A satellite network optimization method based on mobile edge computing service cache configuration

Abstract

The application discloses a satellite network optimization method based on mobile edge computing service cache configuration and relates to the technical field of satellite network service cache optimization. In view of the problems of high task offloading delay and difficult control of cache cost in a single satellite service mode, the application proposes an optimization framework in which a specific satellite set cooperates to provide edge cache and wireless transmission services for users, and models joint optimization of satellite clustering and service cache as a mixed integer nonlinear programming problem. Lyapunov stochastic optimization is introduced to convert long-term cache constraints into a per-time-slot optimization problem, which is decomposed into a service cache sub-problem and a satellite clustering sub-problem for alternative solving based on generalized Benders decomposition, the satellite clustering sub-problem adopts a Gibbs sampling heuristic algorithm to obtain an approximate optimal solution, and a hyperparameter is introduced to extend to a multi-user scenario in combination with a bisection method. The application is used for mobile edge computing resource management of a low-orbit satellite communication network, and can effectively reduce task offloading delay and ensure controllable long-term cache cost.

Description

Technical Field

[0001] This invention relates to the field of satellite network service cache optimization, specifically a satellite network optimization method based on mobile edge computing service cache configuration. Background Technology

[0002] With the rapid development of the mobile internet, the widespread adoption of mobile devices and the emergence of resource-intensive applications have led to an explosive growth in data traffic. Mobile edge computing can provide users with low-latency computing, caching, and transmission capabilities. Satellite communication networks, as a new type of network that has attracted much attention in recent years, are no longer limited by terrestrial environments due to their flexible space-based networking. Therefore, edge computing architectures based on satellite communication networks have significant advantages in addressing communication needs in special scenarios such as remote areas. The core idea of ​​edge computing architectures based on satellite communication networks is to fully utilize the capabilities of satellite communication networks. On the one hand, it leverages the efficient inter-satellite links within satellite communication networks to empower terrestrial communication networks; on the other hand, by deploying edge computing servers within satellite communication networks and utilizing satellite-side computing power, it provides users with entirely new internet solutions, further meeting end-users' demands for faster, better, and more secure data services.

[0003] Most existing edge service caching research adopts terrestrial edge caching networks based on cellular networks. Multiple users are served by a single base station supporting Mobile Edge Computing (MEC) within the cellular network. In traditional cellular networks, the performance of edge service caching is limited by wireless transmission. A satellite network optimization method based on MEC service caching configuration allocates a dynamically partitioned set of satellites to each user. Each satellite set can be adaptively partitioned based on the user's location and network conditions, providing seamless transmission services. By integrating MEC servers into the satellites, computational and caching resources for task offloading and service caching in edge computing can be further increased. The satellite network optimization method based on MEC service caching configuration can provide users with efficient and reliable wireless transmission, service caching, and task processing services. Summary of the Invention

[0004] To address the technical problems mentioned in the background, this invention aims to provide a satellite network optimization method based on MEC service cache configuration, which solves the problem of selecting the optimal set of satellites for serving user terminals and reduces task offloading latency and cache costs.

[0005] To achieve the above-mentioned technical objectives, the technical solution of the present invention is as follows:

[0006] A satellite network optimization method based on MEC service cache configuration, characterized by the following steps:

[0007] Step (1) Build a satellite communication network that supports MEC. Each satellite node has different computing and caching resources. Assume there are M satellites equipped with MEC servers and U users. The satellite set M = {m i |i = 1, 2, 3, ..., m, ..., M} and the user set Each user terminal has communication capabilities, and satellites equipped with MEC servers can provide computing and caching resources for the user terminals;

[0008] Step (2) models the problem of finding the optimal satellite set and optimizing the service caching strategy for the target user as a non-deterministic polynomial problem of mixed integer nonlinear programming, i.e., an NP-hard long-term optimization problem.

[0009] Step (3) transforms the long-run optimization problem into a time-decoupled instantaneous problem based on Lyapunov optimization;

[0010] Step (4) Based on the Generalized Benders Decomposition (GBD) framework, the time decoupling instantaneous problem based on Lyapunov optimization is decomposed to solve the Lyapunov problem with lower complexity. The instantaneous problem is decomposed into two sub-problems, and then the two sub-problems are solved alternately to obtain the near-optimal satellite set and service caching strategy to solve the NP-hard problem proposed in step (2).

[0011] Step (5) extends the problem to a multi-user scenario to obtain an approximately optimal satellite set and service caching strategy.

[0012] Furthermore, in step (1), considering that each MEC satellite node has different computing and caching resources, the computing and caching resources of satellite m are respectively represented as C. m and S m Assuming the task execution time is T, and T is divided into multiple discrete time points t, the set of satellites serving the target user u is Φ. u (t), Φ u The set of all target users of service (t) is Ω. u (t) indicates that a satellite can simultaneously provide services to different target users, and the satellite sets of different target users can intersect; denoted as v, the other users served by the satellite cluster besides the target user u, are called users within the set. The target user u and users other than those within the set are called users between sets.

[0013] Suppose there are K types of services, and the service set is denoted as K. Different services consume different cache and computing resources when cached on the satellite. Assume that service k requires s cache resources. k And computing resources are f k Using continuous variable x k，m (t)∈[0,1] represents the probability that service k is cached in satellite m at time t, and the service caching strategy of satellite m at time t is x. m (t)=[x 1，m (t), ..., x k，m (t)] T .

[0014] Suppose that at time t, target user u generates an uninstallation task T that requires only one type of service. u (t), and remains constant at each time step, task T u The data volume and workload of (t) are respectively used as (bit) and (GHz) indicates that satellite m needs to cache services at the start position of each time to meet the service requirements of the task. At each time, the task generated by each target user will go through three steps: task unloading, task processing, and result return. The task unloading delay mainly consists of the following two parts:

[0015] 1) Uplink delay: For satellite cluster Φ u (t), using a binary variable c u，m (t) represents that at time t, satellite m∈Φ u (t) Whether it serves the target user u, when c u，m When (t) = 1, it represents service; when c... u，m When (t) = 0, it indicates no service, i.e., whether it belongs to the satellite cluster of target user u at time t. Therefore, the clustering strategy for satellite m at time t is c. m (t)=[c 1，m (t), ..., c U，m (t)] T At time t, the total signal b received by satellite m m (t) is composed of the superposition of signals emitted by the target user u, users within the set, and users between sets, and is represented as:

[0016]

[0017] Where p u For the signal power of target user u, g mu (t) represents the channel coefficients of target user u between time t and satellite m, a u (t) represents the modulation symbol transmitted by the target user u at time t, p v Let g be the signal power of user v within the set.mv (t) represents the channel coefficient of user v within the set between time t and satellite m, a v (t) represents the modulation symbol transmitted by user v within the set at time t, p w For the signal transmission power of user w in the collection, g mw (t) represents the channel coefficients of user w across the set between time t and satellite m, a w Let n(t) be the modulation symbol transmitted by user w between sets at time t, and let n(t) be the value with mean 0 and variance at time t. Gaussian noise;

