Urban low-altitude user equilibrium system with generalized cost

Abstract

This invention discloses a city low-altitude user equilibrium system with generalized cost, comprising: constructing an air-ground cooperative three-dimensional transportation network for users to travel between origin and destination in low-altitude environments; defining a generalized path cost model and constructing an air-ground cooperative three-dimensional transportation network cost model based on the topology of the network; transforming the user equilibrium problem in the air-ground cooperative three-dimensional transportation network into a variational inequality model based on traffic flow within the network; and solving the variational inequality model using a combination of the K-shortest path algorithm and adaptive projection method to calculate the equilibrium flow of the air-ground cooperative three-dimensional transportation network, thereby completing the planning of the city low-altitude travel system. This system accurately characterizes many real-world factors considered by users when traveling in the air-ground cooperative network, providing decision support for urban management departments to effectively construct and fully utilize the performance of the city's three-dimensional transportation network.

Description

Technical Field

[0001] This invention relates to the field of low-altitude travel planning, and specifically to an urban low-altitude user balancing system with generalized costs. Background Technology

[0002] As a crucial component of future transportation infrastructure, low-altitude transportation will profoundly reshape urban transportation networks and industrial spatial layouts. Therefore, effectively integrating low-altitude transportation networks with existing urban ground transportation networks to establish a comprehensive urban low-altitude transportation network and accurately capture users' travel behavior is essential for alleviating urban congestion and fully leveraging the performance of urban air mobility (UAM) systems.

[0003] Traffic flow allocation plays a crucial role in urban network analysis by distributing traffic flow across transportation networks and capturing user travel behavior. Wardrop et al. first identified two criteria for traffic flow allocation: User equilibrium (UE) and System optimization (SO). The UE criterion is that no user can shorten their travel time by changing their route. In contrast, the SO criterion is that the average travel time for all users is minimized. Beckmann et al. first applied the UE criterion to traffic flow allocation in urban road networks and proposed an equivalent nonlinear convex programming model. Based on this, numerous studies have explored the applications of UE, including traffic flow modeling, traffic network design, and traffic emission assessment. However, existing research has focused less on urban air traffic networks.

[0004] In recent years, with the development of Electric Vertical Take-Off and Landing (eVTOL) technology, urban air mobility has received widespread attention from academia and industry. However, existing research mainly focuses on eVTOL design, trajectory optimization, policy formulation, and vertical take-off and landing airport operation. Swaminathan et al. proposed incorporating vertical take-off and landing capabilities into the powertrain architecture of flying cars based on dual power sources such as fuel cells and batteries. Xie et al. optimized the eVTOL speed curve based on differential evolution algorithms. Bulusu et al. explored the potential market for UAM as an alternative to community multimodal transport. Cohen et al. systematically discussed the current status, opportunities, and challenges of UAM.

[0005] However, in future UAM systems, urban air mobility cannot exist in isolation but must be deeply integrated with existing urban ground transportation networks. A few studies have discussed the integration of urban air mobility with ground transportation networks. Gavric et al. developed a micro-simulation platform to integrate amphibious vehicles into urban trunk traffic flow; Xiong et al. alleviated local traffic congestion by deploying eVTOL vertical take-off and landing fields upstream and downstream of urban arterial roads. However, these studies, focusing on the coordination of local facilities, cannot comprehensively assess the overall impact of urban-level three-dimensional transportation networks on ground transportation systems. Addressing the design problem of urban three-dimensional transportation networks, Zhang et al. constructed a three-dimensional transportation network topology based on queuing theory, analyzed the impedance characteristics of different link types, and achieved user equalization based on travel time. Based on this, they further studied the site selection and capacity planning problems of vertical take-off and landing fields. In addition, Wang et al. studied the design problem of urban agglomeration UAM networks based on queuing theory.

[0006] However, regarding user route selection behavior, the aforementioned studies only consider a single criterion based on travel time, neglecting the heterogeneous costs caused by numerous real-world factors. For example, compared to ground vehicles, eVTOL incurs higher energy costs when operating in the air. Furthermore, eVTOL operation in the air is susceptible to weather conditions, and the aforementioned studies have ignored the impact of weather conditions on user route selection. Therefore, the goal of this invention is to accurately characterize the numerous real-world factors considered by users when traveling in a road-air cooperative network, based on the established urban three-dimensional transportation network topology. It aims to construct a generalized cost model that includes time costs, electricity costs, flight pricing costs, and weather risk costs, describing the response mechanism between user route selection behavior and various real-world costs from a micro-level perspective. This provides decision support for urban management departments to effectively construct urban three-dimensional transportation networks and fully utilize their performance. Summary of the Invention

[0007] The purpose of this invention is to provide a generalized cost-based urban low-altitude user equilibrium system, addressing the problem in existing research that only considers ground transportation time costs and neglects the multidimensional cost factors of air-ground cooperative travel. By establishing a three-dimensional transportation network topology including ground roads, vertical take-off and landing airports, and flight links, and comprehensively considering time costs, electricity costs, flight pricing costs, and weather risk costs, a generalized path cost model is constructed. The non-additive user equilibrium problem is transformed into a variational inequality model, which is solved using an algorithm combining K-shortest path and adaptive projection. This enables accurate characterization and equilibrium analysis of user travel behavior in the urban air-ground cooperative transportation network, providing technical support for the planning and operational optimization of urban low-altitude travel systems.

[0008] To achieve the above functions, this invention designs an urban low-altitude user balancing system with generalized cost, executing the following steps S1-S4 to complete the urban low-altitude travel system planning:

[0009] Step S1: Construct an air-ground cooperative three-dimensional transportation network, including road links, queuing links, flight links and evacuation links. Users take eVTOL vehicles to travel between their origin and destination in low-altitude environments within the air-ground cooperative three-dimensional transportation network.

[0010] Step S2: Define a generalized path cost model that includes time cost, flight pricing cost, electricity cost and weather risk cost. Based on the generalized path cost model and the topology of the air-ground cooperative three-dimensional transportation network, construct the air-ground cooperative three-dimensional transportation network cost model.

