Vacation queue-based application service dynamic deployment and update method

Abstract

The application discloses a kind of based on vacation queuing application service dynamic deployment and updating method.The method considers an edge computing system consisting of mobile device, edge server, cloud server, the key performance indicators of system are analyzed by queuing theory related model, deduce closed form expression including but not limited to edge server average delay, the probability that application is deployed on edge server, busy period probability and other related indexes, efficient dynamic application deployment and updating strategy is proposed.Optimization problem is constructed with the goal of minimizing average system delay, where storage space and energy consumption are constrained.The method described in the application constructs an interior point convex approximation optimization method to determine user task offloading probability, application response threshold, application waiting duration, edge server computing resource allocation, so as to minimize the average delay of the entire system.

Description

Technical Field

[0001] This invention belongs to the field of network resource management, specifically relating to a method for dynamic deployment and updating of application services based on vacation queuing. Background Technology

[0002] With the rapid development of smart mobile devices (MDs) and sensors, artificial intelligence (AI) and the Internet of Things (IoT) technologies are widely used in various scenarios such as the industrial internet and autonomous driving. The demand for massive storage and computing power leads to increasingly heavy device workloads. However, MDs suffer from drawbacks such as low energy reserves, weak computing power, and small storage space. Cloud computing was once considered a solution to overcome the limitations of MDs, but due to the long distance between cloud servers and MDs, task offloading often results in significant transmission latency. Edge computing has been proposed as a new paradigm to alleviate the problem of high transmission latency in cloud computing. In an edge computing environment, servers are deployed at the network edge, retaining the energy efficiency advantages of cloud computing while providing low latency. Application deployment refers to storing applications and their related library files, datasets, etc., on servers. Based on this, MDs only need to upload tasks, without transferring the application to the server, greatly reducing the task latency and energy consumption caused by MD transmission. Therefore, optimizing the location of applications on edge servers (ESs) is crucial for maximizing server performance.

[0003] Ideally, all applications could be deployed on Elasticsearch (ES). However, in practice, limited storage space makes it nearly impossible to store all applications on a single ES instance simultaneously, prompting consideration of dynamic application deployment. The most straightforward Dynamic Application Placement (DAP) approach is for ES to respond to tasks immediately upon arrival. If an ES instance doesn't have the required application, it immediately requests it from other ES instances or service instances and deploys it. Once all work is completed, the system removes the corresponding application, freeing up space. However, this policy leads to increased energy consumption due to frequent placements. Therefore, designing a more flexible and efficient DAP strategy is essential for the following reasons:

[0004] 1) For edge servers (ES), optimization is typically aimed at latency and energy consumption, which presents a contradiction in designing DAP (Demand-Based Application) strategies. On the one hand, if the goal is to minimize latency, a strategy of responding immediately when a task arrives is often the first thing that comes to mind. However, this strategy leads to frequent application updates, increasing energy consumption. On the other hand, if the goal is to minimize energy consumption, reducing the frequency of application replacements must inevitably be considered due to the significant energy required for deploying applications. However, drastically reducing the frequency of application deployments may lead to increased latency. Furthermore, without an optimized cleanup strategy, the application may be requested again immediately after being cleaned up, which not only increases latency but also energy consumption. Therefore, when to explicitly request an application also requires in-depth and comprehensive consideration.

[0005] 2) Many studies consider determining application location in a static manner. This is unsuitable for real-time tasks with random arrival times, such as autonomous driving and augmented reality. This necessitates the design of DAP strategies with long-term performance guarantees.

[0006] However, designing and utilizing a novel, efficient edge computing DAP while taking all of the above facts into account is very challenging for several reasons:

[0007] a. Designing a suitable DAP strategy to resolve the trade-off between latency and energy consumption in edge computing is a challenge. In particular, such a strategy may need to handle the random arrival of computational tasks with heterogeneous requirements, thus necessitating the development of queuing models for performance evaluation. Furthermore, different DAPs may be required to address diverse needs, such as strict energy constraints or ultra-low latency.

[0008] b. Queue models integrated with advanced DAP strategies can be difficult to model and analyze because achieving their performance in a closed-form manner is challenging, if not impossible. For example, the Least Recently Used (LRU) method is simple to apply and most commonly used for cache updates or application switching domains. Contrary to its universality, applying the LRU method to represent latency in a closed-form manner on Elasticsearch is challenging, not to mention other more advanced DAP strategies. Furthermore, the performance of such queues is often non-convex with respect to control policies. Additionally, integer constraints in the system setup can further complicate the corresponding DAP optimization. Summary of the Invention

[0009] Purpose of the invention: In view of the single traffic type in the existing traffic scheduling schemes under time-sensitive networks, the present invention provides a method for dynamic deployment and updating of application services based on vacation queuing.

