Nomenclature
- UAM
-
Urban Air Mobility
- GA
-
Genetic Algorithm
- FCFS
-
First-Come-First-Served
- UAV
-
Unmanned Aerial Vehicle
1.0 Introduction
The booming development of the e-commerce economy has brought forth new demands on the logistics distribution system [Reference Jain, Malviya and Arya1]. UAVs as a vital means for last-mile logistics delivery hold immense prospects [Reference Sorbelli, Corò, Das, Palazzetti and Pinotti2]. In light of the current development of UAV manufacturing technology and the demands for achieving urban modernisation governance, UAM is defined as an operational concept involving the use of vertical take off and landing (VTOL) aircraft for manned transportation, logistics, as well as urban governance. Specifically, urban governance encompasses the application of UAVs in environmental monitoring, facility inspection, emergency firefighting and the maintenance and management of green belts. With the vigorous development of UAM, vertiports as crucial nodes connecting UAM networks with ground transportation networks exhibit complex traffic flow characteristics. Rational and scientific assessment methods for vertiport operational capacity play a significant role in the rational and scientific construction of vertiports and in maintaining the orderly and efficient operation of UAM. The versatility of UAVs allows for their wide application in both cargo [3] and passenger transportation [4]. With the ongoing advancement in UAV manufacturing technology and artificial intelligence, certain UAVs can also be employed for tasks such as image recognition [Reference Zeng, Duan, Chen, Peng, Mao and Yang5], UAV inspection [Reference Perry, Guo, Atadero and van de Lindt6], and vegetation maintenance in the city [Reference Gun7, 8]. As the scale of UAM continues to increase, the development of UAM also faces many challenges [Reference Preis9] including UAM operation regulations [Reference Kopardekar10], pollution [Reference Ackerman and Gregory11], operational safety separation standards [Reference Zou, Zhang, Zhong, Liu, Feng and Safety12] and route network planning [Reference Li, Zhang, Yi and Liu13]. However, many of these issues have been addressed [Reference Straubinger, Rothfeld, Shamiyeh, Büchter, Kaiser and Plötner14], there remains a lack of an operational evaluation system for vertiports, integrating airport throughput and customer satisfaction. Customer satisfaction indicates the overall service quality of the entire vertiport operation.
The urban low-altitude operation environment differs from that of traditional civil aviation because the airspace of the urban air-traffic terminal area is located among complex urban building groups and has complex airspace characteristics. Therefore, it is essential to clarify the operational processes and infrastructure standards of vertiports when studying the capacity of vertiports. The Federal Aviation Administration [Reference Administration15], the International Civil Aviation Organization [Reference Organization16] and the European Aviation Safety Agency [17], among other government organisations, have established size and operational standards for vertiport vertipads, gates and taxiways, as well as designed the general structure of vertical takeoff and landing procedures. Addtionally, Uber has defined the mission segments of UAM [18], which describes the take-off and landing process of UAVs. Based on these segmented flight phases, Schweiger, Knabe and Korn [Reference Schweiger, Knabe and Korn19] have conducted detailed design of departure and arrival procedures for vertiports. Furthermore, Mihir Rimjha [Reference Rimjha and Trani20] has defined the internal operational processes of vertiports.
