A service migration and task re-routing balance and resource management online optimization method for mobile edge computing

Abstract

The application discloses a service migration and task re-routing balance and resource management online optimization method for mobile edge computing, realizes the balance between service migration and task re-routing when edge server access switching of a mobile device occurs, and provides seamless and economically efficient computing services. Considering the dynamic nature of the network and the possible asynchrony of management decisions, including random task generation and time-varying channel conditions, the application constructs a double-time-scale online optimization problem to jointly determine large-time-scale decisions and small-time-scale decisions. Then, based on an improved Lyapunov algorithm, combined with an iterative algorithm of random rounding and Lagrange dual technology, the long-term average service delay of the system reaches asymptotic optimality.

Description

Technical Field

[0001] This invention belongs to the field of communication technology of mobile Internet of Things, and specifically relates to an online optimization method for service migration, task rerouting balancing, and resource management for mobile edge computing. Background Technology

[0002] Driven by the rapid development of 6G, Web 3.0, and their enabling smart mobile devices, the mobile internet has grown rapidly. With the advancement of technologies such as autonomous vehicles, smart glasses, and haptic clothing, various computationally intensive and latency-sensitive high-tech applications have emerged, such as V2X communication, immersive extended reality (XR), and human digital twins (HDT). However, mobile devices themselves struggle to meet the stringent service requirements of cloud computing systems for these resource-constrained applications due to their infrastructure limitations. Mobile edge computing (also known as multi-access edge computing) provides high processing power with relatively low latency by offloading heavy workloads (i.e., computational tasks) from mobile devices to edge servers deployed on wireless access points.

[0003] Mobile edge computing has garnered significant research attention due to its immense potential in improving computing and communication efficiency, including access selection and handover, service migration and application placement, and joint allocation of computing and communication resources. However, several key issues remain unresolved, particularly how to provide seamless and low-cost edge computing services to heterogeneous mobile devices. Intuitively, a wireless access handover might be triggered when a mobile device leaves the wireless coverage area of ​​its current edge server. To continue providing edge computing services to this device, a common approach is to migrate the required application instances from the previously accessed edge server to a new one. However, as noted by European telecommunications standards, service migration itself can lead to potential service interruptions. Therefore, in addition to service migration, task rerouting should be prioritized to reroute the mobile device's computing tasks back to its previously hosted server. While task rerouting avoids the overhead of large-scale application migration, it inevitably introduces latency and energy consumption. Therefore, balancing service migration and task rerouting is crucial and highly challenging in the optimized management of mobile edge computing systems.

[0004] 1) To improve the Quality of Service (QoS) of mobile edge computing systems, it is necessary to jointly optimize access selection, service migration, task rerouting, and computing resource allocation across all devices to maximize overall system performance. However, these decisions are highly dependent on the cache state of each edge server (i.e., application instances in the cache), are typically non-linear, and the decisions regarding access selection, service migration, and task rerouting are discrete, while the allocation of computing and communication resources may be continuous. This makes the optimization problem a mixed-integer non-linear programming problem, i.e., NP-hard.

[0005] 2) In mobile edge computing systems, due to time-varying channel conditions, device mobility, and the randomness of task generation, all optimization decisions (access selection, service migration, task rerouting, and resource allocation) need to be dynamically adjusted. This necessitates online optimization and long-term performance guarantees; however, this requires statistical analysis of future network dynamics, which is difficult to obtain.

[0006] 3) For each mobile device, access selection, service migration, and task rerouting may not change in real time. Frequent access switching can cause severe Doppler shift, and frequent service migrations or task rerouting changes can lead to considerable configuration overhead. In contrast, to better handle time-varying task generation and channel states, computational and communication resource allocation requires a higher update frequency. This suggests that decision variables in online optimization problems should be optimized asynchronously across different time scales, rather than on a single time scale as in traditional research. Summary of the Invention

[0007] Purpose of the invention: This invention provides an online optimization method for service migration, task rerouting balancing, and resource management in mobile edge computing. It aims to minimize the long-term average service latency of all mobile devices while ensuring system stability, limited energy consumption, and sufficient caching capacity, thereby providing seamless and cost-effective edge computing services for mobile devices.

