Multi-layer edge computing resource fusion management method oriented to air-space-ground cooperation

Abstract

A space-air-ground cooperation-oriented resource fusion allocation method belongs to the field of space-air-ground integrated resource management, resource allocation comprises fusion allocation of computing resources and communication resources, the allocation method adopts a three-stage SteinColberg game, and the three-stage game comprises the following steps: (1) a satellite calculates an optimal resource price according to a resource request amount of an unmanned aerial vehicle; (2) the unmanned aerial vehicle calculates the optimal resource request quantity according to the resource pricing of the satellite, and calculates the optimal resource pricing of the unmanned aerial vehicle according to the resource request quantity of the user; and (3) the user calculates the optimal resource request quantity according to the optimal resource pricing of the unmanned aerial vehicle.

Description

Technical Field

[0001] The present invention proposes a multi-layer edge computing resource fusion management method for air-ground-space collaboration. Firstly, the process of air-ground-space collaboration providing edge computing is modeled as a three-stage Stan Kohlberg game. Then, the utility functions and optimal value solution methods of satellites, UAVs and users in this game are given respectively, and the processing steps and methods of each stage in the three stages are described in detail. Background Art

[0002] With the popularization of infrastructure such as satellites and drones, it has become possible for the Space-Air-Ground Integration Network (SAGIN) to provide network coverage and computing services for ground users. When the mobile terminal is located in extreme locations such as mountains and oceans, it is impossible to communicate with existing communication base stations, and the satellite and drone resources in SAGIN are limited. Therefore, it is very important to effectively utilize the limited communication and computing resources in satellites and drones. This paper considers the process of a SAGIN network providing communication and computing services to ground data acquisition equipment (referred to as users). In this scenario, the ground acquisition equipment is responsible for soil testing, fire monitoring, and marine water quality testing in remote mountainous areas. Network services in remote areas are limited, and the data collected by ground equipment cannot be processed and transmitted back in real time. In order to meet the user's demand for communication and computing resources, this paper uses the SAGIN network to provide users with relevant resources. The scenario diagram of this paper is as follows: Figure 1 :

[0003] In this scenario, the drone is responsible for collecting relevant data from the detector and processing some of the data. Considering the limited computing power of the drone, the drone can forward part of the data to the satellite, which will process the remaining data. After the satellite and the drone complete the processing, they will return the data results to the ground station. In the above process, the drone and the satellite work together to serve ground users. The drone and the satellite need to allocate reasonable communication resources to ensure data transmission, and also need to allocate reasonable computing resources to ensure data processing.

[0004] The Stackelberg game is an economic model used to describe the dynamic interaction between companies with different market powers. In this game, one company as a leader makes a decision first, and then other companies as followers make their own decisions after observing the leader's decision. In SAGIN, the service providers are satellites and drones, and the service consumers are user devices. The resource leasing process between the two can be modeled as a Stackelberg game. At present, many studies have applied game theory to solve resource management in SAGIN.

[0005] Conjugate gradient descent is an iterative algorithm for solving large-scale sparse linear equations. Its core idea is to use conjugate directions to gradually approach the solution until convergence. The key to the conjugate gradient method is to construct a series of search directions that are conjugate to the residual vector. The residual vector is updated after each iteration, and the new residual vector is orthogonal to the previous search direction. This orthogonal property allows the algorithm to achieve the maximum descent in the current search direction at each step. Summary of the invention

[0006] In the SAGIN scenario, communication and computing resources are usually allocated to each user synchronously and there is a certain coupling relationship between the two types of resources. The present invention comprehensively considers the supply and demand relationship between satellites, drones and users, and integrates and models the allocation process of communication and computing resources of satellites and drones into a three-stage Stan Kohlberg game, thereby realizing the integrated allocation of communication and computing resources and improving the resource utilization efficiency and user service experience in SAGIN.

