the system; for The utilization rate of the service desk is a system operation status indicator that describes the busyness of the service desk and changes dynamically with the intensity of customer arrivals. From equations (1), (2), and (3), the equation for the dynamic queue length can be obtained, as shown in equation (4): Establish a quantitative relationship between steady-state queue length and server utilization and service time fluctuation: （5） In the formula: This is the average queue length when the queue reaches a stable state after long-term operation. Steady-state service desk utilization rate represents the average number of customers being served. It is the service time variation coefficient; the second term in the formula represents the average number of customers waiting in line. Based on equation (5), we can derive... about Explicit analytical solution: Equation (6) is A cubic polynomial; The equation is approximated as a hyperbolic rational function. Replace complex explicit solutions : In the formula: Represents the queue length; Let be the parameters of the hyperbolic rational function; Parameters are determined by minimizing the integral error. : In the formula: This represents the expected maximum queue length; Substituting equation (7) into equation (4), we obtain the final solvable differential equation: In the formula: Effective outflow rate; The multi-queue network model building unit is used to extend the dynamic model of a single queue to multiple queues using the principle of flow conservation, thus obtaining a multi-queue queuing network model. The solution unit is used to incorporate time delay into the queuing network model, solve the delay differential equation, and obtain the dynamic length of each queue throughout the entire time period.

6. An electronic device, comprising a processor and a memory communicatively connected to the processor and used for storing processor-executable instructions, characterized in that: The processor is used to execute the method described in any one of claims 1-4.

7. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it implements the method described in any one of claims 1-4.

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