[0008] An online optimization method for service migration, task rerouting balancing, and resource management in mobile edge computing includes the following steps:

[0009] (1) Construct a mobile edge computing system consisting of M distributed edge servers and I heterogeneous mobile devices. Each mobile device in the system has a computationally intensive task flow to be executed, and the random movement of the mobile device will trigger its dynamic access connection switching.

[0010] (2) The mobile device selects local computing or computing offload based on its available resource capacity, including the calculation of system overhead, which includes local computing energy consumption, transmission energy consumption from the mobile device to the edge server, and computing energy consumption of the computing task offloaded to the edge server.

[0011] (3) The edge server allocates transmission bandwidth resources and CPU computing resources to potential access devices, including the calculation of service migration energy consumption and computing task rerouting energy consumption. Based on this, the mobile device adaptively selects the service mode by combining dynamic channel conditions, random task generation and its own cache capacity. The service mode includes service migration or task rerouting.

[0012] (4) Construct a dual time-scale mobility management model to balance the overhead of service migration and task rerouting. Here, t∈[0,T] is the large time-scale indicator, each large time frame contains K hourly frames, and τ∈[tK,TK+K-1] is the small time-scale indicator. Access selection, service migration and task rerouting are operated under the large time-scale, while task offloading and computing resource allocation are operated under the small time-scale.

[0013] (5) With the goal of minimizing long-term average service latency, determine the long-term optimization problem and constraints of edge computing, including the upper limit constraint of bandwidth allocation, the long-term stability constraint of local task queue, the cache capacity constraint of server m, the long-term stability constraint of energy consumption of mobile edge computing system, the edge server computing resource allocation constraint, the selection constraints of service migration and task rerouting and the consideration of decision variables.

[0014] (6) Equivalence problem reconstruction: Based on the improved Lyapunov online algorithm, the long-term problem is decomposed into a series of deterministic problems, including uniformly distributing the migration delay and energy consumption of each large time slot t to all small time slots τ within t, transforming the problem according to the total service delay and total energy consumption in each small time slot τ, and defining an energy loss queue Q. i Let (τ) describe the deviation between the energy consumption of device i's computational task in hourly slot τ and the long-term energy budget, combined with the local task buffer queue, where the quadratic Lyapunov function is defined as follows:

[0015]

[0016] Where, Θ(τ)=[Q i (τ),S i [τ] represents the set of the energy-deficient queue and the local task buffer queue, and the conditional Lyapunov drift function is derived:

[0017]

[0018] (7) Decouple the decision into two sub-problems with different time scales. Based on the instantaneous values ​​of the energy loss queue and local task backlog queue of all mobile devices, transform the optimization problem of joint access selection, service migration and task rerouting for each large time slot t into an overall planning problem. Based on the optimal decisions of access selection, service migration and task rerouting for each large time slot t, optimize the task offloading decision, transmission and computing resource allocation decision for each small time slot τ.

[0019] Furthermore, in the mobile edge computing system, each mobile device has one computationally intensive task flow to be executed.

[0020] The system overhead calculation process in step (2) includes the following steps:

[0021] (2-1) Define f i md The CPU computing speed of mobile device i is represented, and the local computing latency is represented as follows:

[0022]

[0023] Among them, v i β is the task size for mobile device i. i This represents the number of CPU cycles required to complete a 1-bit computation task.

[0024] Based on the energy model in CMOS circuits, the local computing power consumption is determined as follows:

[0025]

[0026] in, The effective switching capacitor for mobile device i is determined by the chip architecture of the mobile device;

[0027] (2-2) Define SNR i,m (τ) represents the instantaneous signal-to-noise ratio (SNR) from mobile device i to edge server m in hourly slot τ, and its mathematical expression is:

[0028]

[0029] Where, p i Let W be the transmission power of mobile device i, θ be the path loss exponent, and W be the transmission power of mobile device i. m For communication bandwidth, L i,m (τ) represents the distance between mobile device i and edge server m, N0 is the spectral density of channel noise power, and h i,m (τ) represents the fading amplitude;

[0030] According to the Shannon-Hartley formula, the transmission rate between mobile device i and edge server m is obtained, and its mathematical expression is as follows:

[0031]

[0032] in, α represents the decision variable for device i to choose to access server m. i (τ) represents the decision variable for transmission bandwidth allocation;

[0033] (2-3) Based on the transmission rate between mobile device i and edge server m, obtain the transmission delay for task unloading:

[0034]

[0035] Its corresponding transmission energy consumption is:

[0036]

[0037] (2-4) Definition Given the computing speed of edge server m, the computation latency of mobile device i performing its computing task on edge server m is:

[0038]

[0039] Where, ρ i (τ) represents the CPU resource allocation decision, and the corresponding computing energy consumption is:

[0040]

[0041] in, The effective switching capacitor for edge server m is determined by the chip architecture of the edge server.