[0007] 1. Game Modeling and Flowchart

[0008] This paper studies the integrated management of computing and communication resources mentioned above, including L2U (satellite-UAV) computing and communication resource integrated allocation and U2U (UAV-user) computing and communication resource integrated allocation. LEO satellites provide part of the computing and communication resources to each UAV by allocating computing and communication resources, and each UAV allocates its computing and communication resources to provide services to connected users. That is, the UAV leases computing and communication resources from the satellite, and then uses the leased resources and its own resources to provide computing services to users. Since the UAV has its own certain communication computing resources, the working modes of the UAV in this study are: full relay and semi-relay (the UAV and the satellite jointly provide communication computing resources).

[0009] In this study, the specific bandwidth and computing resource allocation schemes are not studied. The minimum granularity of this study is the size of TP (communication resources) and CP (computing resources). In each time slot, the LEO satellite first determines the price of L2U computing and communication resources according to the needs of the drone to maximize its profit. Then, each drone purchases an appropriate amount of L2U computing and communication resources from the LEO satellite, determines the price of U2U computing and communication resources, and allocates its own U2U computing and communication resources to users. The total amount of allocated U2U computing and communication resources cannot exceed the sum of its own computing and communication resources requested from the LEO satellite. Finally, each user determines the amount of computing and communication resources to rent from the drone.

[0010] According to the above process, the computing and communication resource supply problem in SAGIN can be expressed as a three-stage Stackelberg game. The flowchart of the game is as follows: Figure 2 As shown:

[0011] In the first stage, the LEO satellite acts as a leader and determines the L2U computing and communication resource price according to the needs of the UAV. Then, in stage two, the UAV, as a follower of stage one, makes decisions on the L2U computing and communication resource requests from the LEO satellite, and then, as a leader of stage three, allocates its U2U data rate to users according to the optimal U2U computing and communication resource price to maximize their utility. In stage three, each user, as a follower of stage two, determines the optimal computing and communication resource request amount according to the U2U computing and communication resource price of its connected UAV. The improved three-stage Stackelberg game proposed in this paper fully considers the interaction between the strategies of the three game participants: the determination of the U2U computing and communication resource price depends in part on the computing and communication resource requests from the LEO satellite, where the available U2U computing and communication resources cannot exceed the sum of the requests and its own computing and communication resources.

[0012] Second, three-stage game steps and formula

[0013] In each round of the game, both parties need to maximize their own benefits, that is, maximize their own utility functions. The following will describe the relevant content and formulas of each stage of the Stan Kohlberg game:

[0014] 2.1 Phase 1: The satellite determines the price of L2U computing and communication resources based on the needs of the UAV.

[0015] Assume that the number range of the drones competing with the current satellite s is [1~N], where N is the maximum number of drones. The utility function U of the satellite s,t (TP s,t ,CP s,t )as follows:

[0016]

[0017] Where n is the number of the drone, n∈[1~N], TP s,t Pricing the communication resources of satellite s in time slot t, CP s,t Pricing the computing resources of satellite s in time slot t, σ s is the energy consumption weight of the satellite, σ s =0.3,ρ sg is the transmission power from satellite s to ground station g, μ s is the energy consumption coefficient of satellite s in a single CPU cycle, μ s =0.2, c s is the computing power of satellite s, c s =5GB / s, ε is the computing task compression ratio, ε = 0.01, r sg(t) is the link transmission rate from satellite s to the ground station in time slot t, is the optimal communication resource request of UAV n in time slot t,

[0018]

[0019] Where a is the user communication resource satisfaction coefficient, a=10, M is the maximum number of user devices requesting resources from drone n, that is, the set of user numbers requesting resources from drone n is [1~M], σ m is the energy consumption weight of user m, m∈[1~M], σ m =0.1,σ n is the energy consumption weight of UAV n, σ n =0.2,ρ nm is the transmission power of the communication link between UAV n and user m, ρ sn is the transmission power of the communication link between satellite s and UAV n, r sn (t) is the data transmission rate of the link between satellite s and UAV n in time slot t, is the indicator variable of the UAV communication resource supply mode, is the maximum communication resource of UAV n, r nm (t) is the data transmission rate of the link between drone n and user m in time slot t, and In order to make Related TP not equal to 0 s,t The constraint threshold, TP s,t Upper threshold, for The above formula shows that when the satellite communication resource pricing does not exceed the threshold When the optimal communication resource request of the UAV in the game is greater than 0, the satellite communication resource pricing is too high, that is, it exceeds the threshold When , the UAV that is playing games with it will no longer request communication resources. The specific expression is as follows:

[0020]

[0021] in, Indicates the communication resource FQ requested by drone n from the satellite n,t If it is greater than or equal to the sum of the resource requests from all users to UAV n, the UAV adopts the relay mode and does not need to provide communication resources. Otherwise, the UAV needs to adopt the semi-relay mode and provide communication resources together with the satellite. For drone working mode The influencing variable, ρ ng is the link transmission power from UAV n to ground station g, rng (t) is the link transmission rate from UAV n to ground station g in time slot t, FQ n,t is the communication resource request of UAV n in time slot t, is the optimal communication resource request amount of user m in time slot t.

[0022] is the optimal computing resource request of UAV n in time slot t,

[0023]

[0024] Where b is the user computing resource satisfaction coefficient, b = 6, It is the indicator variable of the UAV computing resource supply mode. is the maximum computing resource of UAV n, and In order to make CP not equal to 0 s,t The constraint threshold, TP s,t Upper threshold, for The above formula shows that when the satellite computing resource pricing does not exceed the threshold When the optimal computing resource request of the UAV in the game is greater than 0, the satellite computing resource pricing is too high, that is, it exceeds the threshold When , the UAVs that are playing games with it will no longer request computing resources. The specific expression is as follows:

[0025]

[0026] in, represents the computing resources PQ requested by drone n from the satellite in time slot t n,t Greater than or equal to the sum of all users' requests to drone n At this time, the drone adopts relay mode and does not need to provide computing resources. Otherwise, the drone needs to adopt semi-relay mode and provide computing resources together with the satellite. For drone working mode The influencing variables, μ n is the energy consumption coefficient of a single CPU cycle of UAV n, μ n =0.15, c n is the computing power of drone n, c n =500MB / s, PQ n,t is the computing resource request of UAV n in time slot t, is the optimal computing resource request of user m in time slot t.

[0027] The utility function of satellite s is obtained above. The above function is too complex, and the utility gradient of low-orbit satellite s is difficult to obtain, so it is impossible to obtain the optimal value by a single derivation. We designed an iterative algorithm based on conjugate gradient descent to obtain the optimal resource sales price of LEO satellites:

[0028] The utility function of satellite s is obtained above, and the following algorithm 1 is designed to obtain the optimal resource sales price of LEO satellite:

[0029] Algorithm 1 LEO satellite resource pricing iterative algorithm based on conjugate gradient descent

[0030] 1): Initialization: LEO satellite sets the total amount of communication and computing resources Determine the initial communication and computing resource prices Initialize the number of iterations k = 1, the iteration step γ = 0.01, and the exit threshold ∈ = 0.001;

[0031] 2). Calculate the satellite s utility function U s,t (TP s,t ,CP s,t )exist The gradient at

[0032] 3). If k = 1, Otherwise the search direction is updated as: in

[0033] 4). Update satellite resource quotation

[0034] 5). Let k = k + 1;

[0035] 6). Repeat steps 2)-5) until: and This time Break out of the loop;

[0036] 7). According to Calculate the resource request amount for each drone;

[0037] 8). If or Execute step 9) sequentially, otherwise jump to step 14);

[0038] 9). Let k = 1,

[0039] 10). According to Calculate the resource request amount for each drone;

[0040] 11). If or Updates to communication and computing resource pricing:

[0041]

[0042] 12).k=k+1;

[0043] 13). Repeat steps 10)-12) until: and

[0044] 14). The optimal resource pricing of satellite s in time slot t is obtained as:

[0045] in represents the communication and computing resource pricing of satellite s in time slot t after the kth iteration, d ( k ) is the search direction of the optimal value of the kth iteration, is the utility function gradient of satellite s in the kth iteration time slot t, β k-1 is the weight of the k-1th iteration direction, the numerator is the square of the modulus of the k-th gradient, the denominator is the modulus of the k-1th gradient, β k-1 d (k-1) is the influence of the k-1th iteration search direction on the kth iteration direction, This setting ensures that the new direction d (k) is an adjustment in the current gradient direction while maintaining the old direction d (k-1) The conjugation property. is the communication resource increment of the kth iteration, is the calculated resource increment for the kth iteration. In steps 2-5, the resource sales price of the LEO satellite is updated in the direction of increasing its utility function. is the gradient of the satellite utility function until it converges to the optimal price In step 7-12, the resource request amount of each drone under the optimal resource pricing is counted. If the current resource pricing makes the total resource request amount of each drone or Exceeding the satellite's communication resource limit Computing resource limits Then search again for the optimal price to make it lower than the upper limit of each resource. It is the iterative increment of communication resources when the communication resources exceed the upper limit. It is the iterative increment of computing resources when the computing resources exceed the upper limit.

[0046] 2.2 Phase 2: The drone acts as a follower in phase 1, making decisions on L2U computing and communication resource requests from LEO satellites, and then acts as a leader in phase 3, allocating its U2U data rate to users based on the optimal U2U computing and communication resource price.

[0047] In the first stage, the satellite s is given its optimal communication and computing resource pricing by Algorithm 1 After receiving the price, the drone will incorporate it into its own utility function and maximize its utility function to obtain the optimal communication and computing resource request amount.

[0048] The utility function U of drone n in time slot t n,t (TP n,t ,CP n,t ,FQ n,t ,PQ n,t )for:

[0049]

[0050]

[0051] in[·] + =max(·,0),TP n,t ,CP n,t Pricing for the communication and computing resources when UAV n rents resources to users in time slot t.

[0052] The above formulas (2, 4) give the optimal communication and computing resource requests that maximize the utility function of UAV n: Satellite s obtains the optimal resource pricing that maximizes its own utility function according to Algorithm 1 and broadcasts it to drone n. The drone obtains the optimal resource request quantity that maximizes its own utility function according to formulas (2, 4). The two parties compete with each other and continuously iterate and update resource pricing and request quantity until both parties cannot increase their revenue by changing pricing and request quantity. At this time, the two parties reach a Nash equilibrium.

[0053] The drone determines the optimal amount of communication and computing resources to request from the satellite. In the end, drones will serve as the leader in the drone-user game and determine the optimal pricing for leasing communication and computing resources to users.

[0054]

[0055] where z∈{1,2,3,4}, Pricing the optimal communication resources of UAV n in time slot t under different conditions, The corresponding pricing for different optimal communication resources Constraints:

[0056]

[0057] in Pricing the optimal computing resources of drone n in time slot t under different conditions, Pricing for different optimal computing resources Constraints:

[0058]

[0059] 2.3 Phase 3: Each user, as a follower in Phase 2, determines the optimal amount of computing and communication resource requests based on the U2U computing and communication resource prices of the connected drones.

[0060] In the second stage, drone n gives the optimal communication and computing resource pricing In time slot t, the utility function U of user m is m,t (FQ m,t ,PQ m,t )for:

[0061]

[0062] Where aln(1+FQ m,t )、bln(1+PQ m,t ) are the communication and computing resource satisfaction functions of user m, are the rental costs of communication and computing resources of user m, is the data transmission energy consumption of user m.

[0063] The optimal communication and computing resource requests of a user to maximize his utility function for:

[0064]

[0065] In time slot t, when the LEO satellite broadcasts L2U resource pricing When , each UAV responds to the satellite with the optimal resource request according to formula (2, 4) The satellite solves the L2U optimal resource pricing according to Algorithm 1. After the satellite and the UAV reach Nash equilibrium, the UAV determines the U2U optimal resource pricing according to Formulas (7, 8) based on the optimal resource request amount. And broadcast it to all detection devices within its range. The detection devices price the U2U resources and use formulas (12, 13) to derive the optimal U2U resource request amount. In this three-stage game, each layer can obtain the optimal value under the current strategy according to the above formula, so as to maximize its own utility function. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Edge service scenario diagram of detection equipment for air-ground collaboration

[0067] Figure 2 Flowchart of the three-stage Stan Kohlberg game of air-ground collaboration DETAILED DESCRIPTION

[0068] Next, the specific implementation of the scheme is described. In the following implementation scenario, the number of satellites is 1, the number of drones is 100, and the number of users is 2000. The satellite, users, and drones move dynamically. In the same time slot, the positions of the satellite, drone, and user are relatively static, and the link transmission power and rate remain unchanged. The satellite can cover all drones in any time slot. Then the implementation of this scheme in time slot t is as follows:

[0069] Step 1: The drone receives the user's service request and records the user's request information and total resource request in the current time slot

[0070] Step 2: The satellite sets the initial resource pricing, which is then broadcast to all drones.