[0018] Since all satellites in the satellite cluster will share the target user's channel state information, interference within the cluster is eliminated by designing a coordinated beamforming vector. Specifically, the zero-forced beamformer for target user u uses projection transformation calculations to project the target user u's channel vector onto a subspace perpendicular to the channel directions of users within the cluster, thereby eliminating interference between users within the cluster. Its beamforming vector h at time t... u (t) is represented as:

[0019]

[0020] in For satellite cluster Φ u (t) at time t corresponding to |Φ u (t)|×|Φ u The identity matrix of (t)| This is the channel coefficient matrix between the satellite cluster and the target user u at time t for users within the set. Each column... Let be the channel vector from user v to each satellite in the satellite cluster within the set at time t. Let be the channel vector from target user u to each satellite in the satellite cluster at time t. For G -u The pseudo-inverse matrix of (t) is used to represent the channel matrix G of the users in the set. -u (t) is conjugate transposed and then combined with G. -u (t) multiplied by itself yields phalanx. It is an orthogonal projection matrix that maps the channel vector g of the target user u. u (t) is projected onto a subspace perpendicular to the channel direction of all users within the set, so that the interference to users within the set is zero after beamforming.

[0021] The transmission rate r of target user u at time t u (t) can be represented as:

[0022]

[0023] Where W is the system bandwidth, h u (t) H for h u The conjugate transpose of (t). This is the channel vector from user w in the set to each satellite in the satellite cluster at time t. The uplink transmission delay of target user u is:

[0024]

[0025] 2) Task processing latency: Assume that the cache resources of service k are equal to the service data size s. k Proportional to the total cache resources of satellite m at time t, the total cache resources are:

[0026]

[0027] Where ξ k Let k be the cache resource coefficient. Assuming the offloading task is not decomposable, the offloading task for target user u will be handled by the satellite m with the highest probability of deploying the service in the satellite cluster, i.e. in This indicates the type of service requested by target user u at time t, and the probability that satellite m will not execute this task is... In this scenario, the task will be offloaded to the cloud for processing. Assuming R is the data transmission rate of the backbone network, the task processing latency is:

[0028]

[0029] in Indicates task T u Edge computation delay of (t), Indicates task T u (t) Transmission delay when offloading to the cloud;

[0030] To reduce the load on the backbone network and process tasks on the MEC server as much as possible, assuming R is a small value, offloading to the cloud would result in significant latency. Considering uplink latency, we can obtain the task T. u The total unloading delay of (t) is:

[0031]

[0032] Furthermore, in step (2), in order to reduce the bandwidth consumption of the backhaul link, it is necessary to limit the number of satellites in the satellite cluster. The satellite cluster size constraint is as follows:

[0033]

[0034] Where B is the maximum number of satellites in the satellite cluster, assuming the total cache resources cannot exceed the threshold limit Cost.th , represented as:

[0035]

[0036] Furthermore, for satellite m, the cache and computing resources consumed by the caching service cannot exceed the resource limit of that satellite:

[0037]

[0038] First, consider the single-target user uninstallation scenario, where we analyze only the uninstallation tasks generated for a single target user u. The problem of minimizing the long-term latency of target user u can be expressed as:

[0039]

[0040] Where X(t) = [x m (t)|m∈Φ u [(t)] and C(t) = [c m (t)|m∈Φ u [(t)] represents the service cache matrix and satellite clustering matrix of the target user u, respectively. Variables c and x make the above problem an NP-hard problem of mixed integer nonlinear programming.

[0041] To solve this NP-hard problem, the long-run optimization problem is first transformed into a time-decoupled instantaneous problem based on Lyapunov optimization. Then, the instantaneous problem is decomposed into two subproblems, and these subproblems are solved alternately to obtain an approximately optimal satellite cluster and service caching strategy.

[0042] Based on Lyapunov optimization, a virtual cache resource vector P(t) is constructed at time t, representing the cache to be processed at the current time. Assuming the initial state is P(0) = 0, the state transition of the vector is expressed as:

[0043] P(t+1)=[P(t)+a(t)-b(t)] (12)

[0044] in and b(t) = Cost th These represent the task arrival rate and service rate of the virtual cache resource vector, respectively, where [.] denotes max{., 0}, and the Lyapunov function is expressed as... The Lyapunov drift is Δ(t) = L(t+1) - L(t). According to the above definition, the Lyapunov drift can be expressed as:

[0045]

[0046] in As an auxiliary term introduced for Lyapunov drift, formula (13) can be derived as follows:

[0047]

[0048] Based on the Lyapunov optimization framework, the total cache resource constraint, i.e., formula (10), can be transformed into a drift minimization problem at each time step. Therefore, the long-term optimization problem can be transformed into an instantaneous optimization problem, which is denoted as the P-Lyapunov problem. The optimization objective is drift plus penalty:

[0049]

[0050] Where V is a non-negative weighting factor, the value of which is selected based on the trade-off between cached resource vector drift and offloading latency;

[0051] For the P-Lyapunov problem, the complexity of traditional search algorithms, such as branch and bound, is exponential in the worst case, making it difficult to obtain a solution in a reasonable time. In particular, the computational complexity increases significantly when the network size increases. Therefore, the problem will be decomposed based on the GBD framework to reduce the computational complexity of solving the P-Lyapunov problem.

[0052] Furthermore, in step (4), an optimization algorithm for solving the P-Lyapunov problem is proposed based on the GBD framework. To meet the requirements of the GBD framework, the variable c is fixed, resulting in a convex optimization problem with respect to the variable x. The P-Lyapunov problem is analyzed, and the optimization objective consists of two parts: Lyapunov drift and Lyapunov penalty. Lyapunov drift is denoted as L-drift, and Lyapunov penalty is denoted as L-penalty.

[0053] L-drift=P(t)(Ξ T X(t)C(t) T -Cost th (16a)

[0054]

[0055] Where Ξ is the service cost vector. For task T uThe service type vector (t) is represented by ⊙, which indicates the element-wise multiplication of two vectors or matrices. Analysis shows the relationship between the drift and penalty components and the variable x: when x increases, the Lyapunov drift does not decrease, and the Lyapunov penalty at the current moment does not increase. Since the Lyapunov penalty is a concave function of x, the optimization objective obtained by directly adding these two components is non-convex with respect to x, and therefore does not meet the decomposition requirements of GBD. A service caching probability constraint is added to ensure that at least one satellite in the satellite cluster of the target user u will cache the requested service. This operation will not affect the optimality of the delay, but improper selection of the service caching probability may result in no satellite meeting the conditions. In this case, the service caching probability is reduced from 1 until at least one satellite in the satellite cluster will cache the requested service. By adding a service caching probability constraint to the satellite cluster, the instantaneous optimization problem, i.e., formula (15), can be rewritten as:

[0056]

[0057] When c is fixed, the goal is to optimize the Lyapunov drift, which is a convex function of x, and Equation (17b) is a function of the form h(g(x)), where h(x) = maxx and g(x) = P(t)⊙(o T X(t) is a convex function of x. According to the convexity preservation property of composite functions, when g(x) and h(x) are both convex functions and h(x) is not decreasing, h(g(x)) is a convex function. Therefore, (17b) is also a convex function of x. In summary, formula (17) satisfies the requirements of the GBD framework. Next, formula (17) will be decomposed into a service caching problem and a satellite clustering problem. The service caching problem will be taken as the primary problem, i.e., P-primal, and the satellite clustering problem will be taken as the master problem, i.e., P-master. The satellite clustering strategy matrix will be determined. Then, formula (17) can be decomposed into two subproblems:

[0058]

[0059] in Let c be the set of variables, v be the optimal function of variable c, and v be the set of feasible options. The definition is as follows:

[0060]

[0061] Where s = [s1, s2, ..., s] k ] T Let s be the service cache demand vector, where the k-th element is s k Let f = [f1, f2, ..., f2] represent the cache resources required for service k. k ] TTo serve the computational demand vector, where the k-th element f k This represents the computing resources required for service k. T with f T Multiply each of these values ​​by the cache strategy matrix X(t) to obtain the total cache resource usage of each satellite, which is then used for the cache resources in formula (21).