[0042] Furthermore, step (3) includes the following calculation process:

[0043] (3-1) Define state variables The mathematical expression describing the application instance required by device i to be installed on server m' at the start of time t is:

[0044]

[0045] in, Indicates service migration decision, Indicates task rerouting decision;

[0046] (3-2) When the service migration mode is adopted, the service migration latency occurs only once in a large time scale time slot, and its expression is:

[0047]

[0048] When the task rerouting mode is used, the routing delay of the computation task is generated in each small time scale time slot, and its expression is:

[0049]

[0050] Taking all mode choices into account, the total service latency for executing the computational task of mobile device i in each large time scale can be expressed as:

[0051]

[0052] Among them, z i (τ) represents the unloading decision;

[0053] (3-3) When the service migration mode is adopted, the expression for the energy consumption of service migration is:

[0054]

[0055] Where p es This represents the transmission power of the edge server, and its value can be predetermined.

[0056] When using the task rerouting mode, the expression for calculating the routing energy consumption of a task is:

[0057]

[0058] Taking all mode choices into account, the total energy consumption for performing the computational task on mobile device i in each large time scale can be expressed as:

[0059]

[0060] (3-4) For any edge server m, within a large time slot t, the cache space occupied by application instances migrated from other edge servers is represented as:

[0061]

[0062] For any edge server m, if an application instance has been installed and selected to be retained before the large time slot t to handle rerouting tasks, the cache space it occupies is represented as follows:

[0063]

[0064] Furthermore, the long-term optimization problem and constraints in step (5) are specifically expressed as follows:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] Where C1 represents the bandwidth allocation upper limit constraint; C2 represents the long-term stability constraint of the local task queue, where S i (τ) represents the local task queue backlog; C3 represents the cache capacity constraint of server m, where C1 represents the maximum cache capacity limit for server m; C2 represents the long-term stability constraint on system energy consumption, where C3 represents the maximum cache capacity limit for server m. This represents the total energy consumption of the system. C5 represents the long-term stable upper limit of system energy consumption; C5 represents the computing resource allocation constraint, where C6 represents the cache location of the application instance on device i; C7 represents the selection constraints for service migration and task rerouting; C8 represents that service migration, task rerouting, and offloading are binary decision variables.

[0074] In the method, the equivalent problem reconstruction in step (6) includes the following calculation process:

[0075] This step evenly distributes the migration delay and energy consumption of each large time slot t to all small time slots τ within t. The total service delay and total energy consumption in each small time slot τ are then expressed as:

[0076]

[0077]

[0078] in, and These represent the service migration latency and migration energy consumption for each hourly slot τ, respectively.

[0079] Therefore, the original optimization problem is transformed into:

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] Define the energy loss queue Q i Let (τ) describe the deviation between the energy consumption of device i's computational task during hourly slot τ and the long-term energy budget, and let Q be the value of Q. i The expression for (τ) is as follows:

[0089]

[0090] Combined with the local task buffer queue, define a quadratic Lyapunov function:

[0091]

[0092] Where, Θ(τ)=[Q i (τ),S i [τ] is the set of the energy-deficient queue and the local task buffer queue;

[0093] Next, the conditional Lyapunov drift function is derived:

[0094]

[0095] Based on this, construct the Lyapunov drift-penalty function:

[0096]

[0097] Where V∈(0,+∞) are Lyapunov control parameters;

[0098] Meanwhile, the Lyapunov drift-penalty function satisfies the following theorem:

[0099]

[0100] in, γ is the time slot length of the smaller time slot;

[0101] The original optimization problem is transformed into finding the minimum of the right-hand side of the Lyapunov drift-penalty function, while keeping the decision variables and constraints unchanged across the two time scales.