[0011] Step S3: Based on the traffic flow of road links, queuing links, flight links and evacuation links in the air-ground cooperative three-dimensional transportation network, and the cost model of the air-ground cooperative three-dimensional transportation network, the user equilibrium problem in the air-ground cooperative three-dimensional transportation network is transformed into a variational inequality model.

[0012] Step S4: Using a combination of the K-shortest path algorithm and the adaptive projection method, solve the variational inequality model, calculate the equilibrium flow of the air-ground coordinated three-dimensional transportation network, and output the flow distribution of each path, the cost value of the air-ground coordinated three-dimensional transportation network, and the utilization rate of different links to complete the planning of the urban low-altitude travel system.

[0013] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0014] This invention verifies the performance of the proposed method for urban low-altitude three-dimensional transportation networks using three small-scale networks and conducts sensitivity analysis on various costs affecting network performance. Then, a large-scale network is used to verify the effectiveness of the proposed method. First, experiments are conducted using three small-scale networks (corresponding to short-distance, medium-distance, and long-distance travel scenarios, respectively) to compare the changes in total user travel time and generalized costs before and after introducing air-ground cooperative paths, verifying the model's rationality. Subsequently, sensitivity analysis is performed on key parameters such as traffic demand level, user time value, flight pricing, energy consumption, eVTOL flight speed, and horizontal wind speed, revealing the impact of different factors on user path selection and overall network efficiency. Finally, the model is applied to a large-scale Sioux-Falls network to verify the convergence and computational efficiency of the adaptive projection algorithm in complex traffic networks. The results show that this invention can effectively reduce total travel time and optimize the urban air-ground cooperative transportation system. This invention has the following innovations:

[0015] 1. Based on the construction of a three-dimensional transportation network structure, a user equilibrium model for a land-air cooperative network that considers the generalized cost of users is proposed, which realizes the accurate characterization of users' travel behavior in the three-dimensional transportation network.

[0016] 2. Based on the characteristics of the model, an equivalent variational inequality model was established, and the existence and uniqueness of the proposed model solution were verified under mild conditions. The model was solved by the designed adaptive projection algorithm, providing a new modeling and solution approach for integrating urban low-altitude networks with existing road networks.

[0017] 3. Based on verifying the feasibility of the model and algorithm, a sensitivity analysis was conducted on the key parameters affecting the performance of the three-dimensional transportation network, and the following conclusions were drawn: the construction of a three-dimensional transportation network in short-distance travel scenarios can effectively alleviate urban congestion under saturated or oversaturated traffic demand; the key to fully leveraging the performance of the three-dimensional transportation network lies in accurately matching the queuing system service rate with the demand characteristics under different distance scenarios; flight pricing, flight energy consumption, and horizontal wind speed are all important factors affecting the performance of the three-dimensional transportation network. Attached Figure Description

[0018] Figure 1 This is a flowchart of a city low-altitude user balancing system with generalized cost provided by an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of the topology of an air-ground cooperative three-dimensional transportation network provided according to an embodiment of the present invention;

[0020] Figure 3 This is a schematic diagram of the topology of three types of networks provided according to embodiments of the present invention;

[0021] Figure 4 This is a comprehensive performance analysis diagram of the road network before and after the integration of air-ground cooperative paths according to an embodiment of the present invention;

[0022] Figure 5 This is a traffic demand level sensitivity analysis diagram provided according to an embodiment of the present invention;

[0023] Figure 6 This is a user time value sensitivity analysis diagram provided according to an embodiment of the present invention;

[0024] Figure 7 This is a flight pricing sensitivity analysis chart provided according to an embodiment of the present invention;

[0025] Figure 8 This is a flight speed sensitivity analysis diagram provided according to an embodiment of the present invention;

[0026] Figure 9 This is a flight energy consumption sensitivity analysis diagram provided according to an embodiment of the present invention;

[0027] Figure 10 This is a horizontal wind speed sensitivity analysis diagram provided according to an embodiment of the present invention;

[0028] Figure 11 This is a topology diagram of the Sioux-Falls three-dimensional transportation network provided according to an embodiment of the present invention. Detailed Implementation

[0029] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0030] This invention provides an urban low-altitude user equalization system with generalized cost, referring to... Figure 1 Perform the following steps S1-S4 to complete the urban low-altitude travel system planning:

[0031] Step S1: Construct an air-ground cooperative three-dimensional transportation network, including road links, queuing links, flight links and evacuation links. Users take eVTOL vehicles to travel between their origin and destination in low-altitude environments within the air-ground cooperative three-dimensional transportation network.

[0032] The eVTOL vehicle described in this invention has amphibious capabilities, meaning it can travel on the ground like a regular private car and also fly in the air. In recent years, such amphibious vehicles have received widespread attention from academia and industry.

[0033] All eVTOL vehicles are electrically powered, which aligns with the concept of green and low-carbon travel.

[0034] We assume that all users can accurately perceive the generalized cost of different paths, and that the travel demand between OD pairs is fixed, which follows the unified assumptions of existing user equilibrium studies.

[0035] The topology of the air-ground cooperative three-dimensional transportation network constructed in this invention is as follows: Figure 2 As shown in the diagram. Nodes 1 to 4 are road nodes, and H and T represent vertical takeoff and landing airports. In the air-ground cooperative integrated transportation network, travelers consider various real-world costs when choosing their travel routes. When a user chooses an air-ground cooperative route, the route cost includes weather risk costs (affected by horizontal wind speed), flight pricing, time costs, and electricity costs. The user's travel process includes three stages:

[0036] Step S1.1: The user rides an eVTOL vehicle and queues in the departure queue link to enter the departure airport's vertical takeoff and landing (VTOL) terminal. Figure 1 (Middle node H), perform vertical takeoff and reach the preset safe altitude;

[0037] Step S1.2: The user rides an eVTOL vehicle and flies to the destination's vertical takeoff and landing airport via a flight link. Figure 1 (Middle node T);

[0038] Step S1.3: The user lands in an eVTOL vehicle at the destination's vertical takeoff and landing airport, and then enters the road network via the destination's evacuation link.