[0062] The Lagrangian function for the service caching problem can be derived as follows:

[0063]

[0064] Where μ and λ are Lagrange multiplier vectors, the P-master function problem can be rewritten based on the Lagrange function as follows:

[0065]

[0066] Where d0 is the P-master objective value variable, representing the lower bound estimate of the optimal function, and Λ is the constraint set of λ in the infeasibility constraints, ensuring the mathematical validity of the infeasibility constraints:

[0067]

[0068] 1) Solution to the P-primal problem: Since the P-primal problem is a convex optimization problem, the problem in the P-master problem can be rewritten as:

[0069]

[0070] Where X(t) (τ) μ represents the optimal solution obtained by solving formula (18) in the τth iteration. (τ) and λ (τ) Let represent the optimal Lagrange multiplier vector obtained by solving formula (18) in the τ-th iteration, τ1∈{τ|If formula (18) (τ) The feasible} is the set index of feasible iteration rounds, τ2∈{τ|If formula (18) (τ) The set index of infeasible iterations is}.

[0071] The P-primal problem can be solved using convex optimization. In each iteration, the solution to the P-primal problem is added as a new constraint to the P-master problem. As can be seen from the definition of the set Y, when c is fixed, the P-primal problem is not always feasible; if the P-primal problem is feasible, then the optimal solution and the bounded optimal solution generation constraints can be obtained.

[0072] d0≥L * (X(t) (τ) C(t), μ(τ) (28)

[0073] Otherwise, the constraints of the P-primal problem cannot be satisfied. However, an approximate optimal solution that minimizes the impact on server computation and caching capacity constraints can be obtained by solving the following problem:

[0074]

[0075] Using the optimal solution to the above problem (X(t)) (τ) C(t), λ (τ) Generate infeasible constraints:

[0076]

[0077] 2) Solution to the P-master Problem: P-master is a 0 / 1 programming problem. A satellite clustering algorithm based on Gibbs sampling is used to obtain an approximate optimal solution to P-master. The objective value F of P-master is defined as:

[0078]

[0079] Where β > 0, The parameters are used to weight the contribution of feasible constraints in each iteration. represents the weighting parameters in the τ1th feasible iteration. All idle satellites are considered as vertices in the graph. It is a picture The clustering state of all vertices and satellite m in the cluster is c. u，m The clustering state of satellites other than satellite m is Based on the optimization objective value F of P-master, the state transition probability distribution of satellite m can be obtained as follows:

[0080]

[0081] in For Gibbs sampling parameters, when Furthermore, as the sampling period approaches infinity, the system will converge to the optimal value. In the probability distribution, the calculation of the optimization objective value F depends on the value of d0. When the clustering variable c of the satellites... u,m Given that the problem of minimizing F becomes the problem of minimizing d0 in an unconstrained convex optimization, we can obtain the optimal optimization objective F of satellite m in the current cluster state. Furthermore, we can perform sampling based on the above probability distribution to complete the state transition of satellite m.

[0082] After updating the cluster state of satellite m, the cluster state of the next satellite is updated by randomly selecting the next satellite. The probability of the state update is:

[0083]

[0084] Where ρ > 0 is a parameter for adjusting the state update probability. When the new target value is much larger than the current target value, the difference between the two target values ​​can be limited to ρ to ensure a larger state update probability, using F and Let represent the current state and the new state, respectively. During the satellite clustering state transition, the probability of accepting the new state is η, while the probability of maintaining the current state is 1-η.

[0085] The satellite clustering algorithm based on Gibbs sampling to solve the P-master is shown in Algorithm 1:

[0086]

[0087] The GBD-based algorithm alternately solves the two subproblems, as shown in Algorithm 2.

[0088]

[0089] Furthermore, when multiple users simultaneously generate task unloading requests, optimizing the satellite set and service caching strategy becomes more complex, requiring the algorithm to be extended to multi-user scenarios. In multi-user scenarios, the satellite set is divided into the following cases:

[0090] (a): All users share the same set of satellites;

[0091] (b): The satellite sets of each user are completely different;

[0092] (c): Different users have the same satellite collection.

[0093] In case (a), the problem is similar to the single-target user optimization problem. In case (b), the problem is decomposed into multiple independent single-target user optimization problems. In case (c), the satellites in the overlapping area can be regarded as a set of satellites serving each independent target user, and at the same time, task offloading requests are generated. It is assumed that the offloading request of the same type of service can be regarded as a request from a single user, and the corresponding tasks can also be merged into a single task.

[0094] Assume the set of users sharing the same satellite cluster is B0, and the offloading request is represented by T. u (t): Let represent the data size, workload, and service type vectors, respectively. Assume that each user in B0 requests only one service at each time slot, and that the service types requested by different users in different time slots are possible. The satellite clustering strategy matrix and service caching strategy matrix for each user in B0 at time t can be represented as follows: and Based on Lyapunov optimization, the instantaneous satellite clustering and service caching problem in multi-user scenarios can be denoted as the P2-Lyapunov problem.

[0095]

[0096] Fixed variables The question is for It is still non-convex; we can transform it into a convex problem by adding constraints:

[0097]

[0098] Where Θ is a hyperparameter used to balance the optimality and feasibility of the problem. When computational resources are sufficient, all services requested by the user set can be cached on the satellite cluster. Therefore, the minimum lower bound of the average offload latency can be obtained:

[0099]

[0100] If the satellite ensemble lacks sufficient resources, all tasks will be offloaded to the cloud for processing. In this case, the upper bound of the maximum average latency is:

[0101]

[0102] To balance optimality and feasibility, the value of Θ needs to be determined. Therefore, a binary classification-based GBD joint optimization algorithm is proposed to obtain the optimal value of Θ, along with corresponding satellite clustering and service caching strategies.

[0103]

[0104] The gain effect brought about by adopting the above technical solution:

[0105] This invention proposes an edge service caching strategy, which utilizes a specific set of satellites—not a single satellite—to collectively provide edge caching and wireless transmission services to each user. To minimize long-term average latency under caching cost constraints, a mixed-integer nonlinear programming problem is constructed by jointly optimizing the satellite set and the service caching strategy. To address this problem, this invention proposes a joint optimization algorithm based on Lyapunov optimization and GBD. This proposed joint optimization algorithm outperforms existing algorithms and can effectively reduce long-term latency and caching costs. Attached Figure Description

[0106] Figure 1 Flowchart of algorithm optimization for MEC service caching;

[0107] Figure 2 The average latency per user in the simulated scenario;

[0108] Figure 3 The average cache cost per user in the simulation scenario;

[0109] Figure 4 This represents the average latency for multiple users in a simulated scenario.