[0102] In the method, in step (7), the optimization problem of joint transmission and computing resource allocation is transformed into the following sub-problems:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] in,

[0109] This problem is a linear programming problem. The optimal solution for the allocation of transmission and computational resources is obtained by using the Lagrange duality method.

[0110] By comparing the optimal strategy with the service latency of local computation, the task offloading decision z for device i is determined. i The optimal solution for (τ), i.e., if the local computation service latency is small, then z i (τ) = 0, no unloading is performed; otherwise, z i (τ) = 1 to calculate unloading.

[0111] Furthermore, step (7) further includes the following process for decoupling the decision into two sub-problems with different time scales:

[0112] Define a binary variable y i (t) serves as a selection indicator for both, and its expression is:

[0113]

[0114] Service migration decision and task rerouting decision Meet the conditions

[0115] Given the instantaneous values ​​of the energy deficit queue and local task backlog queue for all current mobile devices, the joint access selection, service migration, and task rerouting optimization problem in each large time slot t is transformed into the following sub-problems:

[0116]

[0117]

[0118]

[0119] (C3)y i (t)∈{0,1},

[0120] This problem is an integer programming problem. Random rounding is used to find the optimal solutions for access selection, service migration, and task rerouting. Based on the optimal decisions for access selection, service migration, and task rerouting in each large time slot t, the task offloading decision, transmission and computing resource allocation decision are optimized in each small time slot τ.

[0121] Beneficial effects: Compared with the prior art, the substantial progress and significant effects of the present invention are as follows:

[0122] 1) In order to ensure the seamless continuity and cost-effectiveness of edge computing services in dynamic environments, this invention constructs an online optimization problem with two time scales. With the goal of minimizing the long-term average service latency of the system, it adaptively selects service migration or task rerouting for each mobile device and jointly manages its access selection, computing and communication resource allocation.

[0123] 2) This invention considers the randomness of task generation and the changes in channel conditions caused by random device movement. To address this, a low-complexity online algorithm based on an improved Lyapunov optimization method is proposed through equivalent problem reconstruction. This algorithm decomposes the long-term problem into a series of deterministic problems without requiring any statistical information. Then, the decision-making process is further decoupled into two different time scales, and an iterative algorithm is developed to obtain a near-optimal solution. Attached Figure Description

[0124] Figure 1 This is a schematic diagram of the structure of a mobile edge computing system supporting multiple heterogeneous devices constructed by the method described in this invention;

[0125] Figure 2 A diagram of a dual-timescale network optimization decision model for mobile edge computing;

[0126] Figure 3 A flowchart of the proposed dual-timescale online optimization algorithm OATTL;

[0127] Figure 4 A performance comparison of service latency as the number of edge servers changes;

[0128] Figure 5 Comparison of service latency performance under different timeslot length K settings. Detailed Implementation

[0129] To illustrate the technical solutions disclosed in this invention in detail, further explanation is provided below with reference to specific embodiments and accompanying drawings.

[0130] To ensure seamless and cost-effective computing services for heterogeneous devices in a mobile edge computing system under dynamic network changes, this invention proposes an online optimization method for service migration and task rerouting balancing and resource management in mobile edge computing. When a mobile device experiences an access switch, it achieves a balance between service migration and task rerouting, providing seamless and cost-effective edge computing services for the mobile device. Considering the dynamic nature of the network (including random task generation and time-varying channel conditions) and the potential asynchronicity of different management decisions, this invention constructs a dual-timescale online optimization problem to jointly determine (1) which edge server each mobile device should access; (2) whether each mobile device should choose service migration or task rerouting; and (3) how to allocate computing and communication resources among mobile devices with task offloading requests.

[0131] Unlike existing technologies and edge service computing methods, the method described in this invention proposes a novel online management framework for mobile edge computing systems to balance the overhead of service migration and task rerouting, ensuring service continuity. To adapt to dynamically changing mobile environments and asynchronous decision management, this invention designs an improved Lyapunov algorithm to solve the proposed dual-timescale joint resource optimization problem from a long-term dynamic perspective. It combines an iterative algorithm using random rounding and Lagrange duality techniques to achieve asymptotic optimization of the system's long-term average service latency.