[0010] Technical solution: A method for dynamic deployment and update of application services based on vacation queuing. The method is designed for multi-user devices, edge servers, and cloud servers. It uses user task uninstallation probability, application response threshold, application waiting duration, and edge server computing resource allocation as optimization variables. Based on the vacation queue, it solves the closed-form expressions of the corresponding indicators, with the goal of minimizing the average task latency of the entire system.

[0011] The method includes the following steps:

[0012] (1) Build a multi-user device, edge server and cloud server to form an edge computing network, and establish an edge server task processing latency model based on the edge computing network;

[0013] (2) Design an optimizable dynamic application deployment and update strategy, where the optimizable variable is the application response threshold. and application wait duration At this point, the probability that the task will reach its waiting time is:

[0014] ,

[0015] In the formula, for The rate at which type of task reaches the edge server, and the average waiting time are:

[0016] ,

[0017] The average duration of the undeployed period is:

[0018] ,

[0019] The average duration of the entire cycle is calculated as follows:

[0020] ,

[0021] In the formula, This represents the average duration of the deployment period. This refers to the average duration of the task processing period derived from the deployment cycle. The average duration of the period that increases due to the duration of waiting;

[0022] (3) The complete decision variables of the edge computing system are determined as: user task offloading probability. Application response threshold Application wait duration and edge server computing resource allocation ;

[0023] (4) Calculate the average latency of the entire system, including the computation time of the task on the mobile device. And the computation time of the task on the edge server. ;

[0024] Therefore, the expression for the optimization objective is as follows:

[0025] ,

[0026] In the formula, Average latency for processing S-shaped tasks on mobile devices The rate at which an S-shaped task reaches the mobile device m. The time required for the edge server to request application s from the cloud server. The average latency of S-shaped tasks in the edge server;

[0027] (5) Constructing the optimization problem: Based on queuing-related theories, a function for minimizing the system latency of the edge computing network is constructed. The function expression for the optimization problem of the dynamic deployment and update strategy of application services based on vacation queuing is as follows:

[0028] ,

[0029] The constraints are:

[0030] ，

[0031] ,

[0032] ,

[0033] ,

[0034] ,

[0035] ,

[0036] ,

[0037] ,

[0038] In the formula, For edge server CPU power consumption, The energy consumed in deploying applications on edge servers. For local traffic density, Traffic density for the S-shaped queue of the edge server. The expected space distribution for applications on edge servers. The standard deviation of the space occupied by applications on the edge server. The probability that the space occupied by all applications exceeds the storage space of the edge server;

[0039] (6) Based on the relevant theory of vacation queues, calculate the closed-form expressions for the unresolved indicators in steps (2), (4), and (5); the average latency of S-shaped tasks in the edge server is:

[0040] ,

[0041] In the formula, The rate at which edge servers process S-shaped tasks. The time required for the edge server to request applications from cloud services;

[0042] The average duration of the task processing period from the deployment cycle is:

[0043] ,

[0044] The average duration of the period that increases due to waiting time is:

[0045] ,

[0046] Average duration of the entire cycle:

[0047] ,

[0048] application The probability of occupying edge server space is:

[0049] ,

[0050] The average duration of the busy period is:

[0051] ,

[0052] The average duration of the off-season is:

[0053] ,

[0054] The probability of a busy period is: The probability of an off-season is Substituting all the closed expressions above into (5), at this point all the optimization parameters in (5) have closed expressions;

[0055] (7) Obtain the user task unloading probability based on the interior point convex approximation method. Application response threshold Application wait duration and edge server computing resource allocation The optimal value of minimizes the average system delay.