[0039] Step S2: Define a generalized path cost model that includes time cost, flight pricing cost, electricity cost and weather risk cost. Based on the generalized path cost model and the topology of the air-ground cooperative three-dimensional transportation network, construct the air-ground cooperative three-dimensional transportation network cost model.

[0040] The specific steps of step S2 are as follows:

[0041] Step S2.1: Users typically choose suitable travel routes based on the generalized cost of the path. In traditional ground transportation network equilibrium studies, generalized cost mainly includes travel time cost and ticket price cost (electricity price or fuel cost). However, in air-ground cooperative three-dimensional transportation networks, the factors influencing user route selection are more complex. Unlike traditional ground travel, flight pricing is widely used in UAM system-related studies to ensure the fairness of resource allocation. Furthermore, eVTOL flights are more susceptible to extreme weather conditions. Therefore, users must also consider the risk costs associated with weather when choosing air-ground cooperative routes.

[0042] The generalized path cost model is defined as follows:

[0043] ;

[0044] in, This represents the generalized path cost model. Indicates the path time cost. Indicates the cost of flight pricing. Indicates electricity cost. Indicates the cost of weather risks; For OD The set of ground paths between them; Indicates OD pair The set of air-to-ground collaborative paths between them; Represents the set of OD pairs;

[0045] Step S2.2: Based on the generalized path cost model and the topology of the air-ground cooperative three-dimensional transportation network, construct the air-ground cooperative three-dimensional transportation network cost model, which includes time cost, flight pricing cost, electricity cost and weather risk cost; divide the path time cost in the air-ground cooperative three-dimensional transportation network cost model into travel time of road links, travel time of queue links, travel time of flight links and travel time of evacuation links.

[0046] For surface road links, the BPR impedance function proposed by the U.S. Federal Highway Administration is widely used to capture the impact of road travel time and traffic flow. The travel time of the road link is calculated as follows:

[0047] ;

[0048] In the formula, This represents the travel time of road link r. Indicates the free-flow velocity of road links and evacuation links; This represents the capacity of road link r; Represents a set of road links; This represents the traffic flow along road link r;

[0049] Among them, the traffic flow of road link r The calculation is as follows:

[0050] ;

[0051] In the formula, Denotes the set of OD pairs, and ; Indicates OD pair The set of paths between; Indicates OD pair Traffic on path j between them; This represents the association variable between road link r and the path. If road link r belongs to an OD pair... When the path j is between ,otherwise ;

[0052] Considering the capacity limitations of vertical airports and the unique characteristics of eVOTL services, the passage process of eVTOL vehicles in queuing links is described as a standard M / M / 1 / C queuing problem. Therefore, the travel time of a queuing link can be calculated as the average dwell time of a user in the queuing system; the calculation of the travel time of the queuing link is as follows:

[0053] ;

[0054] In the formula, This represents the travel time of the queuing link u. Represents the set of queuing links. This represents the probability in the initial state; Indicates the average service rate; This represents the average queue length within the queuing system.

[0055] Among them, the probability in the initial state The calculation is as follows:

[0056] ;

[0057] Average queue length in a queuing system The calculation is as follows:

[0058] ;

[0059] In the formula, Traffic flow representing queuing link u (i.e., the average arrival rate of users in the queuing chain) and the average service rate The ratio; Let u be the capacity of the queuing link.

[0060] Among them, the traffic flow of queuing link u The calculation is as follows:

[0061] ;

[0062] In the formula, The variable representing the association between queuing link u and the path, when queuing link u belongs to the OD pair. When the path j is between, ,otherwise Average service rate ,in This represents the average speed at which an eVTOL vehicle takes off and lands vertically. For safety, this ensures that a safe distance is always maintained between the two eVTOL vehicles;

[0063] Assume that the eVTOL vehicle maintains a constant cruise speed during vertical takeoff and landing and horizontal flight. This steady-state operation mechanism has been widely adopted in UAM-related research. Therefore, the travel time of the flight link is calculated as the sum of the time of the vertical takeoff and landing phase and the travel time of the flight link; the travel time of the flight link is calculated as follows:

[0064] ;

[0065] In the formula, This represents the travel time of flight link F. The flight altitude between takeoff and landing field m and takeoff and landing field n is set as a fixed value based on existing literature; The length of the flight link F; The horizontal cruising speed of eVTOL vehicles; This represents the set of flight links connecting any two vertical takeoff and landing airports, and ;

[0066] The travel time of the evacuation link is calculated as the time it takes for an eVTOL vehicle to pass through the evacuation link at free-flow speed; the travel time of the evacuation link is calculated as follows:

[0067] ;

[0068] In the formula, Indicates the travel time of evacuation link e. The length of the evacuation link, and ; A set of evacuation links for vertical takeoff and landing airports; This indicates the free-flow velocity of road links and evacuation links.

[0069] The path time cost in the cost model of the air-ground cooperative three-dimensional transportation network is as follows:

[0070] ;

[0071] In the formula, This represents the path time cost in the cost model of the air-ground coordinated three-dimensional transportation network. Represents the value of a user's time. This represents the association variable between flight link F and the path. If flight link F belongs to an OD pair... When the path j is between ,otherwise ; The variable representing the association between evacuation link e and the path, if evacuation link e belongs to an OD pair. When the path j is between ,otherwise .

[0072] Based on existing UAM (Universal Access Management) management practices, users must compete for scarce flight link resources by paying a certain fare. To reflect the principles of fairness and cost-effectiveness in resource use, flight costs are related to the length of the flight link. The flight pricing cost in the air-ground cooperative three-dimensional transportation network cost model is as follows:

[0073] ;

[0074] In the formula, This indicates the ticket price for a flight link per unit distance. This represents the flight pricing cost in the cost model of the air-ground coordinated three-dimensional transportation network.