[0132] Based on the aforementioned technical solutions and existing technologies well-known to those skilled in the art, further, in combination with... Figure 1 and Figure 2 The implementation process of the method described in this invention is explained in detail below.

[0133] Step 1: Build a mobile edge computing network system with various heterogeneous mobile devices and multiple edge servers, and construct the function model of the system.

[0134] like Figure 1 As shown, the heterogeneous devices have a base number of I and are numbered i. Each mobile device has a compute-intensive task flow to execute. Each device can access different servers for compute offloading, and due to the random movement of devices, dynamic access connection switching may be triggered. The edge servers have a base number of M and are numbered m. Each edge server is deployed on a distributed base station and can provide communication and computing services to a group of potential access devices, provided that: i) the application instances installed on this server are suitable for these access devices; ii) this server can install well-matched service application instances to support these access devices through service migration; iii) this server can reroute the computing tasks of these access devices to servers with the required application instances installed.

[0135] Frequent access switching, service migration, and task rerouting incur significant overhead and cannot be performed in real time. In contrast, inherent task offloading and corresponding communication and computing resource allocation require immediate and frequent responses to adapt to time-varying task numbers and channel conditions. Therefore, this invention considers constructing a dual-timescale mobility management model within an online optimization framework, such as... Figure 2 As shown, t∈[0,T] represents the large time scale, and each large time frame contains K hourly frames, i.e., τ∈[tK,TK+K-1] represents the small time scale. Access selection, service migration, and task rerouting operate on the large time scale, while task offloading and computational resource allocation operate on the small time scale.

[0136] With the goal of minimizing long-term average service latency, the long-term optimization problem and constraints for edge computing are defined as follows:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145] Where C1 represents the bandwidth allocation upper limit constraint; C2 represents the long-term stability constraint of the local task queue, where S i (τ) represents the local task queue backlog; C3 represents the cache capacity constraint of server m, where C1 represents the maximum cache capacity limit for server m; C2 represents the long-term stability constraint on system energy consumption, where C3 represents the maximum cache capacity limit for server m. This represents the total energy consumption of the system. C5 represents the long-term stable upper limit of system energy consumption; C5 represents the computing resource allocation constraint, where C6 represents the cache location of the application instance on device i; C7 represents the selection constraints for service migration and task rerouting; C8 represents that service migration, task rerouting, and offloading are binary decision variables.

[0146] Step 2: Through equivalent problem reconstruction, a low-complexity online algorithm based on the improved Lyapunov optimization method is proposed, which decomposes the long-term problem into a series of deterministic problems.

[0147] For ease of analysis, this invention distributes the migration delay and energy consumption of each large time slot t evenly across all smaller time slots τ within t. The total service delay and total energy consumption in each smaller time slot τ are then expressed as:

[0148]

[0149]

[0150] in, and Let τ represent the service migration latency and migration energy consumption for each hourly slot. Therefore, the original optimization problem is transformed into:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] Define the energy loss queue Q i Let (τ) describe the deviation between the energy consumption of device i's computational task during hourly slot τ and the long-term energy budget, and let Q be the value of Q. i The expression for (τ) is as follows:

[0160]

[0161] Combined with the local task buffer queue, define a quadratic Lyapunov function:

[0162]

[0163] Where, Θ(τ)=[Q i (τ),S i [τ] represents the set of the energy-deficient queue and the local task buffer queue. Next, the conditional Lyapunov drift function is derived: Unlike traditional Lyapunov drift functions, this invention considers constructing a K-slot conditional Lyapunov drift function based on the stable queue backlog of all smaller slots within each larger slot. Based on this, a Lyapunov drift-penalty function is constructed:

[0164]

[0165] Where V∈(0,+∞) are Lyapunov control parameters. Meanwhile, the Lyapunov drift-penalty function satisfies the following theorem:

[0166]

[0167] in, γ is the time slot length of the smaller time slot.

[0168] In summary, the original optimization problem can be transformed into finding the minimum of the right-hand side of the Lyapunov drift-penalty function, while keeping the decision variables and constraints on both time scales unchanged.

[0169] Step 3: Decouple the decision into two sub-problems with different time scales, and develop an iterative algorithm to obtain an asymptotically optimal solution. The flowchart is as follows: Figure 3 As shown.