Airport capacity has been defined by many scholars, some scholars define airport capacity as the number of landings and takeoffs within a given delay time threshold [Reference Li21], while other scholars define airport capacity as the maximum throughput of an airport in a given time period [Reference Vascik and Hansman22]. This study mainly considers maximising throughput for a given demand arrival. In traditional civil aviation, the assessment of airport capacity relies primarily on mathematical models, historical data, air traffic controller workload and simulation software [Reference Zhao23]. Early studies on airport capacity are primarily based on mathematical models. These methods involved modeling runways and gates using Poisson arrival flow to construct airport capacity assessment models [Reference Bowen and Pearcey24, Reference Blumstein25]. Additionally, some researchers [Reference Chen, Yu, Cao, Zhou, Wei and Hu26] evaluated the runway capacity of single-runway airports by setting throughput and service quality objective functions with aircraft wake separation constraints. The airport capacity assessment method based on air traffic controller workload primarily involves considering the maximum controller workload that can be handled within a unit of time [Reference Callantine and Palmer27–Reference Liu30]. With the advancement of computer and artificial intelligence technologies, an increasing number of scholars are using simulation software [Reference Long, Stouffer-Coston, Kostiuk, Kula and Yackovetsky31–Reference Bertino, Boyajian and Johnson33] to simulate real airport scenarios and assess the capacity of airports by collecting data through specific nodes. A large amount of weather data and ground operation data are generated during airport operations. Consequently, many scholars start to use data mining techniques such as machine learning to uncover intrinsic features within this data for assessing airport operational capacity [Reference Tien, Taylor, Vargo and Wanke34–Reference Wan, Peng, Tian, Gao and Ye36]. UAM has not yet been operated at a large scale, resulting in limited historical operational data. Additionally, there is still a lack of an established air traffic control system specifically tailored for UAVs. Therefore, the capacity assessment methods for vertiports are still in the stage of mathematical model development and computer simulation. Mathematical modeling methods for assessing the capacity of vertiports are mainly focused on the theory of planning models and network flow. The network flow model for vertiports involves constructing the flow transfer states between essential elements such as vertipads, gates and hangars to determine the maximum arrival and departure flow of the vertiport [Reference Ahn and Hwang37]. On the other hand, by estabilishing constraints including aircraft safety intervals, vertipads and other elements, a capacity assessment method with throughput as an objective function is constructed based on planning model [Reference Kleinbekman, Mitici and Wei38–Reference Venkatesh, Payan, Justin, Kee and Mavris40]. The capacity assessment models using computer simulation are mainly divided into numerical simulation and scenario simulation. Numerical simulation relies on discrete arrival and departure sequences to calculate operational parameters of UAVs, thereby evaluating operational capacity [Reference Bertram and Wei41, Reference Alvarez, Jones, Bryan and Weinert42]. On the other hand, scenario simulation involves using specific simulation software to simulate actual operational scenarios of aiports [Reference Zhenglei, Xiaolei, Chaojia, Bin, Hao, Jiajia and Jihui43].
For the complex terminal area airspace of vertiports, most of the existing research on vertiports is to evaluate the theoretical capacity of vertiports by using mathematical models and computer simulations. However, there are certain time delays for UAVs in vertiports. Therefore, the capacity assessment of vertiports needs to consider the balance between the throughput of vertiports and the delay of UAVs, which has not been taken into account in many existing research. Meanwhile, airport capacity is an evaluation indicator related to multiple factors for airport operation capability. In traditional civil aviation, airport capacity can refer to the number of aircraft that an airport can serve within a certain period of time, or it can also refer to the passenger throughput within a period of time. Therefore, the vertiport capacity evaluation method that combines multiple factors such as the throughput of the vertiport, the aircraft delay level, and the aircraft payload, which is regarded as a research gap.
In this study, a method for evaluating the capacity of vertiports based on a combination of customer satisfaction, capacity and delay level is proposed. By selecting four different types of UAVs and considering constraints such as aircraft safety separation, endurance and the elements of vertiport, this study evaluates the practical capacity of vertiports and customer satisfaction based on genetic algorithm. The main structure of this paper is as follows. Section 2 analyses the operational scenarios and basic parameters of vertiports. Capacity assessment model of vertiports is introduced in Section 3. Section 4 presents the realisation of the capacity assessment model using genetic algorithms, Section 5 analyses the experimental results of the proposed model. Finally, Section 6 concludes this study and provides outlooks for future research.
2.0 Problem statement
2.1 Scenario analysis
Compared with the traditional civil aviation transportation scenario, vertiports need to provide vertipads, gates and taxiways [Reference Administration15–17] to meet the basic requirements of UAM. The vertipad has the same function as the runway in traditional civil aviation, aiming to provide the final landing area and the initial take-off area for aircraft. Additionally, to avoid the aerodynamic influence of nearby obstacles and other aircraft, a pad safety area needs to be set up for vertipad. The gate is used for UAVs to conduct turnaround operations such as loading and unloading cargo or passenger boarding and it also requires a certain amount of space to ensure the operational safety of the aircraft. A taxiway is a predetermined route demarcated for UAVs to make transfers on the ground. UAVs can fly along the predetermined route close to the ground or be towed by other means of transportation for moving. The terminal building is the relevant operation area where passengers conduct security checks and luggage check-in. The main elements of the vertiport are shown in Fig. 1.
Figure 1. Vertiport main elements.