[0071] Step 3: The drone receives the initial resource pricing from the satellite and calculates and updates the optimal communication resource request according to the following formula and computing resource requests The optimal resource request is then sent to the satellite providing the service:

[0072]

[0073] Where a is the user communication resource satisfaction coefficient, a=10, M is the maximum number of user devices requesting resources from drone n, that is, the set of user numbers requesting resources from drone n is [1~M], σ m is the energy consumption weight of user m, m∈[1~M], σ m =0.1,σ n is the energy consumption weight of UAV n, σ n =0.2,ρ nm is the transmission power of the communication link between UAV n and user m, ρ sn is the transmission power of the communication link between satellite s and UAV n, r sn (t) is the data transmission rate of the link between satellite s and UAV n in time slot t, is the indicator variable of the UAV communication resource supply mode, is the maximum communication resource of UAV n, r nm (t) is the data transmission rate of the link between drone n and user m in time slot t, and In order to make Related TP not equal to 0 s,t The constraint threshold, TP s,t Upper threshold, for The above formula shows that when the satellite communication resource pricing does not exceed the threshold When the optimal communication resource request of the UAV in the game is greater than 0, the satellite communication resource pricing is too high, that is, it exceeds the threshold When , the UAV that is playing games with it will no longer request communication resources. The specific expression is as follows:

[0074]

[0075] in, Indicates the communication resource FQ requested by drone n from the satellite n,t If the number of requests from all users to UAV n is greater than or equal to the sum of the requests from all users to UAV n, the UAV adopts the relay mode and does not need to provide communication resources. Otherwise, the UAV needs to adopt the semi-relay mode and provide communication resources together with the satellite. For drone working mode The influencing variable, ρ ng is the link transmission power from UAV n to ground station g, r ng (t) is the link transmission rate from UAV n to ground station g in time slot t, FQ n,t is the communication resource request of UAV n in time slot t, is the optimal communication resource request amount of user m in time slot t.

[0076] is the optimal computing resource request of UAV n in time slot t,

[0077]

[0078] Where b is the user computing resource satisfaction coefficient, b = 6, It is the indicator variable of the UAV computing resource supply mode. is the maximum computing resource of UAV n, and In order to make CP not equal to 0 s,t The constraint threshold, TP s,t Upper threshold, for The above formula shows that when the satellite computing resource pricing does not exceed the threshold When the optimal computing resource request of the UAV in the game is greater than 0, the satellite computing resource pricing is too high, that is, it exceeds the threshold When , the UAVs that are playing games with it will no longer request computing resources. The specific expression is as follows:

[0079]

[0080] in, represents the computing resources PQ requested by drone n from the satellite in time slot t n,t Greater than or equal to the number of requests from all users to drone n At this time, the drone adopts relay mode and does not need to provide computing resources. Otherwise, the drone needs to adopt semi-relay mode and provide computing resources together with the satellite. For drone working mode The influencing variables, μ n is the energy consumption coefficient of a single CPU cycle of UAV n, μ n =0.15, c n is the computing power of drone n, c n =500MB / s, PQ n,t is the computing resource request of UAV n in time slot t, is the optimal computing resource request of user m in time slot t.

[0081] Step 4: The satellite receives the latest resource request from the drone and feeds it into the following satellite utility function:

[0082]

[0083] Where n is the number of the drone, n∈[1~N], TP s,t Pricing the communication resources of satellite s in time slot t, CP s,t Pricing the computing resources of satellite s in time slot t, σ s is the energy consumption weight of the satellite, σ s =0.3,ρ sg is the transmission power from satellite s to ground station g, μ s is the energy consumption coefficient of satellite s in a single CPU cycle, μ s =0.2, c s is the computing power of satellite s, c s =5GB / s, ε is the computing task compression ratio, ε = 0.01, r sg (t) is the link transmission rate from satellite s to the ground station in time slot t.