[0056] Furthermore, in step (1), the system model considers M mobile devices (MDs), dedicated edge servers (ES) deployed at the base station, and cloud servers (CS). The s-shaped computing task has an average rate of The Poisson distribution reaches The computational cost of S-shaped tasks follows a mean of The exponential distribution. ES has limited storage space, while cloud servers can store applications without limit. Therefore, ES tends to request applications from CS, and the time taken is: ,in, For application Size, This refers to the transmission rate between ES and CS. When the task arrives at the mobile device, it... The probability of offloading the task to an edge server for processing is certain; otherwise, the mobile device handles the task itself. Based on this, the local processing arrival rate of the S-type task on mobile device m can be obtained as follows:

[0057] ,

[0058] Approximate the distribution of all arriving tasks as an exponential distribution, and obtain the average computational cost for mobile devices to process tasks as follows:

[0059] .

[0060] Furthermore, based on the classic queuing theory model M / M / 1, the average latency for processing tasks on mobile devices is obtained as follows:

[0061] ,

[0062] Tasks from MDs are categorized by task type and managed in different queues. Arriving tasks are processed using the First-Come, First-Served (FCFS) method. Therefore, the task arrival rate for the queue processing S-type tasks on the edge server is:

[0063] .

[0064] Furthermore, when an S-type task is unloaded to Elasticsearch, if there are no applications on Elasticsearch... ES will not immediately request the application from CS. Instead, it continues until accumulation Only S-shaped tasks request the application. (The application is requested from the CS.) Previously, Elasticsearch required storage to be allocated in advance. Space. Due to limited storage space, if allocated to applications... If there is insufficient remaining space, ES may delete some other applications or files. This occurs when the S-type task queue... When empty, the application It can also be in Accessed within a certain time, meaning ES will be Internal storage applications Instead of deleting it. If there are S-shaped tasks in If a task arrives, ES will continue processing the task until the queue becomes empty again. If no task is available, ES will continue processing the task. If it arrives within the area, then apply. This will be deleted. To better analyze this queue model, the entire processing is divided into four stages:

[0065] a) Deployment period This period is used for application deployment;

[0066] b) Waiting period This phase begins when the task queue becomes empty. If a task is completed, the phase ends immediately or is completed entirely. This phase ends when the application is deleted.

[0067] c) Undeployed period This refers to an application being deleted, and the tasks that arrived were not accumulated. Each period;

[0068] d) Treatment period This refers to the period during which the CPU processes a task. Depending on whether the CPU enters this period from a waiting period or a deployment period, this period can be divided into two categories: This represents the processing phase that begins after the deployment phase. This represents the processing period that begins after the waiting period.

[0069] Furthermore, the method comprehensively considers the following four strategic factors:

[0070] a) User task uninstallation probability It should be between 0 and 1, and can be either 0 or 1;

[0071] b) Apply response thresholds The response threshold should be greater than or equal to 1 and should be an integer.

[0072] c) Apply wait duration The application's waiting time should be greater than or equal to 0.

[0073] d) Edge server computing resource allocation The sum of computing power allocated to all queues should be less than or equal to the total computing power of the edge servers.

[0074] Furthermore, the average latency for mobile devices to process S-shaped tasks is calculated using the following method:

[0075] ,

[0076] The computation time of a task on the edge server is calculated using the following method:

[0077] ,

[0078] In the formula, The time required to transfer an S-type task from a mobile device m to an edge server is derived from the following formula: , The average size of an S-shaped task. Let m be the transmission rate from the mobile device to the edge server.

[0079] Furthermore, the power consumption for processing tasks in step (5) is composed of both busy and idle periods, with the CPU power during the idle period being 60% of that during the busy period. Local traffic density Calculated using the following method:

[0080] ,

[0081] Traffic density of edge server S-shaped queues Calculated using the following method:

[0082] ,

[0083] Expected space distribution of applications on edge servers Calculated using the following method:

[0084] ,

[0085] Standard deviation of the space distribution occupied by applications on edge servers Calculated using the following method:

[0086] .

[0087] Beneficial effects: Compared with the prior art, the substantial progress and significant effects of the present invention are as follows:

[0088] 1) Consider an edge computing system consisting of MDs, ES, and CS. Given constraints on energy consumption and storage space, a long-term optimization problem is constructed to minimize the average latency of edge computing. In this system, the novel and efficient DAP strategy proposed in this invention is employed, which features optimizable response thresholds and latency. Furthermore, offloading probability and computational resource allocation are also considered as optimization variables.

[0089] 2) This DAP strategy resolves the trade-off between latency and energy consumption in edge computing. In particular, it can handle the random arrival of computing tasks with heterogeneous demands. Using holiday queuing theory, the system performance is analyzed and derived using closed-form expressions, such as average edge server latency, busy period probability, and expected processing cycle length.