In this study, UAVs originate from the final approach fix, then proceed to decelerate and select a landing vertipad to complete the landing mission. Subsequently, UAVs taxi from the taxiway to the gates, unload cargo or recharge, then return to the vertipad to complete departure mission. If the UAV requires maintenance or other operations, it needs to enter the hangar for servicing. With the definition of the approach and departure procedures in the terminal area for UAVs as outlined by Schweiger et al. [Reference Schweiger, Knabe and Korn19], the summary of terminal area operations is illustrated in Fig. 2. This study primarily addresses resource allocation issues during the final approach procedure (3,A), initial departure procedure (3,D) and ground operations in the vertiport. While ensuring the safety and endurance of UAVs, the aim is to maximise the throughput and customer satisfaction of vertiports.
Figure 2. Vertiport operations schematic diagram.
2.2 Research assumptions
Since the arrival traffic flow of UAVs and the speed of UAVs are complex during takeoff and landing, in order to establish a capacity assessment model for vertiports, and after some reasonable simplifications, the following assumptions are proposed:
-
(1) All aircraft arriving at the vertiport complete the landing procedure, followed by the turnaround procedure, and then depart.
-
(2) There are sufficient gates to accommodate aircraft and departure aircraft always have sufficient battery power.
-
(3) The traffic characteristics of arriving aircraft follow a Poisson distribution, while the initial remaining battery power of these aircraft follows a normal distribution.
-
(4) The final approach and initial departure procedures of aircraft are simplified to uniform deceleration and uniform acceleration stages.
3.0 Vertiport capacity assessment model
To meet the future demand for large-scale UAM, this study propose a capacity assessment model for vertiports based on the analysis of key elements and operational processes within the vertiport, considering multiple aircraft types, multiple vertipads and factors such as customer satisfaction and delay levels. The definitions of the main notations used in the paper are shown in Table 1.
Table 1. Definitions of main notations used in the paper
In the process of evaluating the capacity of vertiports, it is necessary to formulate the objective function based on airport operation flow and customer satisfaction. Therefore, the objective function of the optimisation model is as follows:
\begin{align} \max TP & = \sum\limits_{t = 0}^T {\sum\limits_{k \in K} {\sum\limits_{i \in I} {\sum\limits_{j \in J} {x_{i,j,t}^k} } } } \\[-32pt] \nonumber \end{align}
\begin{align} \max SRV & = \sum\limits_{t = 0}^T {\sum\limits_{k \in K} {\sum\limits_{i \in I} {\sum\limits_{j \in J} {C(i)flag(i,j,t,t^{\prime}(i),k)x_{i,j,t}^k} } } } \end{align}
Equation (1) represents the throughput of the vertiport, while Equation (2) considers the maximum payload of the aircraft and the actual arrival time, thus reflecting the quality of airport service, also referred to as customer satisfaction. In Equations (1) and (2),
$T$
refers to the simulation scenario time horizon,
$i$
and
$j$
represent the aircraft index and the serial number of the vertipad occupied by aircraft with index
$i$
respectively,
$C(i)$
denotes the maximum payload of aircraft with index
$i$
. The task indicator for aircraft arrival or departure is denoted as
$k$
, where
$k = {\rm{A}}$
indicates that aircraft
$i$
is performing an arrival task, and
$k = {\rm{D}}$
indicates that aircraft
$i$
is performing a departure task.
$t$
represents the starting time when aircraft
$i$
occupies the vertipad, while
$t^{\prime}(i)$
represents the time when aircraft
$i$
arrives above the landing vertipad.
$flag(i,j,t,t^{\prime}(i),k)$
denotes whether the aircraft is meeting the endurance constraint at time
$t$
for the task execution. Only aircraft that satisfy the endurance constraint are eligible for satisfaction rewards. The specific definition is as follows:
\begin{align} flag(i,j,t,t^{\prime} (i),k) & = \left\{ {\begin{array}{l@{\quad}c}1 & {}{if\ k = {\rm{D\ or\ }}t - t^{\prime}(i) \le endurance (i)}\\[3pt] 0 & {}{t - t^{\prime} (i) \geq endurance (i)}\end{array}} \right. \\[-10pt] \nonumber \end{align}
\begin{align} t^{\prime} ({i + 1}) & = t^{\prime}(i) + \Delta t \\[6pt] \nonumber \end{align}
In Equation (3),
$endurance(i)$
represents the endurance time (seconds) of aircraft
$i$
, where
$\Delta t$
is the time interval between adjacent arriving aircraft,
$\Delta t\sim \exp \!( {{\lambda _0}} )$
.