[0084] Next, the satellite uses the following algorithm to maximize the above utility function and obtain the satellite communication and computing resource pricing when the satellite utility function is maximized: The optimal resource pricing is then broadcast to all drones:

[0085] 1): Initialization: LEO satellite sets the total amount of communication and computing resources Determine the initial communication and computing resource prices Initialize the number of iterations k = 1, the iteration step γ = 0.01, and the exit threshold ∈ = 0.001

[0086] 2). Calculate the satellite s utility function U s,t (TP s,t ,CP s,t )exist The gradient at

[0087] 3). If k = 1, Otherwise the search direction is updated as: in

[0088] 4). Update satellite resource quotation

[0089] 5). k = k + 1

[0090] 6). Repeat steps 2-5 until: and This time Break out of the loop

[0091] 7). According to Calculate resource requests for each drone

[0092] 8). If or Execute step 9 in sequence, otherwise jump to step 14

[0093] 9). Let k = 1,

[0094] 10). According to Calculate resource requests for each drone

[0095] 11). If or Updates to communication and computing resource pricing:

[0096]

[0097] 12).k=k+1

[0098] 13). Repeat steps 10-12 until: and

[0099] 14). The optimal resource pricing of satellite s in time slot t is obtained as:

[0100] in represents the communication and computing resource pricing of satellite s in time slot t after the kth iteration, d (k) is the search direction of the optimal value of the kth iteration, is the utility function gradient of satellite s in the kth iteration time slot t, β k-1 is the weight of the k-1th iteration direction, the numerator is the square of the modulus of the k-th gradient, the denominator is the modulus of the k-1th gradient, β k-1 d (k-1) is the influence of the k-1th iteration search direction on the kth iteration direction, This setting ensures that the new direction d (k) is an adjustment in the current gradient direction while maintaining the old direction d (k-1) The conjugation of is the communication resource increment of the kth iteration, is the computational resource increment for the kth iteration. In steps 2)-5), the resource sales price of the LEO satellite is updated in the direction of increasing its utility function. is the gradient of the satellite utility function until it converges to the optimal price In steps 7)-12), the resource request amount of each drone under the optimal resource pricing is counted. If the current resource pricing makes the total resource request amount of each drone or Exceeding the satellite's communication resource limit Computing resource limits Then search for the best price again to make it lower than the upper limit of each resource; It is the iterative increment of communication resources when the communication resources exceed the upper limit. It is the iterative increment of computing resources when the computing resources exceed the upper limit;

[0101] Step 5: Repeat steps 3 and 4 until the satellite and the drone reach a Nash equilibrium.

[0102] Step 6: The drone receives the user's resource request and determines the optimal price for leasing communication and computing resources to the user based on the following formula: And broadcast the optimal resource pricing to all users:

[0103]

[0104] where z∈{1,2,3,4}, Pricing the optimal communication resources of UAV n in time slot t under different conditions, The corresponding pricing for different optimal communication resources Constraints:

[0105]

[0106] in Pricing the optimal computing resources of drone n in time slot t under different conditions, Pricing for different optimal computing resources Constraints:

[0107]

[0108] Step 7: The user first receives the resource pricing of the drone and determines the optimal request quantity for leasing communication and computing resources from the drone according to the following formula: And send the optimal resource request amount to the drone providing the service:

[0109]

[0110] Step 8: Repeat steps 6 and 7 until the drone and the user reach a Nash equilibrium.