[0090] 3) To address the construction problem, this invention proposes a novel method called VQODAP, which integrates Black-Browser (BB) and Nova Scotia (NOVA) to handle integer and non-convex constraints, thereby obtaining the optimal solution for the non-convex objective. In the proposed solution, we use BB to decompose the primal problem and apply NOVA to achieve suboptimal results. Attached Figure Description

[0091] Figure 1 This is a system model diagram of the method described in this invention;

[0092] Figure 2 This is a transformation diagram of different periods in this invention;

[0093] Figure 3 The example shows a line graph of the average system delay under different task arrival rates.

[0094] Figure 4 Here are line graphs showing the average system delay under different energy constraints in the example;

[0095] Figure 5 This is a bar chart showing the ratio of average update frequency to task arrival rate across different available storage spaces in the instance. Detailed Implementation

[0096] To illustrate the technical solutions disclosed in this invention in detail, the invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0097] First, the key problem addressed by the method described in this invention is to propose a dynamic application deployment and update strategy in an edge computing system that optimizes application response thresholds and application waiting durations. This strategy, combined with user task unloading probability optimization and edge server computing resource allocation optimization, aims to minimize average system latency. The overall model diagram of this method is shown below. Figure 1 As shown.

[0098] The main idea of ​​this invention is to design an optimizable dynamic application deployment and update strategy, supplemented by other optimization variables to minimize system latency. The key is the designed dynamic application deployment and update strategy: when a task is unloaded to an edge server, if there is no application on the edge server, it will not immediately request the application from the cloud server, but will wait until n tasks accumulate before requesting the application. When the task queue is empty, the application can still be accessed for a period of time; that is, the edge server will store the application during this time instead of deleting it. If a task arrives during this time, the edge server will continue processing the task until the queue becomes empty again; if no task arrives during this time, the application will be deleted.

[0099] Specifically, a method for dynamically deploying and updating application services based on vacation queuing includes the following steps:

[0100] Step 1: Establish a system model

[0101] The system model considers M mobile devices (MDs), dedicated edge servers (ES) deployed at base stations, and cloud servers (CS). The S-shaped computing task operates at an average rate of... The Poisson distribution reaches The computational cost of S-shaped tasks follows a mean of The exponential distribution. ES has limited storage space, while cloud servers can store applications without limit. Therefore, ES tends to request applications from CS, and the time taken is: ,in, For application Size, This refers to the transmission rate between ES and CS. When the task arrives at the mobile device, it... The probability of offloading the task to an edge server for processing is certain; otherwise, the mobile device handles the task itself. Based on this, the local processing arrival rate of the S-type task on mobile device m can be obtained as follows:

[0102] ,

[0103] Approximate the distribution of all arriving tasks as an exponential distribution, and obtain the average computational cost for mobile devices to process tasks as follows:

[0104] ,

[0105] Further, based on the classic queuing theory model M / M / 1, the average latency for processing tasks on mobile devices is obtained as follows:

[0106] ,

[0107] Tasks from MDs are categorized by task type and managed in different queues. Arriving tasks are processed using the First-Come, First-Served (FCFS) method. Therefore, the task arrival rate for the queue processing S-type tasks on the edge server is:

[0108] .

[0109] Step 2: Design dynamic application deployment and update strategies

[0110] When an S-type task is unloaded to Elasticsearch, if there are no applications on Elasticsearch... ES will not immediately request the application from CS. Instead, it continues until accumulation Only S-shaped tasks request the application. (The application is requested from the CS.) Previously, Elasticsearch required storage to be allocated in advance. Space. Due to limited storage space, if allocated to applications... If there is insufficient remaining space, ES may delete some other applications or files. This occurs when the S-type task queue... When empty, the application It can also be in Accessed within a certain time, meaning ES will be Internal storage applications Instead of deleting it. If there are S-shaped tasks in If a task arrives, ES will continue processing the task until the queue becomes empty again. If no task is available, ES will continue processing the task. If it arrives within the area, then apply. This will be deleted. To better analyze this queue model, the entire processing is divided into four stages:

[0111] a) Deployment period This period is used for application deployment;

[0112] b) Waiting period This phase begins when the task queue becomes empty. If a task is completed, the phase ends immediately or is completed entirely. This phase ends when the application is deleted.

[0113] c) Undeployed period This refers to the period when the application is deleted, but the number of tasks that arrive has not accumulated to N.