\begin{align} & x_{i,j,t}^k + \sum\limits_{k^{\prime} \in K} {\sum\limits_{i^{\prime} \in I} {\sum\limits_{t^{\prime} = t}^{t + {\alpha _i} + {\theta _{i,i^{\prime}}}} {x_{i^{\prime},j,t^{\prime}}^k} } } \le 1 \\[-24pt] \nonumber \end{align}
\begin{align} & \sum\limits_{k \in K} {\sum\limits_{i \in I} {\sum\limits_{j \in J} {x_{i,j,t}^k} } } \le m \\[-24pt] \nonumber \end{align}
\begin{align} & \sum\limits_{t \in T} {\sum\limits_{j \in J} {x_{i,j,t}^{\rm{A}}} } \le 1 \\[-24pt] \nonumber \end{align}
\begin{align} & \sum\limits_{t \in T} {\sum\limits_{j \in J} {x_{i,j,t}^{\rm{D}}} } \le 1 \\[-24pt] \nonumber \end{align}
\begin{align} & x_{i,j,t}^{\rm{A}} = x_{i,j^{\prime},t + 2{\beta _i} + {l_0}}^{\rm{D}} \\[-24pt] \nonumber \end{align}
\begin{align} & t^{\prime}(i)\left( {\sum\limits_{t \in T} {\sum\limits_{j \in J} {x_{i,j,t}^{\rm{A}}} } } \right) \le t \le \left( {t^{\prime}(i) + endurance(i)} \right)\left( {\sum\limits_{t \in T} {\sum\limits_{j \in J} {x_{i,j,t}^{\rm{A}}} } } \right) \end{align}
Equation (5) ensures that for any given vertipad
$j \in J$
, only one aircraft can be serviced within its required occupancy time
${\alpha _i}$
and safety interval
${\theta _{i,i^{\prime}}}$
for the aircraft
$i$
. Equation (6) ensures that the number of aircraft landing on the vertipad at any given time should not exceed the number of vertipads
$m$
. Equations (7) and (8) signify that for any aircraft
$i \in I$
with a specific serial number, it can arrive at and depart from the vertiport only once. Equation (9) states that aircraft arriving at the vertiport must depart after a turnaround, where
${\beta _i}$
represents taxiing time (fixed at 15 seconds) and
${l_0}$
represents turnaround time (fixed at 300 seconds). Equation (10) states that the landing time of the aircraft must be later than the time it arrives over vertiport, and the landing must commence within the endurance time.
${\theta _{i,i^{\prime}}}$
refers to the safety spacing required between the aircraft
$i$
and aircraft
$i^{\prime}$
during the approach procecedure, simplified as uniform deceleration motion.
4.0 Realisation of capacity assessment
The multi-angle assessment model established for vertiport capacity in this paper belongs to the category of single-objective optimisation problems. Due to the vast search space involved in finding feasible solutions and the complexity of optimisation objectives, employing swarm intelligence algorithms can improve search efficiency through the collaboration of multiple agents, thereby addressing large-scale integer programming problems. Due to the discrete nature of the decision variables in this model and the fact that genetic algorithms exhibit characteristics such as convergence and robustness, which is widely used in solving network flow problems and large-scale integer problems [Reference Brown and Sumichrast44], this paper chooses to use genetic algorithms to solve this capacity assessment model. Based on the characteristics of the decision variables and constraints in this model, the solution steps of the genetic algorithm are divided into operations such as encoding, selection, crossover, mutation, repair and recombination.
4.1 Encoding
Genetic algorithms construct a population of feasible solutions by encoding individuals into arrays, and then filter these individuals through a fitness function. The encoding form of individuals in the population significantly influences the efficiency of genetic algorithm solutions. The capacity assessment method constructed in this paper is a large-scale integer programming problem. As the number of vertipads and demand increases, the size of the feasible solution space grows exponentially. Therefore, selecting a reasonable encoding form is key to efficiently solving this problem. If according to the constraints and initial form of decision variables in the capacity assessment model, the encoding form of decision variables as shown in Fig. 3.
Figure 3. The initial encoding form of decision variables.