[0170] Due to service migration decision and task rerouting decision Conditions must be met Therefore, define a binary variable y. i (t) serves as a selection indicator for both, and its expression is:

[0171]

[0172] Given the instantaneous values ​​of the energy deficit queue and local task backlog queue for all current mobile devices, the joint access selection, service migration, and task rerouting optimization problem in each large time slot t is transformed into the following sub-problems:

[0173]

[0174]

[0175]

[0176] (C3)y i (t)∈{0,1},

[0177] This is an integer programming problem, and the optimal solutions for access selection, service migration, and task rerouting can be obtained using random rounding techniques. Based on the optimal decisions for access selection, service migration, and task rerouting obtained for each large time slot t, the task offloading decision, transmission, and computing resource allocation decisions are optimized for each small time slot τ.

[0178] First, the optimization problem of jointly allocating transmission and computational resources is transformed into the following sub-problems:

[0179]

[0180]

[0181]

[0182]

[0183]

[0184] in, This problem is a linear programming problem, and the optimal solution for allocating transmission and computational resources can be obtained by using the Lagrange duality method.

[0185] Finally, by comparing the optimal strategy with the service latency of local computation, the task offloading decision z for device i is determined. i The optimal solution for (τ), i.e., if the local computation service latency is small, then z i (τ) = 0, no unloading is performed; otherwise, z i (τ) = 1 to calculate unloading.

[0186] like Figure 4 As shown, the service latency of all algorithms decreases with the increase in the number of edge servers. This is because deploying more servers significantly improves the computing and caching capabilities at the edge, thereby reducing the workload of individual servers and thus lowering the computing latency per server. Furthermore, the OATTL proposed in this invention outperforms the two benchmark schemes. This is because the single-timescale scheme JMH cannot capture time-varying network dynamics and cannot adjust computing resource allocation strategies in a timely manner. As edge computing resources increase, mobile devices tend to offload tasks to the edge for execution. While O2TL can adjust resource allocation in a timely manner, it does not consider the adjustment of transmission resources, causing transmission efficiency to decrease significantly with the increase in tasks. In contrast, OATTL can accurately capture network dynamics, adjust bandwidth and CPU resource allocation, and fully utilize the computing power at the edge.

[0187] For example Figure 5 As shown, Figure 5Service latency performance under different timeslot lengths K is presented. As the parameter K increases, the service latency increases for all algorithms. This is because the update frequency of access selection and service migration decreases with increasing timeslot length K, affecting the efficiency of task offloading and resource allocation in controlling overall system service latency and energy consumption. Furthermore, the JMH method, due to its single decision-making timescale, exhibits poor control over service latency and cannot accurately capture rapid dynamic changes in task quantity and channel state. In contrast, both the O2TL method and the proposed OATTL method consider decision-making at two timescales to adapt to dynamic network changes, and the proposed OATTL demonstrates better control over service latency and energy consumption. This is because O2TL supports dynamic allocation of communication resources. Moreover, the proposed OATTL jointly optimizes task rerouting decisions, effectively offsetting the significant latency and energy costs associated with service migration.

[0188] Combination Figure 4 and Figure 5 When communication bandwidth resources are the same, increasing the number of edge servers reduces the total service latency by 20% compared to the two baseline schemes. This demonstrates that the proposed algorithm can effectively control service latency even with increased edge server density, showcasing good adaptability to complex environments. When K=20, the proposed OATTL method reduces the total service latency by 25% compared to the two baseline schemes; when K=50, the total service latency is reduced by 55%, demonstrating the effectiveness and advancement of the proposed algorithm in asynchronous environments.