[0114] d) Treatment period This refers to the period during which the CPU processes a task. Depending on whether the CPU enters this period from a waiting period or a deployment period, this period can be divided into two categories: This represents the processing phase that begins after the deployment phase. This represents the processing period that begins after the waiting period.

[0115] At this point, the probability that the task will reach its waiting time is:

[0116] ,

[0117] In the formula, for The rate at which tasks reach the edge server. The average waiting time is:

[0118] ,

[0119] The average duration of the undeployed period is:

[0120] ,

[0121] The average duration of the entire cycle is calculated as follows:

[0122] ,

[0123] In the formula, This represents the average duration of the deployment period. This refers to the average duration of the task processing period derived from the deployment cycle. This represents the average duration of the period that increases due to the duration of waiting.

[0124] Step 3: Construct the optimization problem

[0125] The method comprehensively considers the following four strategic factors:

[0126] a) User task uninstallation probability It should be between 0 and 1, and can be either 0 or 1;

[0127] b) Apply response thresholds The response threshold should be greater than or equal to 1 and should be an integer.

[0128] c) Apply wait duration The application's waiting time should be greater than or equal to 1.

[0129] d) Edge server computing resource allocation The sum of computing power allocated to all queues should be less than or equal to the total computing power of the edge servers.

[0130] Calculate the average latency of the entire system, including the computation time of tasks on mobile devices. And the computation time of the task on the edge server. Therefore, the optimization objective is:

[0131] ,

[0132] In the formula, Average latency for processing S-shaped tasks on mobile devices The rate at which an S-shaped task reaches the mobile device m. The time required for the edge server to request application s from the cloud server. Let be the average latency of an S-shaped task in the edge server. The optimization problem is as follows:

[0133] ,

[0134] The constraints are:

[0135] ,

[0136] ,

[0137] ,

[0138] ,

[0139] ,

[0140] ,

[0141] ,

[0142] ,

[0143] In the formula, For edge server CPU power consumption, The energy consumed in deploying applications on edge servers. For local traffic density, Traffic density for the S-shaped queue of the edge server. The expected space distribution for applications on edge servers. The standard deviation of the space occupied by applications on the edge server. The probability that the space occupied by all applications exceeds the storage space of the edge server.

[0144] Step 4: Derive closed-form expressions using holiday queues.

[0145] Based on the relevant theory of vacation queues, a closed-form expression for the indicator is calculated.

[0146] The average latency of S-shaped tasks in edge servers is:

[0147] ,

[0148] In the formula, The rate at which edge servers process S-shaped tasks. This refers to the time required for edge servers to request applications from cloud services. The average duration of task processing periods from the deployment cycle is:

[0149] ,

[0150] The average duration of the period that increases due to waiting time is:

[0151] ,

[0152] Average duration of the entire cycle:

[0153] ,

[0154] application The probability of occupying edge server space is:

[0155] ,

[0156] The average duration of the busy period is:

[0157] ,

[0158] The average duration of the off-season is:

[0159] ,

[0160] The probability of a busy period is: The probability of an off-season is .

[0161] Step 5: Interior point convex optimization algorithm

[0162] To address the difficulty of integer constraints, a branch-and-bound algorithm is employed. Through state-space search, the entire problem is systematically enumerated into candidate subproblems. By relaxing the integer constraints using Black-Browser (BB), the optimization problem remains non-convex. NOVA is used to solve the subproblems. The key idea is to replace the non-convex objective and constraints with appropriate convex functions, thereby converging to a stationary solution. The non-convex objective is replaced by the following equation:

[0163] ,

[0164] In the formula, Here are the regularization parameters. Use the following formula to replace the non-convex constraint condition:

[0165] ,

[0166] In the formula, This is the Lipschitz constant.

[0167] To fully illustrate the dynamic application deployment and update strategy proposed in this invention, performance is evaluated using the following three metrics:

[0168] (1) Average system delay;

[0169] (2) The ratio of average update frequency to task arrival rate.

[0170] In this embodiment, all algorithms and simulation experiments written in Matlab were completed on a PC with a 2.9GHz CPU and 16GB of memory. It is assumed that there are 20 mobile devices and 20 applications, and that tasks arrive randomly. The dynamic application update strategy proposed in this invention is called VQODAP. Other comparison methods are as follows:

[0171] a) FRA: Once a task arrives, ES will immediately request the relevant application from CS. After all relevant tasks have been processed, ES will immediately delete the relevant application to free up storage space for undeployed applications.