For better encoding, this paper separately lists the IDs of the UAVs for encoding. Based on their occupancy time and safety interval, the starting time of subsequent UAV occupancy of the vertipad is calculated. For the vertiport with four vertipads, the relationship between arrival sequence and time is shown in Fig. 4. Equations (11)–(14) illustrate the arrival times of aircraft with different IDs for the four vertipads. If their calculated arrival times precede their arrival over the vertiport, they will be adjusted in subsequent repair operations.
\begin{align} {t_{4k + 1}} & = sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],1} \big) + {\alpha _{ID1}} + {\theta _{ID\left( {4k + 1} \right),ID1}} \\[-10pt] \nonumber \end{align}
\begin{align} {t_{4k + 2}} & = sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],2} \big) + {\alpha _{ID2}} + {\theta _{ID\left( {4k + 2} \right),ID2}} \\[-10pt] \nonumber \end{align}
\begin{align} {t_{4k + 3}} & = sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],3} \big) + {\alpha _{ID3}} + {\theta _{ID\left( {4k + 3} \right),ID3}} \\[-10pt] \nonumber \end{align}
\begin{align} {t_{4k + 4}} & = sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],4} \big) + {\alpha _{ID4}} + {\theta _{ID\left( {4k + 4} \right),ID4}} \\[-10pt] \nonumber \end{align}
\begin{align} ID1 & = ID \big( {sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],1} \big)} \big) \\[-10pt] \nonumber \end{align}
\begin{align} ID2 & = ID \big( {sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],2} \big)} \big) \\[-10pt] \nonumber \end{align}
\begin{align} ID3 & = ID \big( {sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],3} \big)} \big) \\[-10pt] \nonumber \end{align}
\begin{align} ID4 & = ID \big( {sort \big( {\left[ {{t_{4k - 3}},{t_{4k - 2}},{t_{4k - 1}},{t_{4k}}} \right],4} \big)} \big) \\[6pt] \nonumber \end{align}
Figure 4. The encoded form after processing the decision variables.
In Equations (11)–(18),
${t_{4k + 1}}$
represents the starting time of occupancy of the aircraft
$4k + 1$
on the landing vertipad. The elements of array
$a$
are arranged in ascending order, and counting starts from the smallest element, the element at position
$b$
corresponds to
$sort\left( {a,b} \right)$
.
$ID\left( {sort\left( {a,b} \right)} \right)$
is the ID number corresponding to
$sort\left( {a,b} \right)$
.
4.2 Genetic operations
The genetic operations include selection, crossover, mutation, recombination and repair operations. In this study, the binary tournament principle is employed to select the generated population. All components of the objective function aim to maximise their values; however, due to the different dimensions, normalisation is required. The normalisation formulas for throughput and customer satisfaction are provided as Equation (19) and (20).
\begin{align} TP^{\prime} = \frac{{\sum\limits_{t = 0}^T {\sum\limits_{k \in K} {\sum\limits_{i \in I} {\sum\limits_{j \in J} {x_{i,j,t}^k} } } } - pad \cdot T/\left( {\max\! \left( {{\theta _{i,j}}} \right) + \max\! \left( {{\alpha _i}} \right)} \right)}}{{pad \cdot T/\left( {\min \!\left( {{\theta _{i,j}}} \right) + \min \!\left( {{\alpha _i}} \right)} \right) - pad \cdot T/\left( {\max \!\left( {{\theta _{i,j}}} \right) + \max \!\left( {{\alpha _i}} \right)} \right)}} \end{align}
\begin{align} SRV^{\prime} = \frac{{\sum\limits_{t = 0}^T {\sum\limits_{k \in K} {\sum\limits_{i \in I} {\sum\limits_{j \in J} {C(i)flag(i,j,t,t^{\prime}(i),k)x_{i,j,t}^k} } } } }}{{\max \!\left( {C(i)} \right) \cdot \lambda }} \end{align}
\begin{align} \max Z = {\omega _1} \cdot TP^{\prime} + \left( {1 - {\omega _1}} \right) \cdot SRV^{\prime} \end{align}
In Equations (19)–(21),
${\omega _1}$
represents the weighting coefficients,
$pad$
denotes the number of vertipads,
$\lambda $
refers to the approach demand of each simulation scenario. Equation (21) represents the objective function of the vertiport capacity assessment model, which combines vertiport throughput and customer satisfaction.
Genetic algorithm crossover and mutation are aimed at creating new individuals within the population. By introducing random and small-scale mutations, genetic algorithms can maintain population diversity and prevent the model from getting trapped in local optima. Crossover refers to the exchange of alleles between different individuals, while the mutation process involves randomly swapping genes at two different positions within the same individual. The crossover and mutation processes of this model are illustrated in Fig. 5.
Figure 5. The schematic diagram of the crossover and mutation processes.