[0075] The electricity cost incurred by users riding in eVTOL vehicles will be calculated based on the route mileage and the electricity price per unit mileage. The electricity cost in the air-ground cooperative three-dimensional transportation network cost model is as follows:

[0076] ;

[0077] in, Indicates the length of the road link; Indicates the length of the queuing link; Indicates the length of the evacuation link; Indicates the length of the flight link;

[0078] The first term on the right side of the equation represents the energy cost incurred by the user while traveling on the ground link; the second term represents the energy cost incurred by the user during vertical takeoff and landing and horizontal flight. This represents the electricity cost in the cost model of the air-ground coordinated three-dimensional transportation network. Indicates electricity price; This indicates the energy consumption of an eVTOL vehicle while it is driving on the ground. This indicates the energy consumption of an eVTOL vehicle while it is in the air. This aligns with the objective fact that the energy consumption of eVTOL vehicles during flight is far higher than that during ground driving.

[0079] Related research indicates that wind interference is a key factor affecting the operation, safety, and regulation of the UAM system. The UAM weather operation standard jointly proposed by NASA and AvMet Applications Inc. classifies wind conditions into three levels based on the impact of horizontal wind speed on flight safety: green zone (horizontal wind speed < 15 ± 5 kts), yellow zone (horizontal wind speed < 20 ± 10 kts), and red zone (horizontal wind speed > 25 kts). Therefore, to quantify the impact of weather factors on user route selection behavior, this invention introduces a weather risk cost related to horizontal wind speed. When the wind condition is at the green level, the flight link is safe to use, and the weather risk cost is 0; when the horizontal wind speed is at the yellow level, wind interference affects route selection, and this impact is quantified by a linear cost function related to the wind speed level; when it is at the red level, the system considers the flight link unavailable, and the weather risk cost is set to infinity. The weather risk cost in the air-ground cooperative three-dimensional transportation network cost model is as follows:

[0080] ;

[0081] In the formula, This represents the weather risk cost in the cost model of the air-ground coordinated three-dimensional transportation network. Indicates horizontal wind speed; Indicates OD pair The set of air-to-ground collaborative paths between them, and ; For OD The set of paths between; This refers to the conversion factor between currency units and horizontal wind speed units. Specifically, when the horizontal wind speed exceeds 15 kts, the user needs to pay a conversion factor for every additional kts of wind speed. Yuanlai quantifies the impact of weather on users' choice of air-ground integrated travel modes.

[0082] Step S3: Based on the traffic flow of road links, queuing links, flight links and evacuation links in the air-ground cooperative three-dimensional transportation network, and the cost model of the air-ground cooperative three-dimensional transportation network, the user equilibrium problem in the air-ground cooperative three-dimensional transportation network is transformed into a variational inequality model.

[0083] The specific steps of step S3 are as follows:

[0084] Step S3.1: The air-ground cooperative three-dimensional transportation network includes the following flow conservation constraints:

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] In the formula, and These represent the traffic flow of the flight link and the evacuation link, respectively. For OD Total demand between;

[0092] Among them, constraints (14)-(17) represent the mapping relationship between different types of link traffic and path traffic. Constraint (18) guarantees the non-negativity of path traffic, and constraint (19) guarantees the OD pair The sum of all path flows between them equals the OD travel demand.

[0093] Step S3.2: Compared with existing research on user equilibrium in transportation networks, the generalized costs of different path types are heterogeneous, making the generalized costs of paths non-additive. Therefore, traditional mathematical programming models are no longer applicable. This invention proposes a variational inequality model based on path flow to describe the user equilibrium problem of a three-dimensional transportation network with generalized costs. The generalized cost vector function of paths is defined as follows:

[0094] ;

[0095] In the formula, For flow vector variables;

[0096] Define the feasible set of path flows As shown below:

[0097] ;

[0098] Obviously, set It is a compact set; therefore, the variational inequality model of the user equilibrium problem in the air-ground coordinated three-dimensional transportation network can be expressed as finding a vector Makes the following equation always true:

[0099] .

[0100] Proposition 1: (Equivalence) That is, the solution of model (22) satisfies the user equilibrium condition of the three-dimensional transportation network.

[0101] Proof: Obviously, model (22) is equivalent to:

[0102] ;

[0103] Therefore, if and only if vector When the solution to mathematical programming (24) is... The solution is the variational inequality model (22):

[0104] ;

[0105] Based on the complementary relaxation KKT conditions of the variational inequality model, the following can be derived:

[0106] ;

[0107] In the formula, The path traffic vector under user load conditions; Let be the path generalized cost vector under user equilibrium conditions; The minimum value of the generalized cost vector of the path under user equilibrium state; symbol The product of the two terms is zero. Therefore, this is equivalent to the user equilibrium condition of a three-dimensional transportation network, thus proving proposition 1.

[0108] Proposition 2: (Existence) That is, the solution to model (22) exists.

[0109] Proof: Set It is a compact set. First, we verify the generalized cost function of the path. In the set The continuity in time cost. Clearly, for generalized travel costs, time cost... In the middle, the travel time of road links (Based on BPR calculations) Continuously differentiable; travel time of the flight link Travel time of evacuation links It is a linear continuous function independent of link traffic. For the passage time of a queuing link... In real-world transportation systems, capacity constraints Typically set to a large value, and requires Therefore, time cost Continuous. Regarding weather costs. Horizontal wind speed The weather risk cost is calculated using a fixed preset value, which ensures... Within the range of horizontal wind speeds Continuous under the condition of horizontal wind speed. At this time, paths containing flight links, queuing links, and evacuation links will no longer be generated, and weather risk costs will increase. Continuous. In addition, flight costs. and electricity cost All are linear continuous functions independent of flow rate. In summary, the generalized cost function... In close proximity Since the above is continuous, according to Nagurney's Theorem 1.4, the solution to the VI model (21) exists, thus proving Proposition 2.

[0110] Proposition 3: (Uniqueness) If The solution to the variational inequality model (22) is unique.