Claims

1. A multi-layer edge computing resource fusion management method for air-ground collaboration, characterized in that It is divided into three stages: 2.1 Phase 1: The satellite determines the price of L2U computing and communication resources based on the needs of the drone; The number range of the drones competing with the current satellite s is [1~N], where N is the maximum number of drones; the utility function U of the satellite s,t (TP s,t ,CP s,t )as follows: Where n is the number of the drone, n∈[1~N], TP s,t Pricing the communication resources of satellite s in time slot t, CP s,t Pricing the computing resources of satellite s in time slot t, σ s is the energy consumption weight of the satellite, σ s =0.3,ρ sg is the transmission power from satellite s to ground station g, μ s is the energy consumption coefficient of satellite s in a single CPU cycle, μ s =0.2, c s is the computing power of satellite s, c s =5GB / s, ε is the computing task compression ratio, ε = 0.01, r sg (t) is the link transmission rate from satellite s to the ground station in time slot t, is the optimal communication resource request of UAV n in time slot t, Where a is the user communication resource satisfaction coefficient, a=10, M is the maximum number of user devices requesting resources from drone n, that is, the set of user numbers requesting resources from drone n is [1~M], σ m is the energy consumption weight of user m, σ m =0.1, m∈[1~M],σ n is the energy consumption weight of UAV n, σ n =0.2,ρ nm is the transmission power of the communication link between UAV n and user m, ρ sn is the transmission power of the communication link between satellite s and UAV n, r sn (t) is the data transmission rate of the link between satellite s and UAV n in time slot t, is the indicator variable of the UAV communication resource supply mode, is the maximum communication resource of UAV n, r nm (t) is the data transmission rate of the link between drone n and user m in time slot t, and In order to make Related TP not equal to 0 s,t The constraint threshold, TP s,t Upper threshold, for The above formula shows that when the satellite communication resource pricing does not exceed the threshold When the optimal communication resource request of the UAV in the game is greater than 0, the satellite communication resource pricing is too high, that is, it exceeds the threshold When , the UAV that is playing the game with it will no longer request communication resources; the specific expression is as follows: in, Indicates the communication resource FQ requested by drone n from the satellite n,t If the number of requests from all users to UAV n is greater than or equal to the sum of the requests from all users to UAV n, the UAV adopts the relay mode and does not need to provide communication resources. Otherwise, the UAV needs to adopt the semi-relay mode and provide communication resources together with the satellite. For drone working mode The influencing variable, ρ ng is the link transmission power from UAV n to ground station g, r ng (t) is the link transmission rate from UAV n to ground station g in time slot t, FQ n,t is the communication resource request of UAV n in time slot t, is the optimal communication resource request of user m in time slot t; is the optimal computing resource request of UAV n in time slot t, Where b is the user computing resource satisfaction coefficient, b = 6, It is the indicator variable of the UAV computing resource supply mode. is the maximum computing resource of UAV n, and In order to make CP not equal to 0 s,t The constraint threshold, TP s,t Upper threshold, for The above formula shows that when the satellite computing resource pricing does not exceed the threshold When the optimal computing resource request of the UAV in the game is greater than 0, the satellite computing resource pricing is too high, that is, it exceeds the threshold When , the UAV that is playing the game with it will no longer request computing resources; the specific expression is as follows: in, represents the computing resources PQ requested by drone n from the satellite in time slot t n,t Greater than or equal to the number of requests from all users to drone n In this case, the drone adopts the relay mode and does not need to provide computing resources. Otherwise, the drone needs to adopt the semi-relay mode and provide computing resources together with the satellite; For drone working mode The influencing variables, μ n is the energy consumption coefficient of a single CPU cycle of UAV n, μ n =0.15, c n is the computing power of drone n, c n =500MB / s, PQ n,t is the computing resource request of UAV n in time slot t, is the optimal computing resource request of user m in time slot t; The utility function of satellite s is obtained above, and the following algorithm 1 is designed to obtain the optimal resource sales price of LEO satellite: Algorithm 1 LEO satellite resource pricing iterative algorithm based on conjugate gradient descent 1): Initialization: LEO satellite sets the total amount of communication and computing resources Determine the initial communication and computing resource prices Initialize the number of iterations k = 1, the iteration step γ = 0.01, and the exit threshold ∈ = 0.001; 2). Calculate the satellite s utility function U s,t (TP s,t ,CP s,t )exist The gradient at 3). If k = 1, Otherwise the search direction is updated as: in 4). Update satellite resource quotation 5). Let k = k + 1; 6). Repeat steps 2)-5) until: and ∈, at this time Break out of