The repair process refers to adjusting the genes to meet the required constraints. In the calculation process for landing and takeoff times, if an aircraft’s calculated time is earlier than its arrival at the airspace over the vertiport, the individual will be repaired by adjusting the aircraft to be near its arrival time gene. Similarly, for departure aircraft, it will be adjusted to be near its departure time gene to complete the repair.
4.3 Algorithm flow
In genetic algorithms, given a specified maximum number of iterations and mutation probability, selection and genetic operations are applied to the initially formed feasible solutions. Additionally, the algorithm iterates continuously until the maximum number of iterations is reached, at which point the objective function achieves a better solution or even the global optimum. The specific steps of the model solving process are as follows:
5.0 Experimental results
In this section, a vertiport equipped with four vertipads is considered. Four types of aircraft include DJI FLYCART 30, Wingcopter 178 Heavy Lift A, T20 and 3WWDZ-21 are used to analyse the vertiport throughput, customer satisfaction, total objective function value and vertiport delay, and the specific relevant parameters are shown in Table 2. By varying the proportions of different types of UAVs, the average endurance time of aircraft, the proportions of different aircraft types, and the weighting values of different components of the objective function, the overall operation of the airport can be analysed. Sensitivity analysis and discussion is conducted on different parameters to understand their impact on the vertiport’s overall performance.
5.1 Numerical example
In the UAM simulation scenario, the operation horizon is set to 900 seconds, and the proportions for each of the four types of aircraft is set at 25% with an approach demand of 96 aircraft and an average remaining endurance time of 300 seconds of approach aircraft. Additionally, the vertiport is equipped with four vertipads and the time step of the simulation is 1 second. The iterative graph of total satisfaction is shown in Fig. 6 and the throughput, customer satisfaction, total objective function value, which is also known as total satisfaction value, are obtained as shown in Table 3.
Table 2. The specific relevant parameters of the UAVs
The FCFS is a common method for takeoff and landing sequences. In order to compare the FCFS algorithm with the algorithm proposed in this paper, the accumulated number of aircrafts under different operational delays for these two algorithms is shown in Fig. 7 and a takeoff or landing is called a movement.
A threshold time of allowable average delay can be chosen and the capacity below this threshold is considered the ‘practical capacity’. In Fig. 7, the vertical line within the box indicated by the arrow represents that the cumulative aircraft movements in a scenario using CEGA is 58, with delays ranging from less than 171 to 189 seconds. Therefore, the practical capacity with the delay time ranging from 171 to 189 seconds is 58. According to Fig. 7, for the same level of delay, the practical capacity of the vertiport under CEGA is higher than that under FCFS. For vertiport equipped with four vertipads, the number of aircraft movements under the CEGA algorithm is always greater than that of the FCFS algorithm under the same level of delay. After 360 seconds, the cumulative movement of the two algorithms remains constant.
Table 3. Results of capacity assessment model
Figure 6. Iterative process of genetic algorithm.
Figure 7. Accumulated aircraft movements under different levels of delay.
In order to compare the aircraft approach and departure delays of the two algorithms, the delays of the first 79 approach and departure aircraft are obtained as shown in Fig. 8. It can be observed that there are some delays under both algorithms, and there is not much difference between the two algorithms in the early stage of the operation. The delay level of the CEGA algorithm is significantly lower than the FCFS algorithm in the middle and late stages of the operation, and the delay time becomes more and more serious with the increase of the number of approach aircraft, but the delay time of the CEGA algorithm is at a low level.
Figure 8. Delay time.
In order to analyse the overall delay of vertiports under two different algorithms, the delay time of aircrafts is plotted in a box line diagram as shown in Fig. 9. It can be seen that the average aircraft delay under the CEGA algorithm operation is 107 seconds with a maximum value of 341 seconds, and the average aircraft delay under the FCFS algorithm operation is 139 seconds with a maximum value of 424 seconds which is significantly higher than the overall delay level of the CEGA algorithm. In addition, delays for aircraft under CEGA operations are more concentrated, mainly in the range of 0 to 200 seconds, while delays under FCFS operations are more dispersed.
Figure 9. Boxplot of delay time distribution comparison.
5.2 Discussion
Vertiport practical capacity and aircraft delay may be related to airport infrastructure, aircraft type and vertipad occupancy time. Infrastructure includes the number of gates and vertipads, and the impact of the number of gates on vertiport capacity has been discussed by Vascik and Hansman [Reference Vascik and Hansman22].