[0111] Proof: First, we discuss the generalized path cost function. The convexity, due to flight pricing costs Electricity cost and risk costs Both are related to path traffic Irrelevant. Therefore, generalized path cost Regarding path traffic The first-order partial derivative is:

[0112] ;

[0113] When a user chooses a ground-based route, the ground link travel time is calculated by the BPR function in equation (2), which is obviously... It is strictly convex. When users choose air-ground coordinated travel routes, the travel times of flight links and evacuation links are independent of traffic flow. Therefore, it is only necessary to verify the travel time of queuing links. convexity. When When, the initial state probability and average arrangement length They can be simplified to:

[0114] ;

[0115] ;

[0116] Therefore, queuing link travel time Adjusted to:

[0117] ;

[0118] The second derivative of the queuing link travel time with respect to link traffic is:

[0119] ;

[0120] In the formula, j=k and Due to the assumption ,therefore In conclusion, It is strictly convex, therefore the generalized cost function The Jacobian matrix is ​​positive definite, that is, the vector function... Regarding flow vectors Monotonic. According to Pang and Facchinei's Theorem 2.3.3(a), model (22) has a unique solution, thus completing the proof. It is worth noting that in actual traffic systems, it is assumed that... This ensures smooth traffic flow and stable operation of the queuing system. For example, traffic management departments can avoid congestion by periodically opening and closing the air-ground coordinated path queuing system. Overall, the mild assumptions are reasonable assumptions for actual traffic congestion control measures.

[0121] Step S4: Using a combination of the K-shortest path algorithm and the adaptive projection method, solve the variational inequality model, calculate the equilibrium flow of the air-ground coordinated three-dimensional transportation network, and output the flow distribution of each path, the cost value of the air-ground coordinated three-dimensional transportation network, and the utilization rate of different links to complete the planning of the urban low-altitude travel system.

[0122] Variational inequality models can be transformed into complementarity problems and solved using commercial solvers. However, convergence difficulties can easily arise in large-scale network experiments or when initial points are poorly chosen. Projection algorithms are widely used to solve VI problems due to their short iterative computation time. Therefore, this embodiment of the invention employs a projection algorithm to solve the model. Furthermore, this embodiment combines the K-shortest path algorithm with adaptive step size techniques to further improve computational efficiency.

[0123] The solution process is as follows:

[0124] Inputs: Road network information; OD (Original Design Location) pair requirements;

[0125] Step 1 Initialization: Set the algorithm convergence accuracy Set the parameters required for the algorithm. , Initial iteration step size The initial number of iterations is k=1. .

[0126] Step 2 generates an initial path set: Following an all-or-nothing allocation method, and satisfying the set... Given an initial flow solution under constraints Based on the K-shortest algorithm, a set of 10 shortest paths is generated for each OD pair w. .

[0127] Step 3: Determine convergence conditions: Update the generalized cost of the path and calculate the projection;

[0128] ;

[0129] ;

[0130] ;

[0131] In the formula, Let OD be the projection of w on the k-th iteration; This represents the cost vector function value for the k-th iteration. For projection operators; Let be the residual norm of OD for the k-th iteration of w; Let OD be the path flow vector for the k-th iteration of w;

[0132] if If the convergence condition is met, stop the iteration; otherwise, proceed to step 4.

[0133] Step 4: Adaptive update step size:

[0134] ;

[0135] ;

[0136] ;

[0137] ;

[0138] In the formula, Let be the step size of the projection in the k-th iteration; and These are intermediate variables in the algorithm.

[0139] if Let k = k + 1, then return to step 3; otherwise, let Repeat step 4.

[0140] Please note the projection operators in steps 3 and 4. and This is equivalent to solving the following quadratic programming problem:

[0141] ;

[0142] In addition, solving hour, .

[0143] The performance of the system designed in this invention is verified using three small networks, and a sensitivity analysis of various costs affecting network performance is performed. Then, the effectiveness of the proposed algorithm is verified using a large-scale network.

[0144] like Figure 3 As shown, three types of networks are set up according to different travel distances. Figure 3 (a), (b), and (c) represent the short-distance, medium-distance, and long-distance travel networks, respectively. Each network contains six nodes and seven links, with nodes C and E being vertical takeoff and landing (VTOL) airports. There are three paths between OD pairs: path OAD (ground path), OBD (ground path), and OCED (air-to-ground cooperative path). Compared to ground travel, eVTOL flights can shorten travel distances. Therefore, in a small-scale network experiment, it is assumed that the air-to-ground cooperative path can shorten ground travel distances by 10%. This embodiment is based on the analysis of electricity prices and wage levels in China. Based on the literature, China's wage levels... The electricity price is Other experimental parameters are set to the following default settings: , , , , , , , , , , .

[0145] Figure 4 To integrate road network performance before and after air-ground cooperative routes. Overall, under saturated traffic conditions, three-dimensional transportation networks are more suitable for medium- to long-distance travel needs. For example, ... Figure 4 As shown in (a), in long-distance travel scenarios, the total travel time for users is 2485.1 hours, a decrease of 46.4% compared to 4640 hours for purely ground-based transportation. This significant improvement is mainly attributed to the absolute speed advantage of air-ground cooperative routes, prompting a large number of users to switch to these routes. In short-distance scenarios, however, the total travel time for users only decreased by 19.6%. To explore the reasons for this, the generalized costs of air-ground cooperative routes and purely ground-based routes were compared for different travel distances. Figure 4 As shown in (b), for medium to long distances, the generalized cost of air-ground cooperative routes is lower than that of ground routes. However, for short distances, the generalized cost of air-ground cooperative routes is 1.88 yuan, higher than the 1.86 yuan of ground routes. This is mainly because the high energy consumption of electricity and the additional flight distance caused by vertical takeoff and landing operations jointly increase the generalized cost of air-ground cooperative routes, reducing the benefits users gain in terms of travel time. Therefore, more users still tend to choose ground transportation. When building a three-dimensional transportation network, urban traffic management departments should prioritize the layout of medium to long-distance travel scenarios to optimize the overall performance of the transportation system.