the loop; 7). According to Calculate the resource request amount for each drone; 8). If or Execute step 9) sequentially, otherwise jump to step 14); 9). Let k = 1, 10). According to Calculate the resource request amount for each drone; 11). If or Updates to communication and computing resource pricing: 12).k=k+1; 13). Repeat steps 10)-12) until: and 14). The optimal resource pricing of satellite s in time slot t is obtained as: in represents the communication and computing resource pricing of satellite s in time slot t after the kth iteration, d (k) is the search direction of the optimal value of the kth iteration, is the utility function gradient of satellite s in the kth iteration time slot t, β k-1 is the weight of the k-1th iteration direction, the numerator is the square of the modulus of the kth gradient, the denominator is the modulus of the k-1th gradient, β k-1 d (k-1) is the influence of the k-1th iteration search direction on the kth iteration direction, This setting ensures that the new direction d (k) is an adjustment in the current gradient direction while maintaining the old direction d (k-1) The conjugation of is the communication resource increment of the kth iteration, is the computational resource increment for the kth iteration. In steps 2)-5), the resource sales price of the LEO satellite is updated in the direction of increasing its utility function. is the gradient of the satellite utility function until it converges to the optimal price In steps 7)-12), the resource request amount of each drone under the optimal resource pricing is counted. If the current resource pricing makes the total resource request amount of each drone or Exceeding the satellite's communication resource limit Computing resource limits Then search for the best price again to make it lower than the upper limit of each resource; It is the iterative increment of communication resources when the communication resources exceed the upper limit. It is the iterative increment of computing resources when the computing resources exceed the upper limit; 2.2 Phase 2: The drone acts as a follower in phase 1 and makes decisions on the L2U computing and communication resource requests from the LEO satellite, and then acts as a leader in phase 3 and allocates its U2U data rate to users according to the optimal U2U computing and communication resource price; In the first stage, the satellite s is given its optimal communication and computing resource pricing by Algorithm 1 After receiving the price, the drone will incorporate it into its own utility function and maximize its utility function to obtain the optimal communication and computing resource request amount. The utility function U of drone n in time slot t n,t (TP n,t ,CP n,t ,FQ n,t ,PQ n,t )for: in[·] + =max(·,0),TP n,t ,CP n,t Pricing the communication and computing resources when UAV n rents resources to users in time slot t; The above formulas (2, 4) give the optimal communication and computing resource requests that maximize the utility function of UAV n: Satellite s obtains the optimal resource pricing that maximizes its own utility function according to Algorithm 1 and broadcasts it to UAV n. UAV n obtains the optimal resource request quantity that maximizes its own utility function according to Formulas (2, 4). The two parties compete with each other and continuously iterate and update resource pricing and request quantity until both parties cannot increase their revenue by changing pricing and request quantity. At this time, the two parties reach a Nash equilibrium. The drone determines the optimal amount of communication and computing resources to request from the satellite. In the end, drones will serve as the leader in the drone-user game and determine the optimal pricing for leasing communication and computing resources to users. where z∈{1,2,3,4}, Pricing the optimal communication resources of UAV n in time slot t under different conditions, The corresponding pricing for different optimal communication resources Constraints: in Pricing the optimal computing resources of drone n in time slot t under different conditions, Pricing for different optimal computing resources Constraints: 2.3 Phase 3: Each user, as a follower in Phase 2, determines the optimal amount of computing and communication resource requests based on the U2U computing and communication resource prices of the connected drones; In the second stage, drone n gives the optimal communication and computing resource pricing In time slot t, the utility function U of user m is m,t (FQ m,t ,PQ m,t )for: Where aln(1+FQ m,t )、bln(1+PQ m,t ) are the communication and computing resource satisfaction functions of user m, are the rental costs of communication and computing resources of user m, is the data transmission energy consumption of user m; The optimal communication and computing resource requests of a user to maximize his utility function for: In time slot t, when the LEO satellite broadcasts L2U resource pricing When , each UAV responds to the satellite with the optimal resource request according to formula (2, 4) The satellite solves the L2U optimal resource pricing according to Algorithm 1. After the satellite and the UAV reach Nash equilibrium, the UAV determines the U2U optimal resource pricing according to Formulas (7, 8) based on the optimal resource request amount. And broadcast it to all detection devices within its range. The detection devices price the U2U resources and use formulas (12, 13) to derive the optimal U2U resource request amount.

Images