An edge computing task offloading admission control method based on cumulative priority

Abstract

This invention discloses an edge computing task offloading admission control method based on cumulative priority, solving the problems of optimal user priority selection and excessive waiting latency in traditional task offloading. By introducing a cumulative priority model into edge computing, the server first serves the highest priority queue, and the priority of waiting tasks accumulates over time. The processing order of tasks in the queue is rearranged according to priority, and a maximum priority threshold is set. When the waiting time of a task reaches this threshold, the user is not allowed to transmit the task to the server. Users engage in a game with each other to minimize their own costs. The existence of a Nash equilibrium is proven through mathematical derivation, and the optimal priority selection strategy for each user under the Nash equilibrium is derived. This method can provide users with optimal priority selection and solve the task starvation problem.

Description

Technical Field

[0001] This invention belongs to the field of edge computing technology, specifically relating to an edge computing task offloading admission control method. Background Technology

[0002] Mobile edge computing deploys services to users on edge servers located close to them, significantly reducing task processing latency and improving service quality. However, edge servers also have their limitations; compared to cloud servers, their storage and computing resources are finite, making it difficult to handle a large number of service requests. To address this issue, access control and server collaboration can be used. Server collaboration involves multiple servers within a certain area, while access control can typically be applied to a single server.

[0003] To provide personalized services to users, a priority system is typically used. In absolute priority, the user's priority remains constant, and the server always serves the highest priority task. Tasks that remain at a low priority level for an extended period may experience "starvation." Cumulative priority, on the other hand, is a dynamic priority system where the priority is related to the waiting time. Under the same conditions, the higher the waiting latency, the higher the cumulative priority, effectively preventing task "starvation."

[0004] Users are inherently selfish, aiming to minimize their own costs. Servers price services based on priority, with higher priority levels commanding higher prices. Users strive to minimize both the price and latency costs associated with their priority choice. Therefore, a game exists between users.

[0005] Current methods typically use absolute priorities when utilizing priorities, meaning that once a task's priority is determined, it cannot be changed. This can lead to low-priority tasks remaining unprocessed for extended periods. Furthermore, the lack of a threshold structure for the priority queue can result in a large backlog of tasks, overwhelming the server and severely impacting user service quality. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides an edge computing task offloading admission control method based on cumulative priority, solving the problems of optimal user priority selection and excessive waiting latency in traditional task offloading. By introducing a cumulative priority model into edge computing, the server first serves the highest-priority queue, and the priority of waiting tasks accumulates over time. The processing order of tasks in the queue is rearranged according to priority, and a maximum priority threshold is set. When the waiting time of a task reaches this threshold, the user is not allowed to transmit the task to the server. Users engage in a game with each other to minimize their own costs. The existence of a Nash equilibrium is proven through mathematical derivation, and the optimal priority selection strategy for each user under the Nash equilibrium is derived. This method can provide users with optimal priority selection and solve the task starvation problem.

[0007] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0008] Step 1: Build an edge computing task offloading system;

[0009] Step 2: Construct the task offloading transmission model, cumulative priority model, and user cost model;

[0010] Step 3: Solve for the optimal response strategy for the hybrid strategy user;

[0011] Step 4: Introduce linear cumulative priority and solve for Nash equilibrium;

[0012] Step 5: Solve for the optimal response strategy for pure policy users and provide admission control by setting time thresholds.

[0013] Further, step 1 specifically includes:

[0014] An edge computing task offloading system is constructed, which includes an edge server that serves N users. Tasks arriving in the buffer follow a Poisson distribution with parameter λ. Homogeneous tasks are considered, with each task having an equal average processing time and a waiting cost of v per unit time. Tasks in the buffer accept user admission suggestions. Rejected tasks are sent to other servers for processing, and the transmission of rejected tasks is suspended during the communication phase.