[0146] To verify the impact of various costs on network performance, this invention conducted sensitivity analyses on traffic demand levels, user time value, flight service pricing, eVTOL energy consumption, eVTOL speed, and horizontal wind speed.

[0147] Figure 5 The results are from a sensitivity analysis of traffic demand levels. Overall, in short- and medium-distance scenarios, the performance of the air-ground coordinated three-dimensional transportation network increases with increasing traffic demand. However, the trend is reversed in long-distance travel scenarios. For example... Figure 5As shown in (a), in short-distance scenarios, the air-ground cooperative three-dimensional transportation network is more suitable for situations where ground traffic is saturated or oversaturated. When the demand-to-segment capacity ratio increases from 0.4 to 0.8, the reduction in users' total travel time increases from 0.37% to 4.4%, with minimal benefits from the air-ground cooperative three-dimensional transportation network. This is similar to the conclusions drawn from the analysis based on travel distance. Under unsaturated traffic conditions, ground links are smooth, and the travel time difference between air-ground cooperative paths and ground roads is not significant. When the demand-to-segment capacity ratio increases to 1.2, ground roads become congested, and the air-ground cooperative path, due to its significantly reduced travel time, dominates with a lower generalized path cost. At this point, 25.9% of users choose the air-ground cooperative travel mode, such as... Figure 5 As shown in (b) of the table, the percentage reduction in total travel time for users increased significantly from 4.4% to 32.2%.

[0148] However, in medium- to long-distance scenarios, the reduction in total travel time shows the opposite trend. Taking long-distance scenarios as an example, when the demand-to-segment capacity ratio increases from 0.4 to 1.2, the reduction in travel time decreases from 78.6% to 52.9%. This seems counterintuitive, as a greater improvement in user travel time is expected as traffic demand increases. The main reason is that in low-demand phases, air-ground coordinated links dominate route selection due to their significant travel time advantage, thereby substantially reducing generalized travel costs. Figure 5 As shown in (b), when the demand-to-segment capacity ratio is 0.4, 100% of users choose the air-ground cooperative route, resulting in a significant increase in the reduction of travel time. As traffic demand rises, the flow rate of the air-ground cooperative route gradually approaches the upper limit of the queuing system's service rate, and the significant increase in user queuing time causes some users to switch to ground routes. However, in terms of sheer numbers, integrating an air-ground cooperative three-dimensional transportation network can significantly improve traffic congestion in medium- and long-distance scenarios.

[0149] Figure 6 The results of the sensitivity analysis on user time value are as follows. Overall, the impact of user time value on network performance exhibits a significant distance dependence. Specifically, in short-distance scenarios, network performance increases with increasing user time value. This is because high-income users prioritize reducing travel time; as user time value increases, the lower travel time cost of air-ground cooperative paths dominates the total cost of the path, thus more users tend to choose air-ground cooperative paths. However, in medium- and long-distance scenarios, network performance shows the opposite trend. Taking the medium-distance scenario as an example, when... When the cost increased from 20 yuan / hour to 100 yuan / hour, the proportion of travel time reduction significantly decreased from 37.4% to 18.1%. This is because even for lower-paid travelers, the substantial time advantage of air-ground coordinated routes attracts a large number of users. Figure 6 As shown in (b) in the figure, when At a rate of only 20 yuan / hour, a staggering 62.5% of users opted for the air-ground coordinated route, causing the queuing system to approach its maximum service load early on. As wage levels increased, the queuing system became overloaded, leading to severe traffic congestion. In conclusion, for urban traffic managers, fully leveraging the performance of a multi-modal transportation network depends not only on attracting high-income users but, more importantly, on accurately matching the queuing system's service load with the demand characteristics of different distance scenarios.

[0150] Figure 7 The results of a sensitivity analysis of flight pricing are as follows. Overall, the performance of the three-dimensional transportation network decreases as flight pricing increases. Figure 7 As shown in (a) of the diagram, taking a medium-distance scenario as an example, when the flight price increases from 0 yuan / km to 1 yuan / km, the proportion of travel time reduction decreases from 31.6% to 0. This is because the high cost of flights drives up the cost of higher air-to-ground collaborative routes, and users tend to choose the lower-cost pure ground routes. However, lower pricing is not always better, as... Figure 7 As shown in (b), in long-distance scenarios, when the flight price increases from 0 yuan / km to 0.2 yuan / km, the travel time reduction rate increases from 25.4% to 42.9%. This is because excessively low flight costs cause user demand to approach the upper limit of the queuing system's service load, leading to queuing congestion. When the price is appropriately increased, a better balance is achieved between user demand and the queuing system's service load (e.g., ...). Figure 7 (as shown in (b)). The above results suggest that there may exist optimal flight pricing that optimizes the performance of the three-dimensional transportation network.

[0151] Figure 8 The results of the sensitivity analysis for eVTOL flight speed are as follows. Overall, under saturated traffic demand, increasing eVTOL speed has a negligible impact on network performance in medium- to long-distance scenarios. However, in short-distance travel scenarios, increasing eVTOL speed has a significant impact on network performance. Specifically, for example... Figure 8 As shown in (a), taking the medium-distance scenario as an example, when the flight speed increases from 100km / h to 300km / h, the travel time reduction ratio only decreases from 31.9% to 31.2%, while for short-distance travel, the travel time reduction ratio significantly increases from 0.8% to 20.6%. This is because in the medium-distance travel scenario, even with the lower eVTOL speed, the land-air cooperative path still has a significant travel time advantage, which allows the queuing system to approach its maximum service rate in the early stages of user demand. Figure 8As shown in (b), user demand changes very little as eVTOL speeds increase further. However, for short-distance travel, when eVTOL speeds are lower, the travel time advantage of air-to-ground cooperative routes is weak, and electricity costs are higher, leading most users to choose ground routes. As eVTOL speeds increase, the time cost of air-to-ground cooperative routes becomes more significant and dominates the lower route cost. Therefore, some users shift to air-to-ground cooperative routes.