[0172] b) NRSA: If a task arrives but no corresponding application is found, the application will not be requested immediately. Instead, the application will be requested after n tasks of the same type have accumulated.

[0173] c) AKMA: After all tasks are processed, the system waits for a fixed period of time. If a task arrives during this waiting period, the system immediately begins service until the system becomes empty again. The response strategy is the same as FRA.

[0174] Figure 3 The average system latency is shown under different average arrival rates. Under low load, AKMA reduces average system latency by optimizing latency to decrease the frequency of application deployments. Under high load, NRSA helps MDs offload more tasks to ES by controlling response thresholds. Combining the advantages of AKMA and NRSA, VQODAP performs best regardless of load. Figure 4 The average system delay under different energy constraints is shown, and it can be observed that the average delay decreases as the energy constraint is relaxed. As can be seen from the figure, VQODAP has the shortest average system delay under all energy constraints E. Figure 5 The ratio of application update frequency to task arrival rate is shown under different storage spaces. Under the VQODAP method, this value decreases as the available storage space increases, and is the lowest value in all cases, indicating that VQODAP has the lowest update frequency, thus demonstrating that it consumes the least energy for application updates.

Claims

1. A method for dynamic deployment and updating of application services based on vacation queuing, characterized in that: The method is based on vacation queuing and is designed for multi-user devices, edge servers, and cloud servers. It uses user task uninstallation probability, application response threshold, application waiting duration, and edge server computing resource allocation as optimization variables. Based on the vacation queue, it solves the closed-form expressions of the corresponding indicators, with the goal of minimizing the average task latency of the entire system. The method includes the following steps: (1) Build a multi-user device, edge server and cloud server to form an edge computing network, and establish an edge server task processing latency model based on the edge computing network; (2) Design an optimizable dynamic application deployment and update strategy, where the optimizable variable is the application response threshold. and applications Waiting duration At this point, the probability of the S-shaped task reaching its waiting duration is calculated as follows: ， In the formula, for The rate at which type of task reaches the edge server; The average duration of the waiting period is: ， The average duration of the undeployed period is: ， The average duration of the entire cycle is calculated as follows: ， In the formula, This represents the average duration of the deployment period. This refers to the average duration of the task processing period derived from the deployment cycle. The average duration of the period that increases due to the duration of waiting; (3) The complete decision variable for this edge computing network is determined as: the probability of user S-type task offloading. Application response threshold Application wait duration and edge server computing resource allocation ; (4) Calculate the average latency of the entire edge computing network, including the computation time of the S-shaped task on the mobile device. And the computation time of S-shaped tasks on edge servers Therefore, the optimization objective is: ， In the formula, Average latency for processing S-shaped tasks on mobile devices The rate at which an S-shaped task reaches the mobile device m. For edge servers to request applications from cloud servers The time required The average latency of S-shaped tasks in the edge server; (5) Constructing the optimization problem: Based on queuing-related theories, a function for minimizing the system latency of the edge computing network is constructed. The function expression for the optimization problem of the dynamic deployment and update strategy of application services based on vacation queuing is as follows: ， The constraints are: ， ， ， ， ， ， ， ， In the formula, For edge server CPU power consumption, The energy consumed in deploying applications on edge servers. For local traffic density, The traffic density of the S-shaped queue in the edge server. Applications on edge servers The expected spatial distribution Applications on edge servers The standard deviation of the spatial distribution. For all applications The probability that the space occupied exceeds the edge server's storage space; (6) Based on the relevant theory of vacation queues, calculate the closed-form expressions of the unresolved indicators in steps (2), (4), and (5); The average latency of S-shaped tasks in edge servers is: ， In the formula, The rate at which edge servers process S-shaped tasks. Request applications from cloud services for edge servers The time required; The average duration of the S-shaped task processing period resulting from the deployment cycle is: ， The average duration of the period that increases due to waiting time is: ， Average duration of the entire cycle: ， application The probability of occupying edge server space is: ， The average duration of the busy period is: ， The average duration of the off-season is: ， The probability of a busy period is: The probability of an off-season is ; Substitute all the above closed expressions into step (5). At this point, all the parameters related to the optimization problem in step (5) have closed expressions. (7) Obtain the user task unloading probability based on the interior point convex approximation method. Application response threshold Application wait duration and edge server computing resource allocation The optimal value of minimizes the average system delay.