Claims

1. An online optimization method for service migration, task rerouting balancing, and resource management in mobile edge computing, characterized in that: Includes the following steps: (1) Constructing from Distributed edge servers and A mobile edge computing system composed of heterogeneous mobile devices, in which each mobile device has a flow of computationally intensive tasks to be executed, and random movement of the mobile device will trigger its dynamic access connection switching. (2) The mobile device selects local computing or computing offloading based on its available resource capacity, including the calculation of system overhead, which includes local computing energy consumption, transmission energy consumption from the mobile device to the edge server, and computing energy consumption of computing tasks offloading to the edge server. (3) The edge server allocates transmission bandwidth resources and CPU computing resources to potential access devices, including the calculation of service migration energy consumption and computing task rerouting energy consumption. Based on this, the mobile device adaptively selects the service mode by combining dynamic channel conditions, random task generation and its own cache capacity. The service mode includes service migration or task rerouting. (4) Construct a dual-timescale mobility management model to balance the overhead of service migration and task rerouting, wherein, As a large-scale indicator, each large time frame contains Hourly frames, For small time-scale metrics, access selection, service migration, and task rerouting are operated on a large time-scale, while task unloading and computing resource allocation are operated on a small time-scale. (5) With the goal of minimizing long-term average service latency, determine the long-term optimization problem and constraints of edge computing, including bandwidth allocation upper limit constraints, long-term stability constraints of local task queues, and server... Considerations include cache capacity constraints, long-term stability constraints of energy consumption in mobile edge computing systems, constraints on edge server computing resource allocation, selection constraints for service migration and task rerouting, and their decision variables. (6) Equivalence problem reconstruction: Based on the improved Lyapunov online algorithm, the long-running problem is decomposed into a series of deterministic problems, including converting each large time slot into a series of deterministic problems. The migration delay and energy consumption are evenly distributed to All hour slots within In the middle, according to each hourly gap The problem is transformed using total service latency and total energy consumption, and an energy loss queue is defined. To describe the device The computational task in the hourly slot The discrepancy between energy consumption and long-term energy budget is considered in conjunction with the local task buffer queue, where a quadratic Lyapunov function is defined as follows: in, For energy-loss queue With local task buffer queue The set of values, and derive the conditional Lyapunov drift function: (7) Decouple the decision into two sub-problems with different time scales. Based on the instantaneous values ​​of the energy deficit queue and the local task backlog queue of all mobile devices, for each large time slot The optimization problems of joint access selection, service migration, and task rerouting are transformed into a holistic planning problem, based on the obtained large time slots. Optimal decisions regarding access selection, service migration, and task rerouting are made in each hourly slot. Optimize task unloading decisions, transmission and computing resource allocation decisions.

2. The online optimization method for service migration, task rerouting balancing, and resource management for mobile edge computing according to claim 1, characterized in that: In the mobile edge computing system, each mobile device has one computationally intensive task flow to be executed.

3. The online optimization method for service migration, task rerouting balancing, and resource management for mobile edge computing according to claim 1, characterized in that: The system overhead calculation process in step (2) includes the following steps: (2-1) Definition Indicates mobile device The CPU computing speed and local computing latency are expressed as follows: ， in, For mobile devices Task size, This represents the number of CPU cycles required to complete a 1-bit computation task. Based on the energy model in CMOS circuits, the local computing power consumption is determined as follows: in, For mobile devices The effective switching capacitor is determined by the chip architecture of the mobile device; (2-2) Definition Indicates a time slot ,mobile device To the edge server The instantaneous received signal-to-noise ratio (SNR) is expressed mathematically as follows: ， in, For mobile devices Transmission power, This is the path loss index. For communication bandwidth, For mobile devices With edge servers The distance between them The spectral density of the channel noise power. The amplitude of the decay; According to the Shannon-Hartley formula, obtain the mobile device With edge servers The transmission rate between them can be expressed mathematically as follows: in, Indicates device Select access server Decision variables, Indicates the decision variables for transmission bandwidth allocation; (2-3) Based on mobile devices With edge servers The transmission rate between them, and the transmission latency for task unloading: ， Its corresponding transmission energy consumption is: ； (2-4) Definition For edge servers Computing speed, mobile devices The computing tasks are performed on the edge server. The computation delay for performing the calculations is: ， in, This represents the CPU resource allocation decision, and the corresponding computing energy consumption is: ， in, For edge servers The effective switching capacitor is determined by the chip architecture of the edge server.