[0152] Figure 9 The analysis results show the energy consumption of eVTOL. Overall, the impact of eVTOL energy consumption on network performance exhibits a distance-dependent relationship. Specifically, in short-distance scenarios, network performance decreases as eVTOL energy consumption increases, while in medium- to long-distance scenarios, network performance shows the opposite trend. Figure 9 As shown in (a), in short-distance travel scenarios, when eVTOL energy consumption increases from 20 kWh / 100km to 60 kWh / 100km, the travel time reduction rate decreases from 25.4% to 19.1%, which is consistent with expectations, as higher energy consumption leads to higher path costs. However, in medium- and long-distance scenarios, network performance changes show the opposite trend. Taking the medium-distance scenario as an example, when eVTOL energy consumption increases from 20 kWh / 100km to 60 kWh / 100km, the travel time reduction rate significantly increases from 13.8% to 35.3%. This is mainly because when eVTOL energy consumption is low, air-ground cooperative paths attract a large number of users due to their significant time cost advantage, leading to congestion in the queuing system, such as... Figure 9 As shown in (b), with the increase in energy consumption, some users choose ground routes, alleviating queuing congestion. However, from a quantitative perspective, eVTOL energy consumption has a relatively small impact on the performance of China's low-altitude three-dimensional transportation network for short-distance travel, while in medium- and long-distance scenarios, eVTOL energy consumption is the key to whether the network performance can be fully utilized.

[0153] Figure 10 Based on the sensitivity analysis of horizontal wind speed, overall, horizontal wind speed is a decisive factor in the effectiveness of an air-ground integrated transportation network. For example... Figure 10 As shown in (a), when the horizontal wind speed increases from 15 kts to 21 kts, the reduction in travel time for long-distance travel significantly decreases to 0. All users abandon the use of air-ground cooperative roadway. Furthermore, short-distance scenarios are more sensitive to horizontal wind speed, such as... Figure 10As shown in (b), when the horizontal wind speed is only 17 kts, the user demand for air-to-ground cooperative routes drops from 27.2% to 0. This is because the high cost of weather risks causes users to abandon air-to-ground cooperative routes and switch to ground routes. It is worth noting that, due to the lack of support from existing literature and reports, the weather risk costs of the embodiments of this invention may differ from those in the real world. For traffic managers, in order to fully utilize the performance of the air-to-ground cooperative three-dimensional transportation network, a thorough risk preference survey of users should be conducted to calibrate the risk costs.

[0154] This invention verifies the effectiveness of the proposed model and algorithm in large-scale networks by integrating air-ground cooperative paths into large-scale Sioux-Falls networks. Figure 11 As shown, the original network includes 24 nodes, 76 links, and 528 OD pairs. Information on OD travel, road capacity, and free-flow time for the experimental network can be found on the website. It is worth noting that the lengths of road links and flight links are determined based on actual geographic coordinates. The three-dimensional transportation network contains a total of 96 links, including four vertical takeoff and landing (VTOL) airports, four queue links, four evacuation links, and twelve flight links. Furthermore, to prevent flight conflicts, the VTOL airports located further apart are set at higher flight altitudes. Specific link information is shown in Table 1.

[0155] Table 1. Detailed Link Information

[0156]

[0157] The adaptive projection algorithm met the convergence condition at the 469th iteration, while the convergence metric of the basic projection algorithm was... Always at 1×10 -2 The flow fluctuates and fails to converge effectively. The results show that the adaptive step size technique can significantly improve the convergence performance in the flow allocation process. Table 2 summarizes the flow allocation results for the air-ground cooperative travel mode.

[0158] Table 2. Traffic distribution of air-ground cooperative travel modes

[0159]

[0160] It can be observed that air-ground cooperative links alleviate the pressure on ground traffic flow. Specifically, the access of four vertical takeoff and landing airports resulted in 4.9% of users choosing air-ground cooperative routes. The generalized cost composition of the pure ground traffic network equilibrium model and the air-ground cooperative three-dimensional traffic network model is compared in Table 3 below. Note that the ground traffic network model only includes pure ground routes.

[0161] Table 3. Comparison of Generalized Cost Composition

[0162]

[0163] Overall, the integration of air-ground cooperative three-dimensional transportation networks can effectively reduce total travel time. Specifically, the total travel time for users can be reduced by 11.7%. These results indicate that with the popularization of eVTOL technology, urban management departments can effectively alleviate urban congestion by integrating air-ground cooperative three-dimensional transportation networks.

[0164] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A city low-altitude user balancing system with generalized cost, characterized in that, Perform the following steps S1-S4 to complete the planning of the urban low-altitude transportation system: Step S1: Construct an air-ground cooperative three-dimensional transportation network, including road links, queuing links, flight links and evacuation links. Users take eVTOL vehicles to travel between their origin and destination in low-altitude environments within the air-ground cooperative three-dimensional transportation network. Step S2: Define a generalized path cost model that includes time cost, flight pricing cost, electricity cost and weather risk cost. Based on the generalized path cost model and the topology of the air-ground cooperative three-dimensional transportation network, construct the air-ground cooperative three-dimensional transportation network cost model. Step S3: Based on the traffic flow of road links, queuing links, flight links and evacuation links in the air-ground cooperative three-dimensional transportation network, and the cost model of the air-ground cooperative three-dimensional transportation network, the user equilibrium problem in the air-ground cooperative three-dimensional transportation network is transformed into a variational inequality model. Step S4: Using a combination of the K-shortest path algorithm and the adaptive projection method, solve the variational inequality model, calculate the equilibrium flow of the air-ground coordinated three-dimensional transportation network, and output the flow distribution of each path, the cost value of the air-ground coordinated three-dimensional transportation network, and the utilization rate of different links to complete the planning of the urban low-altitude travel system.

2. The urban low-altitude user balancing system with generalized cost according to claim 1, characterized in that, In step S1, the specific steps for a user to travel between their origin and destination in an eVTOL vehicle within an air-ground cooperative three-dimensional transportation network are as follows: Step S1.1: The user rides an eVTOL vehicle and queues in the queuing link at the departure point, enters the vertical take-off and landing airport at the departure point, performs vertical take-off operations, and reaches the preset safe altitude. Step S1.2: The user rides an eVTOL vehicle and flies to the destination vertical takeoff and landing airport via the flight link; Step S1.3: The user lands in an eVTOL vehicle at the destination's vertical takeoff and landing airport, and then enters the road network via the destination's evacuation link.