[0110] Figure 5 This represents the average cache cost for multiple users in a simulated scenario. Detailed Implementation

[0111] The present invention will now be described in detail with reference to the accompanying drawings.

[0112] Step 1: Build a satellite communication network that supports MEC. Assume there are M satellites equipped with MEC servers and U users, represented by sets... and set This indicates that each user terminal has communication capabilities, and the satellite equipped with an MEC server can provide computing and caching resources for the user terminals.

[0113] Considering that each MEC satellite node has different computing and caching resources, the computing and caching resources of satellite m are represented by C. m and S m Let the task execution duration be T, and divide T into multiple discrete time points t. Let Φ be the set of satellites serving the target user u. u (t), Φ u The set of all target users of service (t) is Ω. u (t) indicates that a satellite can simultaneously provide services to different target users, and the satellite sets of different target users can intersect; denoted as v, the other users served by the satellite cluster besides the target user u, are called users within the set. The target user u and users other than those within the set are referred to as users between sets.

[0114] Suppose there are K types of services, and the service set is denoted as K. Different services consume different cache and computing resources when cached on the satellite. Assume service k requires s cache resources. k And computing resources are f k Using continuous variable x k，m (t)∈[0,1] represents the probability that service k is cached in satellite m at time t, and the service caching strategy of satellite m at time t is x. m (t)=[x 1，m (t), ..., x k，m (t)] T .

[0115] Suppose that at time t, target user u generates an uninstallation task T that requires only one type of service.u (t), and remains constant at each time step, task T u The data volume and workload of (t) are respectively used as (bit) and (GHz) indicates that satellite m needs to cache services at the start position of each time to meet the service requirements of the task. At each time, the task generated by each target user will go through three steps: task unloading, task processing, and result return. The task unloading delay mainly consists of the following two parts:

[0116] 1) Uplink delay: For satellite cluster Φ u (t), using a binary variable c u，m (t) represents that at time t, satellite m∈Φ u (t) Whether it serves the target user u, when c u，m When (t) = 1, it represents service; when c... u，m When (t) = 0, it indicates no service, i.e., whether it belongs to the satellite cluster of target user u at time t. Therefore, the clustering strategy for satellite m at time t is c. m (t)=[c 1，m (t), ..., c U，m (t)] T At time t, the total signal b received by satellite m m (t) is composed of the superposition of signals emitted by the target user u, users within the set, and users between sets, and is represented as:

[0117]

[0118] Where p u For the signal power of target user u, g mu (t) represents the channel coefficients of target user u between time t and satellite m, a u (t) represents the modulation symbol transmitted by the target user u at time t, p v Let g be the signal power of user v within the set. mv (t) represents the channel coefficient of user v within the set between time t and satellite m, α v (t) represents the modulation symbol transmitted by user v within the set at time t, p w For the signal transmission power of user w in the collection, g mw (t) represents the channel coefficients of user w across the set between time t and satellite m, a w Let n(t) be the modulation symbol transmitted by user w between sets at time t, and let n(t) be the value with mean 0 and variance at time t. Gaussian noise;

[0119] Since all satellites in the satellite cluster will share the target user's channel state information, interference within the cluster is eliminated by designing a coordinated beamforming vector. Specifically, the zero-forced beamformer for target user u uses projection transformation calculations to project the target user u's channel vector onto a subspace perpendicular to the channel directions of users within the cluster, thereby eliminating interference between users within the cluster. Its beamforming vector h at time t... u (t) is represented as:

[0120]

[0121] in For satellite cluster Φ u (t) at time t corresponding to |Φ u (t)|×|Φ u The identity matrix of (t)| This is the channel coefficient matrix between the satellite cluster and the target user u at time t for users within the set. Each column... Let be the channel vector from user v to each satellite in the satellite cluster within the set at time t. Let be the channel vector from target user u to each satellite in the satellite cluster at time t. For G -u The pseudo-inverse matrix of (t) is used to represent the channel matrix G of the users in the set. -u (t) is conjugate transposed and then combined with G. -u (t) multiplied by itself yields phalanx. It is an orthogonal projection matrix that maps the channel vector g of the target user u. u (t) is projected onto a subspace perpendicular to the channel direction of all users within the set, so that the interference to users within the set is zero after beamforming.

[0122] The transmission rate r of target user u at time t u (t) can be represented as:

[0123]

[0124] Where W is the system bandwidth, h u (t) H for h u The conjugate transpose of (t). This is the channel vector from user w in the set to each satellite in the satellite cluster at time t. The uplink transmission delay of target user u is:

[0125]

[0126] 2) Task processing latency: Assume that the cache resources of service k are equal to the service data size s. kProportional to the total cache resources of satellite m at time t, the total cache resources are:

[0127]

[0128] Where ξ k Let k be the cache resource coefficient. Assuming the offloading task is not decomposable, the offloading task for target user u will be handled by the satellite m with the highest probability of deploying the service in the satellite cluster, i.e. in This indicates the type of service requested by target user u at time t, and the probability that satellite m will not execute this task is... In this scenario, the task will be offloaded to the cloud for processing. Assuming R is the data transmission rate of the backbone network, the task processing latency is:

[0129]

[0130] in Indicates task T u Edge computation delay of (t), Indicates task T u (t) Transmission delay when offloading to the cloud.

[0131] To reduce backbone network load, tasks should be processed on MEC servers as much as possible. Assuming R is a small value, offloading to the cloud will result in significant latency. Considering uplink latency, the task T can be obtained. u The total unloading delay of (t) is:

[0132]

[0133] Step 2: The problem of finding the optimal satellite set and optimizing service caching strategy for users is modeled as a nondeterministic polynomial NP-hard long-term optimization problem involving mixed integer nonlinear programming. To reduce backhaul link bandwidth consumption, the number of satellites in the satellite cluster needs to be limited. The satellite cluster size constraint is:

[0134]

[0135] Where B is the maximum number of satellites in the satellite cluster, assuming the total cache resources cannot exceed the threshold limit Cost. th , represented as:

[0136]

[0137] Furthermore, for satellite m, the cache and computing resources consumed by the caching service cannot exceed the resource limit of that satellite:

[0138]

[0139] First, consider the single-target user uninstallation scenario, where we analyze only the uninstallation tasks generated for a single target user u. The problem of minimizing the long-term latency of target user u can be expressed as:

[0140]

[0141] Where X(t) = [x m (t)|m∈Φ u [(t)] and C(t) = [c m (t)|m∈Φ u [(t)] represents the service cache matrix and satellite clustering matrix of the target user u, respectively. Variables c and x make the above problem an NP-hard problem of mixed integer nonlinear programming.

[0142] Step 3: Transform the long-term optimization problem into a time-decoupled instantaneous problem based on Lyapunov optimization.