4. The online optimization method for service migration, task rerouting balancing, and resource management for mobile edge computing according to claim 3, characterized in that: Step (3) includes the following calculation process: (3-1) Define state variables To describe the device Required application instances in time Initially installed on the server The mathematical expression for the above is: ， in, Indicates service migration decision, Indicates task rerouting decision; (3-2) When the service migration mode is adopted, the service migration latency occurs only once in a large time scale time slot, and its expression is: ； When the task rerouting mode is used, the routing delay of the computation task is generated in each small time scale time slot, and its expression is: ； Taking all mode options into account, the mobile device is executed on each large timescale. The total service latency of the computation task can be expressed as: in, Indicates the unloading decision; (3-3) When the service migration mode is adopted, the expression for the energy consumption of service migration is: ， in This represents the transmission power of the edge server, and its value can be predetermined. When using the task rerouting mode, the expression for calculating the routing energy consumption of a task is: ； Taking all mode options into account, the mobile device is executed on each large timescale. The total energy consumption of the computational task is expressed as: (3-4) For any edge server In large time slots Within this context, the cache space occupied by application instances migrated from other edge servers is represented as follows: ； For any edge server In large time slots The previously installed application instance, selected to be retained, is used to handle rerouting tasks. Its cache space usage is as follows: 。 5. The online optimization method for service migration, task rerouting balancing, and resource management for mobile edge computing according to claim 4, characterized in that: The long-term optimization problem and constraints in step (5) are specifically expressed as follows: st （C6） , Where C1 represents the bandwidth allocation upper limit constraint; C2 represents the long-term stability constraint of the local task queue, where C3 indicates a backlog in the local task queue; C3 indicates the server. The cache capacity constraint, among which Indicates server The maximum cache capacity is capped; C4 represents the long-term stability constraint on system energy consumption, where... This represents the total energy consumption of the system. C5 represents the long-term stable upper limit of system energy consumption; C5 represents the computing resource allocation constraint, where Indicates device The cache location of the application instance; C6 represents the selection constraints for service migration and task rerouting; C7 represents that service migration, task rerouting, and offloading are binary decision variables.

6. The online optimization method for service migration, task rerouting balancing, and resource management for mobile edge computing according to claim 5, characterized in that: The problem reconstruction in step (6) includes the following calculation process: This step will divide each large time slot The migration delay and energy consumption are evenly distributed to All hour slots within In the middle, each hourly gap The total service latency and total energy consumption are expressed as follows: Among them, and Each hourly slot represents a separate hourly slot. Service migration latency and migration energy consumption; Therefore, the original optimization problem is transformed into: S.t. （C2） （C3） （C4） （C5） （6） （7） Define an energy loss queue To describe the device The computational task in the hourly slot The discrepancy between energy consumption and long-term energy consumption budget, The expression is as follows: Combined with the local task buffer queue, define a quadratic Lyapunov function: ， in, It is a combination of the energy-deficient queue and the local task buffer queue; Next, the conditional Lyapunov drift function is derived: ， Based on this, construct the Lyapunov drift-penalty function: ， in, For Lyapunov control parameters; Meanwhile, the Lyapunov drift-penalty function satisfies the following theorem: in, , The time slot length is the smallest time slot. The original optimization problem is transformed into finding the minimum of the right-hand side of the Lyapunov drift-penalty function, while keeping the decision variables and constraints unchanged across the two time scales.

7. In the online optimization method for service migration and task rerouting balancing and resource management for mobile edge computing according to claim 6, in step (7), the optimization problem of joint transmission and computing resource allocation is transformed into the following sub-problems: St in, ； This problem is a linear programming problem. The optimal solution for the allocation of transmission and computational resources is obtained by using the Lagrange duality method. By comparing the optimal strategy with the service latency of local computing, the device is determined. Task unloading decision The optimal solution, i.e., if the local computation service latency is low, then =0 means no calculation or unloading is performed; otherwise... =1 to perform calculation and unloading.

8. The online optimization method for service migration and task rerouting balancing and resource management for mobile edge computing according to claim 6, in step (7), decoupling the decision into two sub-problems with different time scales further includes the following process: Define binary variables As a selection indicator between the two, its expression is: Service migration decision and task rerouting decision Meet the conditions + =1; Given the instantaneous values ​​of the energy deficit queue and local task backlog queue for all current mobile devices, then in each large time slot... The problems of joint access selection, service migration, and task rerouting optimization are transformed into the following sub-problems: St This is an integer programming problem. Random rounding is used to find the optimal solution for access selection, service migration, and task rerouting. Based on the obtained results for each large time slot... Optimal decisions regarding access selection, service migration, and task rerouting are made in each hourly slot. Optimize task unloading decisions, transmission and computing resource allocation decisions.

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