3. A city low-altitude user balancing system with generalized cost according to claim 1, characterized in that, The specific steps of step S2 are as follows: Step S2.1: Define the generalized path cost model as follows: ； in, This represents the generalized path cost model. Indicates the path time cost. Indicates the cost of flight pricing. Indicates electricity cost. Indicates the cost of weather risks; For OD The set of ground paths between them; Indicates OD pair The set of air-to-ground collaborative paths between them; Represents the set of OD pairs; Step S2.2: Based on the generalized path cost model and the topology of the air-ground cooperative three-dimensional transportation network, construct the air-ground cooperative three-dimensional transportation network cost model, which includes time cost, flight pricing cost, electricity cost and weather risk cost; divide the path time cost in the air-ground cooperative three-dimensional transportation network cost model into travel time of road links, travel time of queue links, travel time of flight links and travel time of evacuation links.

4. A city low-altitude user balancing system with generalized cost according to claim 3, characterized in that, The travel time of the road link described in step S2.2 is calculated as follows: ； In the formula, This represents the travel time of road link r. Indicates the free-flow velocity of road links and evacuation links; This represents the capacity of road link r; Represents a set of road links; This represents the traffic flow along road link r; Among them, the traffic flow of road link r The calculation is as follows: ； In the formula, Denotes the set of OD pairs, and ; Indicates OD pair The set of paths between; Indicates OD pair Traffic on path j between them; This represents the association variable between road link r and the path. If road link r belongs to an OD pair... When the path j is between ,otherwise ; The travel time of the queuing link is calculated as follows: ； In the formula, This represents the travel time of the queuing link u. Represents the set of queuing links. This represents the probability in the initial state; Indicates the average service rate; This represents the average queue length within the queuing system. Among them, the probability in the initial state The calculation is as follows: ； Average queue length in a queuing system The calculation is as follows: ； In the formula, Traffic flow representing queuing link u With average service rate The ratio; Let u be the capacity of the queuing link. Among them, the traffic flow of queuing link u The calculation is as follows: ； In the formula, The variable representing the association between queuing link u and the path, when queuing link u belongs to the OD pair. When the path j is between, ,otherwise Average service rate ,in This represents the average speed at which an eVTOL vehicle takes off and lands vertically. For safe distance; The travel time of the flight link is calculated as follows: ； In the formula, This indicates the travel time of flight link F. The flight altitude between takeoff and landing field m and takeoff and landing field n; The length of the flight link F; The horizontal cruising speed of eVTOL vehicles; This represents the set of flight links connecting any two vertical takeoff and landing airports, and ; The travel time of the evacuation link is calculated as follows: ； In the formula, Indicates the travel time of evacuation link e. The length of the evacuation link, and ; A set of evacuation links for vertical takeoff and landing airports; This indicates the free-flow velocity of road links and evacuation links.

5. A city low-altitude user balancing system with generalized cost according to claim 3, characterized in that, The path time cost in the air-ground cooperative three-dimensional transportation network cost model in step S2.2 is as follows: ； In the formula, This represents the path time cost in the cost model of the air-ground coordinated three-dimensional transportation network. Represents the value of a user's time. This represents the association variable between flight link F and the path. If flight link F belongs to an OD pair... When the path j is between ,otherwise ; The variable representing the association between evacuation link e and the path, if evacuation link e belongs to an OD pair. When the path j is between ,otherwise .

6. A city low-altitude user balancing system with generalized cost according to claim 3, characterized in that, The flight pricing cost in the air-ground cooperative three-dimensional transportation network cost model in step S2.2 is as follows: ； In the formula, This indicates the ticket price for a flight link per unit distance. This represents the flight pricing cost in the cost model of the air-ground coordinated three-dimensional transportation network.

7. A city low-altitude user balancing system with generalized cost according to claim 3, characterized in that, The electricity cost in the air-ground cooperative three-dimensional transportation network cost model in step S2.2 is as follows: ； in, Indicates the length of the road link; Indicates the length of the queuing link; Indicates the length of the evacuation link; Indicates the length of the flight link; This represents the electricity cost in the cost model of the air-ground coordinated three-dimensional transportation network; Indicates electricity price; This indicates the energy consumption of an eVTOL vehicle while it is driving on the ground. This indicates the energy consumption of an eVTOL vehicle while it is in the air.

8. A city low-altitude user balancing system with generalized cost according to claim 3, characterized in that, The weather risk cost in the air-ground cooperative three-dimensional transportation network cost model in step S2.2 is as follows: ； In the formula, This represents the weather risk cost in the cost model of the air-ground coordinated three-dimensional transportation network. Indicates horizontal wind speed; Indicates OD pair The set of air-to-ground collaborative paths between them, and ; For OD The set of paths between; This is the conversion factor between currency units and horizontal wind speed units.

9. A city low-altitude user balancing system with generalized cost according to claim 1, characterized in that, The specific steps of step S3 are as follows: Step S3.1: The air-ground cooperative three-dimensional transportation network includes the following flow conservation constraints: ； ； ； ； ； ； In the formula, and These represent the traffic flow of the flight link and the evacuation link, respectively. For OD Total demand between; Step S3.2: Define the path generalized cost vector function as follows: ； In the formula, For flow vector variables; Define the feasible set of path flows As shown below: ； The variational inequality model of the user equilibrium problem in the air-ground coordinated three-dimensional transportation network is expressed as finding a vector Makes the following equation always true: 。 10. A city low-altitude user equalization system with generalized cost according to claim 1, characterized in that, In step S4, a candidate path set for OD pairs is generated using the K-shortest path algorithm. The adaptive projection method adjusts the iteration step size adaptively based on the projection residual. The iteration convergence condition is that the projection residual is lower than a preset threshold.

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