2. The method for dynamic deployment and updating of application services based on vacation queuing according to claim 1, characterized in that: In step (1), the system model considers M mobile devices, dedicated edge servers deployed at the base station, and cloud servers. The S-shaped computing task has an average rate of The Poisson distribution reaches The computational cost of S-shaped tasks follows a mean of The exponential distribution; Edge servers have limited storage space, while cloud servers can store applications without limit. Therefore, edge servers tend to request applications from cloud servers, and the time taken is: ,in, For application Size, This refers to the transmission rate between the edge server and the cloud server. When the S-shaped task arrives at the mobile device, the mobile device uses... The probability of offloading to an edge server for processing, or with The probability that the mobile device will handle the task itself.

3. The method for dynamic deployment and updating of application services based on vacation queuing according to claim 2, characterized in that: The arrival rate for local processing of S-type tasks on mobile device m is: ， Approximate the distribution of all arrivals for the S-shaped task as an exponential distribution, and obtain the average computational cost for a mobile device to process an S-shaped task as follows: ， Further, based on the classic queuing theory model M / M / 1, the average latency for processing S-shaped tasks on mobile devices is obtained as follows: ， S-type tasks from mobile devices are managed in different S-type queues according to task type, and arriving S-type tasks are also processed in the FCFS manner. The arrival rate of S-shaped tasks processed by the S-shaped queue on the edge server is: 。 4. The method for dynamic deployment and updating of application services based on vacation queuing according to claim 1, characterized in that: When an S-type task is offloaded to an edge server, if there are no applications on the edge server... The edge server will not immediately request applications from the cloud server. Instead, it continues until accumulation Only S-shaped tasks request the application. ; Requesting application from cloud server Previously, edge servers required pre-allocation of storage applications. Due to limited storage space, if allocated to applications... There is insufficient remaining space, and the edge server may delete some other applications or files; When S-shaped task queue When empty, apply It can also be done in Accessed within a certain time frame, meaning the edge server will be... Internal storage applications Instead of deleting it; If there are S-shaped tasks If a task arrives, the edge server will continue processing the task until the queue becomes empty again; if no task arrives... If it arrives within the area, then apply. It will be deleted; To better analyze this queue model, the entire processing is divided into four stages: a) Deployment period This period is used for application deployment; b) Waiting period This phase begins when the task queue becomes empty. If a task is completed, the phase ends immediately or is completed entirely. This phase ends when the application is deleted. c) Undeployed period This refers to an application being deleted, and the tasks that arrived were not accumulated. Each period; d) Treatment period This refers to the period during which the CPU processes a task. Depending on whether the CPU enters this period from a waiting period or a deployment period, this period can be divided into two categories: This represents the processing phase that begins after the deployment phase. This represents the processing period that begins after the waiting period.

5. The method for dynamic deployment and updating of application services based on vacation queuing according to claim 1, characterized in that: The method comprehensively considers the following four strategic factors: a) User task uninstallation probability It should be between 0 and 1, and can be either 0 or 1; b) Apply response thresholds The response threshold should be greater than or equal to 1 and should be an integer. c) Application wait duration The application's waiting time should be greater than or equal to 1. d) Edge server computing resource allocation The sum of computing power allocated to all queues is less than or equal to the total computing power of the edge servers.

6. The method for dynamic deployment and updating of application services based on vacation queuing according to claim 1, characterized in that: The average latency for mobile devices to process S-shaped tasks is calculated using the following formula: ， The computation time for the task on the edge server is calculated as follows: ， In the formula, The time required to transfer an S-type task from a mobile device m to an edge server is derived from the following formula: , The average size of an S-shaped task. Let m be the transmission rate from the mobile device to the edge server.

7. The method for dynamic deployment and updating of application services based on vacation queuing according to claim 1, characterized in that: The power consumption for processing tasks in step (5) consists of both busy and idle periods, with the CPU power consumption during the idle period being 60% of that during the busy period. Local traffic density The calculation is as follows: ， Traffic density of edge server S-shaped queues The calculation formula is as follows: ， Expected spatial distribution of application s on the edge server The calculation formula is as follows: ， Standard deviation of the space distribution occupied by applications on edge servers The calculation formula is as follows: In the formula, S represents the total number of application types. This represents the average computational cost for an S-shaped task. For application The size of W is the transmission rate between the edge server and the cloud server. For application The probability of occupying edge server space.

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