[0143] First, the long-term optimization problem is transformed into a time-decoupled instantaneous problem based on Lyapunov optimization. Then, the instantaneous problem is decomposed into two subproblems. These subproblems are then solved alternately to obtain an approximately optimal satellite cluster and service caching strategy.

[0144] Based on Lyapunov optimization, a virtual cache resource vector P(t) is constructed at time t, representing the cache to be processed at the current time. Assuming the initial state is P(0) = 0, the state transition of the vector is expressed as:

[0145] P(t+1)=[P(t)+a(t)-b(t)] (12)

[0146] in and b(t) = Cost th These represent the task arrival rate and service rate of the virtual cache resource vector, respectively, where [.] denotes max{., 0}, and the Lyapunov function is expressed as... The Lyapunov drift is Δ(t) = L(t+1) - L(t). According to the above definition, the Lyapunov drift can be expressed as:

[0147]

[0148] in As an auxiliary term introduced for Lyapunov drift, formula (13) can be derived as follows:

[0149]

[0150] Based on the Lyapunov optimization framework, the total cache resource constraint, i.e., formula (10), can be transformed into a drift minimization problem at each time step. Therefore, the long-run optimization problem can be transformed into an instantaneous optimization problem, which can be denoted as the P-Lyapunov problem, with the optimization objective being drift plus penalty:

[0151]

[0152] Where V is a non-negative weighting factor, the value of which is selected based on the trade-off between cached resource vector drift and offloading latency.

[0153] For the P-Lyapunov problem, the complexity of traditional search algorithms, such as branch and bound, is exponential in the worst case, making it difficult to obtain a solution within a reasonable timeframe, especially as the number of satellites, users, and service types increases significantly. Therefore, this problem will be decomposed based on the GBD framework to reduce the computational complexity of solving the P-Lyapunov problem.

[0154] Step 4: Decompose the problem based on the GBD framework to solve the Lyapunov problem with low complexity. Decompose the instantaneous problem into two subproblems, and then solve these subproblems alternately to obtain the near-optimal satellite set and service caching strategy to solve the NP-hard problem proposed in Step 2.

[0155] Based on the GBD framework, an optimization algorithm for solving the P-Lyapunov problem is proposed. To satisfy the requirements of the GBD framework, the variable c is fixed, resulting in a convex optimization problem with variable x. Analyzing the P-Lyapunov problem, the optimization objective consists of two parts: Lyapunov drift and Lyapunov penalty. The Lyapunov drift is denoted as L-drift, and the Lyapunov penalty is denoted as L-penalty.

[0156] L-drift = P(t)(ΞTX(t)C(t) T -Cost th (16a)

[0157]

[0158] Where Ξ is the service cost vector. For task T uThe service type vector (t) is represented by ⊙, which indicates the element-wise multiplication of two vectors or matrices. Analysis shows the relationship between the drift and penalty components and the variable x: when x increases, the Lyapunov drift does not decrease, and the Lyapunov penalty at the current moment does not increase. Since the Lyapunov penalty is a concave function of x, the optimization objective obtained by directly adding these two components is non-convex with respect to x, and therefore does not meet the decomposition requirements of GBD. A service caching probability constraint is added to ensure that at least one satellite in the satellite cluster serving the target user u will cache the requested service. This operation will not affect the optimality of the delay, but improper selection of the service caching probability may result in no satellite meeting the conditions. In this case, the service caching probability is reduced from 1 until at least one satellite in the satellite cluster will cache the requested service. By adding a service caching probability constraint to the satellite cluster, the instantaneous optimization problem, i.e., formula (15), can be rewritten as:

[0159]

[0160] When c is fixed, the goal is to optimize the Lyapunov drift, which is a convex function of x, and Equation (17b) is a function of the form h(g(x)), where h(x) = maxx and g(x) = P(t)⊙(o T X(t) is a convex function of x. According to the convexity preservation property of composite functions, when g(x) and h(x) are both convex functions and h(x) is not decreasing, h(g(x)) is a convex function. Therefore, (17b) is also a convex function of x. In summary, formula (17) satisfies the requirements of the GBD framework. Next, formula (17) will be decomposed into a service caching problem and a satellite clustering problem. The service caching problem will be taken as the primary problem, i.e., P-primal, and the satellite clustering problem will be taken as the master problem, i.e., P-master. The satellite clustering strategy matrix will be determined. Then, formula (17) can be decomposed into two subproblems:

[0161]

[0162] in Let c be the set of variables, v be the optimal function of variable c, and v be the set of feasible options. The definition is as follows:

[0163]

[0164] Where s = [s1, s2, ..., s] k ] T Let s be the service cache demand vector, where the k-th element is s k Let f = [f1, f2, ..., f3] represent the cache resources required for service k. k ] TTo serve the computational demand vector, where the k-th element f k This represents the computing resources required for service k. T with f T Multiply each of these values ​​by the cache strategy matrix X(t) to obtain the total cache resource usage of each satellite, which is then used for the cache resources in formula (21).

[0165] The Lagrangian function for the service caching problem can be derived as follows:

[0166]

[0167] Where μ and λ are Lagrange multiplier vectors, the P-master function problem can be rewritten based on the Lagrange function as follows:

[0168]

[0169] Where d0 is the P-master objective value variable, representing the lower bound estimate of the optimal function, and Λ is the constraint set of λ in the infeasibility constraints, ensuring the mathematical validity of the infeasibility constraints:

[0170]

[0171] l) Solution to the P-primal problem: Since the P-primal problem is a convex problem, the problem in the P-master problem can be rewritten as:

[0172]

[0173] Where X(t) (τ) μ represents the optimal solution obtained by solving formula (18) in the τth iteration. (τ) and λ (τ) Let represent the optimal Lagrange multiplier vector obtained by solving formula (18) in the τ-th iteration, τ1∈{τ|If formula (18) (τ) The feasible} is the set index of feasible iteration rounds, τ2∈{τ|If formula (18) (τ) The set index of infeasible iterations is}.

[0174] The P-primal problem can be solved using convex optimization. In each iteration, the solution to the P-primal problem is added as a new constraint to the P-master problem. As can be seen from the definition of the set Y, when c is fixed, the P-primal problem is not always feasible; if the P-primal problem is feasible, then the optimal solution and the bounded optimal solution generation constraint can be obtained.

[0175] d0≥L * (X(t) (τ) ,C(t)μ(τ) (28)

[0176] Otherwise, the constraints of the P-primal problem cannot be satisfied. However, a near-optimal solution that minimizes the constraint impairment can be obtained by solving the following problem:

[0177]

[0178] Using the optimal solution to the above problem (x(t)) (τ) C(t), λ (τ) Generate infeasible constraints:

[0179]

[0180] 2) Solution to the P-master Problem: P-master is a 0 / 1 programming problem. A satellite clustering algorithm based on Gibbs sampling is used to obtain an approximate optimal solution to P-master. The objective value F of P-master is defined as:

[0181]

[0182] Where β > 0, The parameters are used to weight the contribution of feasible constraints in each iteration. represents the weighting parameters in the τ1th feasible iteration. All idle satellites are considered as vertices in the graph. It is a picture The clustering state of all vertices and satellite m in the cluster is c. u,m The clustering state of satellites other than satellite m is Based on the optimization objective value F of P-master, the state transition probability distribution of satellite m can be obtained as follows:

[0183]

[0184] in For Gibbs sampling parameters, when Furthermore, as the sampling period approaches infinity, the system will converge to the optimal value. In the probability distribution, the calculation of the optimization objective value F depends on the value of d0. When the clustering variable c of the satellites... u,m Given that the problem of minimizing F becomes the problem of minimizing d0 in an unconstrained convex optimization, we can obtain the optimal optimization objective F of satellite m in the current cluster state. Furthermore, we can perform sampling based on the above probability distribution to complete the state transition of satellite m.