In this model, the level of aircraft endurance and the weight coefficients of the different terms of the objective function have the potential to affect the change of the objective function value. Therefore, in this section, different operation conditions such as aircraft type proportion, number of vertipads, aircraft endurance level and objective function weights will be researched for their impact on airport operations.
5.2.1 Proportion of aircraft types
In UAM scenarios, the proportion of aircraft in the vertiports may change at any time. In this operational scenario, the vertiport is equipped with four vertipads. Within the 900 seconds simulation period, 96 aircraft are scheduled for approach, with the average remaining power of the aircraft being 300 seconds, and the time step of the simulation is 1 second. Therefore, the DJI FLYCART 30, Wingcopter 178 Heavy Lift A, T20 and 3WWDZ-21 are selected to study the effect of aircraft type proportion on the operation of vertiports with CEGA, and the proportion of various aircraft types is set to 1:1:1:1 (25.0%), 2:1:1:1 (40.0%), 3:1:1:1 (50.0%), 4:1:1:1 (57.1%), 5:1:1:1 (62.5%) in turn. The objective function weight coefficients are all set to 0.5 and the trends of maximum capacity, customer satisfaction and objective function values are shown in Figs. 10 and 11.
Figure 10. Maximum capacity.
Figure 11. Customer satisfaction and objective function values.
For the purpose of exploring the impact of aircraft type proportion on the maximum capacity of vertiports, the trends of the capacity of vertiports under different aircraft type proportion are comparatively analysed. It is observed that the capacity of vertiport gradually decreases with the gradual increase of the proportion of Wingcopter 178 Heavy Lift A, while the capacity fluctuates with the gradual increase of the proportion of other aircraft and the trend of change is not obvious, and the aircraft type proportion has a small impact on the capacity of vertiports.
In Fig. 11, it can be seen that, as the proportion of DJI FLYCART 30 increases, its customer satisfaction and total objective function values keep increasing, with the maximum when the proportion reaches 62.5%. As for the Wingcopter 178 Heavy Lift A, however, its customer satisfaction and total objective function values decrease as the proportion increases, and the customer satisfaction experienced a significant decrease. For the T20 and 3WWDZ-21 UAVs, as the proportion continues to increase, their customer satisfaction and total objective function values fluctuate with the proportion and there is no significant trend. The increased proportion of DJI FLYCART 30 with higher maximum loads will result in a significant increase in the overall vertiport cargo volume and thus improve customer satisfaction. The maximum loads of the T20 and 3WWDZ-21 models are at the average level for all aircraft and do not affect customer satisfaction too much. In order to study the impact of different aircraft proportions on the delay level of vertiports, the delay level of different scenario is shown in Fig. 12.
Figure 12. Status of delays at vertiports with different aircraft type proportions.
In Fig. 12, the axes T2 to 3W indicate the delay time corresponding to the proportions of 3WWDZ-21 at 25.0%, 40.0%, 50.0%, 57.1% and 62.5%, respectively. Similarly, the intervals from W1 to T2, DJ to W1, and origin to DJ on the axis correspond to T20, Wingcopter 178 Heavy Lift A and DJI FLYCART 30, respectively. It can be seen from Fig. 10 that increasing the proportion of DJI FLYCART 30 and 3WWDZ-21 may lead to more severe delays for aircraft in the later stages of the vertiport operation. A small number of delays occurr on the other two types of aircraft, the main possible reason for which is the difference in safety intervals between aircraft.
5.2.2 Endurance level
In order to study the impact of the remaining battery power of UAV on the operation status of vertiports, the mean values of the remaining battery power of UAV fleet are successively set to 150s, 200s, 250s, 300s, 350s and 400s, and its standard deviation is 50s. Customer satisfaction, vertiport capacity and total objective function values are obtained, as shown in Table 4.
Table 4. Results of capacity assessment model
Based on Table 4, it can be seen that the airport customer service satisfaction increases as the average remaining battery level continues to increase and then stabilises at a certain level. In addition, the level of aircraft remaining battery level has little impact on the practical capacity of the airport, and the overall objective function values are generally consistent with the trend in customer service satisfaction. As the level of remaining battery level gradually increases, more aircraft have the time to complete their approach and departure missions and their customer satisfaction gradually increases, resulting in an increase in overall service satisfaction. The reason that remaining battery level does not have a significant impact on vertiport capacity may be that airport capacity is primarily related to spacing and occupancy time.