[0185] After updating the cluster state of satellite m, the cluster state of the next satellite is updated by randomly selecting the next satellite. The probability of the state update is:

[0186]

[0187] Where ρ > 0 is a parameter for adjusting the state update probability. When the new target value is much larger than the current target value, the difference between the two target values ​​can be limited to ρ to ensure a larger state update probability. Using F and... Let represent the current state and the new state, respectively. During the satellite clustering state transition, the probability of accepting the new state is η, while the probability of maintaining the current state is 1-η.

[0188] The satellite clustering algorithm based on Gibbs sampling to solve the P-master is shown in Algorithm 1:

[0189]

[0190] GBD-based algorithms alternately solve the two subproblems, as shown in Algorithm 2:

[0191]

[0192] Step 5: Extend the problem to a multi-user scenario. When multiple users simultaneously generate task offloading requests, optimizing the satellite set and service caching strategy becomes complex. Therefore, the algorithm is extended to a multi-user scenario. In a multi-user scenario, the satellite set is divided into the following cases:

[0193] (a): All users share the same set of satellites;

[0194] (b): The users' satellite sets are completely different;

[0195] (c): Different users have the same satellite collection.

[0196] In case (a), the problem is similar to the single-target user optimization problem. In case (b), the problem is decomposed into multiple independent single-target user optimization problems. In case (c), the satellites in the overlapping area can be regarded as a set of satellites serving each independent target user, and at the same time, task offloading requests are generated. It is assumed that the offloading request of the same type of service can be regarded as a request from a single user, and the corresponding tasks can also be merged into a single task.

[0197] Assume the set of users sharing the same satellite cluster is B0, and the offloading request is represented by T. u (t): Let represent the data size, workload, and service type vectors, respectively. Assume that each user in B0 requests only one service at each time slot, and that the service types requested by different users in different time slots are possible. The satellite clustering strategy matrix and service caching strategy matrix for each user in B0 at time t can be represented as follows: and Based on Lyapunov optimization, the instantaneous satellite clustering and service caching problem in multi-user scenarios can be denoted as the P2-Lyapunov problem.

[0198]

[0199] Fixed variables The question is for It is still non-convex. By adding constraints, it can be transformed into a convex optimization problem.

[0200]

[0201] Where Θ is a hyperparameter used to balance the optimality and feasibility of the problem. When computational resources are sufficient, all services requested by the user set can be cached on the satellite cluster. Therefore, the minimum lower bound of the average offload latency can be obtained:

[0202]

[0203] If the satellite ensemble lacks sufficient resources, all tasks will be offloaded to the cloud for processing. In this case, the upper bound of the maximum average latency is:

[0204]

[0205] To strike a balance between optimality and feasibility, the Θ value needs to be determined. Therefore, a binary classification-based GBD joint optimization algorithm is proposed to obtain the optimal Θ value, along with corresponding satellite clustering and service caching strategies.

[0206]

[0207] The present invention will be analyzed through an example below.

[0208] First, a satellite constellation is built and a system model is implemented to obtain satellite parameters. In a single-user scenario, M=784 is set, with all satellites evenly distributed across 28 orbits, and 28 satellites evenly distributed across each orbit. In a multi-user scenario, the number of users is set to 10.

[0209] Depend on Figure 2 and Figure 4 It can be seen that in both single-user and multi-user scenarios, the average total latency of each algorithm gradually converges to a stable value over time. The algorithm proposed in this invention achieves a near-optimal total latency for the exhaustive search method in both scenarios, while its total latency is significantly lower than that of the block-by-block optimization algorithm, verifying the effectiveness of the proposed joint optimization framework. Figure 3 and Figure 5It can be seen that in both single-user and multi-user scenarios, the average cache cost gradually stabilizes over time. The cache cost of the algorithm proposed in this invention is always lower than that of other comparative algorithms and meets the cache cost threshold constraint, which verifies the effectiveness of the proposed Lyapunov optimization framework in long-term cache cost control.

Claims

1. A satellite network optimization method based on Mobile Edge Computing (MEC) service caching configuration, characterized in that, Includes the following steps: Step (1) Build a satellite communication network that supports MEC. Each satellite node has different computing and caching resources. Assume there are M satellites equipped with MEC servers and U users. Satellite set and user set Each user terminal has communication capabilities, and satellites equipped with MEC servers can provide computing and caching resources for the user terminals; Step (2) models the problem of finding the optimal satellite set and optimizing the service caching strategy for the target user as a non-deterministic polynomial problem of mixed integer nonlinear programming, i.e., an NP-hard long-term optimization problem. Step (3) transforms the long-run optimization problem into a time-decoupled instantaneous problem based on Lyapunov optimization; Step (4) Based on the Generalized Benders Decomposition (GBD) framework, the time decoupling instantaneous problem based on Lyapunov optimization is decomposed to solve the Lyapunov problem with lower complexity. The instantaneous problem is decomposed into two sub-problems, and then the two sub-problems are solved alternately to obtain the near-optimal satellite set and service caching strategy to solve the NP-hard problem proposed in step (2). Step (5) extends the problem to a multi-user scenario to obtain an approximately optimal satellite set and service caching strategy.

2. The satellite network optimization method based on edge computing service cache configuration according to claim 1, characterized in that, In step (1), considering that each MEC satellite node has different computing and caching resources, the computing and caching resources of satellite m are represented as C. m and S m Assuming the task execution time is T, and T is divided into multiple discrete time points t, the set of satellites serving the target user u is Φ. u (t), Φ u The set of all target users of service (t) is Ω. u (t) indicates that a satellite can simultaneously provide services to different target users, and the satellite sets of different target users can intersect; denoted as v, the other users served by the satellite cluster besides the target user u, are called users within the set. The target user u and users other than those within the set are referred to as users between sets. Suppose there are K types of services, and the service set is denoted as K. Different services consume different cache and computing resources when cached on the satellite. Assume that service k requires s cache resources. k And computing resources are f k Using continuous variable x k，m (t)∈[0,1] represents the probability that service k is cached in satellite m at time t, and the service caching strategy of satellite m at time t is x. m (t)=[x 1，m (t), ..., x k，m (t)] T ; Suppose that at time t, target user u generates an uninstallation task T that requires only one type of service. u (t), and remains constant at each time step, task T u The data volume and workload of (t) are respectively used as (bit) and (GHz) indicates that satellite m needs to cache services at the start position of each time to meet the service requirements of the task. At each time, the task generated by each target user will go through three steps: task unloading, task processing, and result return. The task unloading delay mainly consists of the following two parts: 1) Uplink delay: For satellite cluster Φ u (t), using a binary variable c u，m (t) represents that at time t, satellite m∈Φ u (t) Whether it serves the target user u, when c u，m When (t) = 1, it represents service; when c... u，m When (t) = 0, it indicates no service, i.e., whether it belongs to the satellite cluster of target user u at time t. Therefore, the clustering strategy for satellite m at time t is c. m (t)=[c 1，m (t), ..., c U，m (t)] T At time t, the total signal b received by satellite m m (t) is composed of the superposition of signals emitted by the target user u, users within the set, and users between sets, and is represented as: Where p u For the signal power of target user u, g mu (t) represents the channel coefficients of target user u between time t and satellite m, a u (t) represents the modulation symbol transmitted by the target user u at time t, p v Let g be the signal power of user v within the set. mv (t) represents the channel coefficient of user v within the set between time t and satellite m, a v (t) represents the modulation symbol transmitted by user v within the set at time t, p w For the signal transmission power of user w in the collection, g mw (t) represents the channel coefficients of user w across the set between time t and satellite m, a w Let n(t) be the modulation symbol transmitted by user w between sets at time t, and let n(t) be the value with mean 0 and variance at time t. Gaussian noise; Since all satellites in the satellite cluster will share the target user's channel state information, interference within the cluster is eliminated by designing a coordinated beamforming vector. Specifically, the zero-forced beamformer for target user u uses projection transformation calculations to project the target user u's channel vector onto a subspace perpendicular to the channel directions of users within the cluster, thereby eliminating interference between users within the cluster. Its beamforming vector h at time t... u (t) is represented as: in For satellite cluster Φ u (t) at time t corresponding to |Φ u (t)|×|Φ u The identity matrix of (t)| This is the channel coefficient matrix between the satellite cluster and the target user u at time t, where each column represents a user within the set. Let be the channel vector from user v to each satellite in the satellite cluster within the set at time t. Let be the channel vector from target user u to each satellite in the satellite cluster at time t. For G -u The pseudo-inverse matrix of (t) is used to represent the channel matrix G of the users in the set. -u (t) is conjugate transposed and then combined with G. -u (t) multiplied by itself yields phalanx. It is an orthogonal projection matrix that maps the channel vector g of the target user u. u (t) is projected onto a subspace perpendicular to the channel direction of all users within the set, so that the interference to users within the set is zero after beamforming. The transmission rate r of target user u at time t u (t) can be represented as: Where W is the system bandwidth, h u (t) H for h u The conjugate transpose of (t). This is the channel vector from user w in the set to each satellite in the satellite cluster at time t. The uplink transmission delay of target user u is: 2) Task processing latency: Assume that the cache resources of service k are equal to the service data size s. k Proportional to the total cache resources of satellite m at time t, the total cache resources are: Where ξ k Let k be the cache resource coefficient. Assuming the offloading task is not decomposable, the offloading task for target user u will be handled by the satellite m with the highest probability of deploying the service in the satellite cluster, i.e. in This indicates the type of service requested by target user u at time t, and the probability that satellite m will not execute this task is... In this scenario, the task will be offloaded to the cloud for processing. Assuming R is the data transmission rate of the backbone network, the task processing latency is: in Indicates task T u Edge computation delay of (t), Indicates task T u (t) Transmission delay when offloading to the cloud; To reduce the load on the backbone network and process tasks on the MEC server as much as possible, assuming R is a small value, offloading to the cloud would result in significant latency. Considering uplink latency, we can obtain the task T. u The total unloading delay of (t) is:

3. The satellite network optimization method based on edge computing service cache configuration according to claim 1, characterized in that, In step (2), in order to reduce the bandwidth consumption of the backhaul link, it is necessary to limit the number of satellites in the satellite cluster. The satellite cluster size constraint is as follows: Where B is the maximum number of satellites in the satellite cluster, assuming the total cache resources cannot exceed the threshold limit Cost. th , is represented as: Furthermore, for satellite m, the cache and computing resources consumed by the caching service cannot exceed the resource limit of that satellite: First, consider the single-target user uninstallation scenario, where we analyze only the uninstallation tasks generated for a single target user u. The problem of minimizing the long-term latency of target user u can be expressed as: Where X(t) = [x m (t)|m∈Φ u [(t)] and C(t) = [c m (t)|m∈Φ u [(t)] represents the service cache matrix and satellite clustering matrix of the target user u, respectively. Variables c and x make the above problem an NP-hard problem of mixed integer nonlinear programming. To solve this NP-hard problem, the long-run optimization problem is first transformed into a time-decoupled instantaneous problem based on Lyapunov optimization. Then, the instantaneous problem is decomposed into two subproblems, and these subproblems are solved alternately to obtain an approximately optimal satellite cluster and service caching strategy. Based on Lyapunov optimization, a virtual cache resource vector P(t) is constructed at time t, representing the cache to be processed at the current time. Assuming the initial state is P(0) = 0, the state transition of the vector is expressed as: P(t+1)=[P(t)+a(t)-b(t)] (12) in and b(t) = Cost th These represent the task arrival rate and service rate of the virtual cache resource vector, respectively, where [.] denotes max{., 0}, and the Lyapunov function is expressed as... The Lyapunov drift is Δ(t) = L(t+1) - L(t). According to the above definition, the Lyapunov drift can be expressed as: in As an auxiliary term introduced for Lyapunov drift, formula (13) can be derived as follows: Based on the Lyapunov optimization framework, the total cache resource constraint, i.e., formula (10), can be transformed into a drift minimization problem at each time step. Therefore, the long-term optimization problem can be transformed into an instantaneous optimization problem, which is denoted as the P-Lyapunov problem. The optimization objective is drift plus penalty: Where V is a non-negative weighting factor, the value of which is selected based on the trade-off between cached resource vector drift and offloading latency; For the P-Lyapunov problem, the complexity of traditional search algorithms, such as branch and bound, is exponential in the worst case, making it difficult to obtain a solution in a reasonable time. In particular, the computational complexity increases significantly when the network size increases. Therefore, the problem will be decomposed based on the GBD framework to reduce the computational complexity of solving the P-Lyapunov problem.