5.2.3 Number of vertipads
In order to further study the effect of the number of vertipads on the capacity and delay of vertiports, the number of vertipads are set to be 2, 4, 6, 8, 10 and 12 based on the above model. Approach demand aircraft are set to 240 within 15 minutes, and the accumulated number of departures and arrivals under different scenarios with different levels of delays are obtained as shown in Fig. 13.
Figure 13. Accumulated movements under different levels of delays and vertipads.
The number of vertipads is a key factor affecting the operational efficiency of vertiports. It is observed in Fig. 13 that the practical capacity of the vertiport under the operation of the CEGA algorithm is higher for the same acceptable delays when there is a shortage of vertipads. Within a certain range of the number of vertipads, the maximum movements difference between the CEGA and FCFS algorithm for the same level of delay gradually increases with the increase in the number of vertipads, from 22 to 62. However, as the number of vertipads increases to 8 and above, the maximum movement difference decreases. With a number of vertipads reaching 10, the movements under FCFS operation is even more than the CEGA algorithm within a certain delay time range. The reason for the above phenomenon is that when the number of vertipads is sufficient to meet the needs of the approaching aircraft fleet, almost all aircraft can follow the scheduled approach time with almost negligible delays, thus keeping the vertiport in a smooth and orderly state.
The above analysis of Fig. 13 can be applied to the UAM operation scenario. When the vertipads can not meet the demand of planned approaching and departing aircraft, CEGA algorithms can be used for approach and departure scheduling and capacity assessment to improve airport operational efficiency. However, when sufficient vertiport ground resources are available, the FCFS algorithm allows the airport to operate at low delay levels.
5.2.4 Objective function component weighting coefficient
The objective function of this study consists of the number of flights approaching and departing the airport and customer service satisfaction, where customer service satisfaction is related to whether or not the aircraft meets the endurance and the maximum load of the aircraft. The objective weighting coefficients
${\omega _1}$
will affect the values of the components of the objective function, and the objectives of each component can be reasonably balanced to improve the operation of the vertiport. In order to find out the optimal objective weight coefficients,
${\omega _1}$
is in steps of 0.05 and divided into 21 groups from 0 to 1. The number of approaching and departing aircraft, customer satisfaction and total objective function values are obtained as in Table 5.
Table 5. Results with different objective weighting coefficients
Figure 14 shows the trend of the objective function components with the weighting coefficients, it can be seen that there is an overall upward trend in vertiport capacity and a downward trend in customer service satisfaction as
${\omega _1}$
increases. Based on the obtained values of the total objective function, the optimal results are obtained from Experiments 17 and 19, thus the optimal combination of weight coefficients is
${\omega _1} = 0.80$
or
${\omega _1} = 0.90$
. Due to the large difference in capacity between Experiment 17 and Experiment 19, when favouring the capacity, the combination of weighting coefficients for Experiment 17 can be chosen. The combination of weighting coefficients in Experiment 19 is more in favour of customer satisfaction.
Figure 14. Trends in the results of different weighting coefficients.
6.0 Conclusion and future work
In the face of the future development of UAM, a reasonable and scientific method of assessing the capacity of vertiports is helpful to improve the operational efficiency of UAM and the utilisation rate of ground facilities. A method for assessing the operational capacity of a vertiport based on a combination of throughput and customer satisfaction is proposed in this paper, and the main contributions are as follows:
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• In this paper, based on the constraints of aircraft endurance and safety intervals, the air-ground synergistic integration of the dynamic assessment of the operational capacity of vertiports model considering throughput and customer satisfaction are constructed. When the weights of throughput and customer satisfaction are set to 0.8 and 0.2, respectively, the performance of this optimisation model is optimal. The balanced relationship between throughput and customer satisfaction at vertiports per unit time is explored to provide a reference for future UAM operations.
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• Based on the construction of a capacity assessment model, the sensitivity of aircraft type proportion, remaining battery level and the number of vertipads to the operational capacity and delay level is analysed. Meanwhile, a comparative analysis between the proposed assessment algorithm and the FCFS algorithm is conducted and it can be inferred that the CEGA algorithm is beneficial to improve the efficiency of vertiport when the vertiport has limited vertipads.
This study provides a method for assessing the operational capacity of a vertiport based on airport throughput and customer satisfaction. However, the future urban airspace conditions are complex, so the variety of ground facilities of vertiports and the flight procedures under complex terrain condition should be fully taken into account when assessing the capacity of vertiports, and severe weather and emergencies are also key factors in capacity assessment.