4. The satellite network optimization method based on edge computing service cache configuration according to claim 1, characterized in that, In step (4), an optimization algorithm for solving the P-Lyapunov problem is proposed based on the GBD framework. To meet the requirements of the GBD framework, the variable c is fixed, resulting in a convex optimization problem with respect to the variable x. The P-Lyapunov problem is analyzed, and the optimization objective consists of two parts: Lyapunov drift and Lyapunov penalty. Lyapunov drift is denoted as L-drift, and Lyapunov penalty is denoted as L-penalty. L-drift=P(t)(Ξ T X(t)C(t) T -Cost th ) (16a) Where Ξ is the service cost vector. For task T u The service type vector (t) is represented by ⊙, which indicates the element-wise multiplication of two vectors or matrices. Analysis shows the relationship between the drift and penalty components and the variable x: when x increases, the Lyapunov drift does not decrease, and the Lyapunov penalty at the current moment does not increase. Since the Lyapunov penalty is a concave function of x, the optimization objective obtained by directly adding these two components is non-convex with respect to x, and therefore does not meet the decomposition requirements of GBD. A service caching probability constraint is added to ensure that at least one satellite in the satellite cluster serving the target user u will cache the requested service. This operation will not affect the optimality of the delay, but improper selection of the service caching probability may result in no satellite meeting the conditions. In this case, the service caching probability is reduced from 1 until at least one satellite in the satellite cluster will cache the requested service. By adding a service caching probability constraint to the satellite cluster, the instantaneous optimization problem, i.e., formula (15), can be rewritten as: When c is fixed, the goal is to optimize the Lyapunov drift, which is a convex function of x, and Equation (17b) is a function of the form h(g(x)), where h(x) = maxx and g(x) = P(t)⊙(o T X(t) is a convex function of x. According to the convexity preservation property of composite functions, when g(x) and h(x) are both convex functions and h(x) is not decreasing, h(g(x)) is a convex function. Therefore, formula (17b) is also a convex function of x. In summary, formula (17) satisfies the requirements of the GBD framework. Next, formula (17) will be decomposed into a service caching problem and a satellite clustering problem. The service caching problem will be taken as the primary problem, i.e., P-primal, and the satellite clustering problem will be taken as the master problem, i.e., P-master. The satellite clustering strategy matrix will be determined. Then, formula (17) can be decomposed into two subproblems: in Let c be the set of variables, v be the optimal function of variable c, and v be the set of feasible options. The definition is as follows: Where s = [s1, s2, ..., s k ] T Let s be the service cache demand vector, where the k-th element is s k Let f = [f1, f2, ..., f2] represent the cache resources required for service k. k ] T To serve the computational demand vector, where the k-th element f k This represents the computing resources required for service k. T with f T Multiply by the cache strategy matrix X(t) respectively to obtain the total cache resource occupancy of each satellite, which is used for the cache resources in formula (21). The Lagrangian function for the service caching problem can be derived as follows: Where μ and λ are Lagrange multiplier vectors, the P-master function problem can be rewritten based on the Lagrange function as follows: Where d0 is the P-master objective value variable, representing the lower bound estimate of the optimal function, and Λ is the constraint set of λ in the infeasibility constraints, ensuring the mathematical validity of the infeasibility constraints: 1) Solution to the P-primal problem: Since the P-primal problem is a convex optimization problem, the problem in the P-master problem can be rewritten as: Where X(t) (τ) μ represents the optimal solution obtained by solving formula (18) in the τth iteration. (τ) and λ (τ) Let represent the optimal Lagrange multiplier vector obtained by solving formula (18) in the τ-th iteration, τ1∈{τ|If formula (18) (τ) The feasible} is the set index of feasible iteration rounds, τ2∈{τ|If formula (18) (τ) The set index of infeasible iterations is}. The P-primal problem can be solved using convex optimization. In each iteration, the solution to the P-primal problem is added as a new constraint to the P-master problem, from which the set... As can be seen from the definition, when c is fixed, P-primal is not always feasible; if P-primal is feasible, then the optimal solution and the bounded optimal solution generation constraints can be obtained: d0≥L(X(t) (τ) ,C(t),μ (τ) ) (28) Otherwise, the constraints of the P-primal problem cannot be satisfied. However, an approximate optimal solution that minimizes the impact on server computation and caching capacity constraints can be obtained by solving the following problem: Using the optimal solution to the above problem (X(t)) (τ) C(t), λ (τ) Generate infeasible constraints: 2) Solution to the P-master Problem: P-master is a 0 / 1 programming problem. A satellite clustering algorithm based on Gibbs sampling is used to obtain an approximate optimal solution to P-master. The objective value F of P-master is defined as: Where β > 0, The parameters are used to weight the contribution of feasible constraints in each iteration. represents the weighting parameters in the τ1th feasible iteration. All idle satellites are considered as vertices in the graph. It is a picture The clustering state of all vertices and satellite m in the cluster is c. u，m The clustering state of satellites other than satellite m is Based on the optimization objective value F of P-master, the state transition probability distribution of satellite m can be obtained as follows: in For Gibbs sampling parameters, when Furthermore, as the sampling period approaches infinity, the system will converge to the optimal value. In the probability distribution, the calculation of the optimization objective value F depends on the value of d0. When the clustering variable c of the satellites... u，m Given that the problem of minimizing F becomes the problem of minimizing d0 in an unconstrained convex optimization, we can obtain the optimal optimization objective F of satellite m in the current cluster state. Furthermore, we can perform sampling based on the above probability distribution to complete the state transition of satellite m. After updating the cluster state of satellite m, the cluster state of the next satellite is updated by randomly selecting the next satellite. The probability of the state update is: Where ρ > 0 is a parameter for adjusting the state update probability. When the new target value is much larger than the current target value, the difference between the two target values ​​can be limited to ρ to ensure a larger state update probability, using F and Let represent the current state and the new state, respectively. During the satellite clustering state transition, the probability of accepting the new state is η, while the probability of maintaining the current state is 1-η. The satellite clustering algorithm based on Gibbs sampling to solve the P-master is shown in Algorithm 1: GBD-based algorithms alternately solve the two subproblems, as shown in Algorithm 2: Furthermore, when multiple users simultaneously generate task unloading requests, optimizing the satellite set and service caching strategy becomes more complex, requiring the algorithm to be extended to multi-user scenarios. In multi-user scenarios, the satellite set is divided into the following cases: (a): All users share the same set of satellites; (b): The satellite sets of each user are completely different; (c): Different users have the same satellite collection. In case (a), the problem is similar to the single-target user optimization problem. In case (b), the problem is decomposed into multiple independent single-target user optimization problems. In case (c), the satellites in the overlapping area can be regarded as a set of satellites serving each independent target user, and at the same time, task offloading requests are generated. It is assumed that the offloading request of the same type of service can be regarded as a request from a single user, and the corresponding tasks can also be merged into a single task. Assuming the set of users sharing the same satellite cluster is B0, the offload request is represented as: Let represent the data size, workload, and service type vectors, respectively. Assume that each user in B0 requests only one service at each time slot, and that the service types requested by different users in different time slots are possible. The satellite clustering strategy matrix and service caching strategy matrix for each user in B0 at time t can be represented as follows: and Based on Lyapunov optimization, the instantaneous satellite clustering and service caching problem in a multi-user scenario can be denoted as the P2-Lyapunov problem. Fixed variables The question is for It is still non-convex; we can transform it into a convex problem by adding constraints: Where Θ is a hyperparameter used to balance the optimality and feasibility of the problem. When computational resources are sufficient, all services requested by the user set can be cached on the satellite cluster. Therefore, the minimum lower bound of the average offload latency can be obtained: If the satellite ensemble lacks sufficient resources, all tasks will be offloaded to the cloud for processing. In this case, the upper bound of the maximum average latency is: To balance optimality and feasibility, the value of Θ needs to be determined. Therefore, a binary classification-based GBD joint optimization algorithm is proposed to obtain the optimal value of Θ, along with corresponding satellite clustering and service caching strategies.

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