[0015] Furthermore, step 2 specifically includes:

[0016] Step 2-1: The data transmission rate model between the user and the base station is as follows:

[0017]

[0018] Among them B irepresents the bandwidth resources allocated by the base station to user i, h represents the channel gain between the user and the base station, q represents the transmission power between the user and the base station, and w represents the noise power;

[0019] The transmission delay of the task is then:

[0020] Step 2-2: Model the cumulative priority;

[0021] Set up K priority queues, where the Kth priority queue has the highest priority. For tasks arriving at the same time, the server first processes the highest priority task from the Kth priority queue; only when the Kth priority queue is empty will the server process tasks from the (K-1)th priority queue. Let the price of priority queue j be b. j *C, where C is the price coefficient, b j Let b be the rate coefficient, and 0 = b0 < ... k k+1 , where b k+1 If the amount is large enough, users will not make a purchase; the cumulative priority is represented as follows: assuming the task arrives at time t, the payment is b. j After C enters the priority queue j, its priority is b at time t′. j *(t′-t);

[0022] The server uses the M / G / 1 service model, meaning the arrival process follows a Poisson distribution, and the service time follows a general distribution; the average service time for each task is... The variance is x, and the server's workload is...

[0023] The user's costs consist of the cost of purchasing the priority cumulative rate and the cost of waiting for computing services; the server's revenue comes from the fees charged for the priority queue.

[0024] The user's goal is to achieve the following:

[0025]

[0026] Among them, M i W represents the total cost to user i. i Let k be the expected waiting time for user i. i The cost paid by a user for selecting the cumulative priority queue k, where b0 ≤ k i ≤b k+1 v represents the unit time delay cost coefficient, and C represents the price coefficient;

[0027] Suppose that the user's choice of each priority is a set of strategies, P = {p0, p1, ..., p2}. k} represents the probability of choosing a certain priority, and​​ If p j =1 indicates that the user chooses priority j; W(j, p) represents the waiting time for the user to choose priority j when all users follow policy set P; based on the existing formula, we can derive:

[0028]

[0029] W(j, p) is calculated recursively:

[0030]

[0031] Where W0 is the expected service time of the server, and

[0032] Preferably, step 3 specifically comprises:

[0033] When all other users are using policy set P, the cost function for a user using pure policy j is:

[0034] M i =C*W(j,P)+v*j (5)

[0035] Therefore, the optimal strategy for the policy set is argmin. 0≤j≤k {M(j, P)};

[0036] If not purchasing is the optimal strategy, then G(0, P) ≤ G(1, P); therefore, if strategy j * The optimal response strategy is ≥1, which must satisfy:

[0037] G(j * -1, P)≥G(j * ,P)≤G(j * +1, P) (6)

[0038] Due to G(j) * If P is a convex function of j, then only one of the above two inequalities holds; if neither holds, then j * For a unique optimal response strategy, if the first inequality holds, then both 0 and 1 are optimal response strategies; if the second inequality holds, then j... * and j * -1 represents the optimal response strategy; therefore, the set of optimal strategies for any mixed strategy P contains at most two strategies, which are two consecutive integers if two strategies exist.

[0039] Assume D(m, P) = W(m-1, P) - W(m, P) represents the reduced latency when the user chooses priority m instead of m-1, therefore j * For the optimal response strategy to be ≥1, the following must also be satisfied:

[0040]

[0041] If priority 0 is the optimal strategy, then it must satisfy... This means the system's priority pricing is too high, and the user's optimal strategy is not to purchase priority.

[0042] Furthermore, step 4 specifically includes:

[0043] Introducing a linear cumulative priority, where users can choose any value b (b > 0), and the user's purchase cost is C*b, the optimal cumulative rate of purchase priority for all users in the unique symmetric Nash equilibrium is:

[0044] According to the recurrence relation of W(j, p), we have:

[0045]

[0046] And because

[0047]

[0048]

[0049] If priority 0 is the optimal strategy, then it must satisfy...

[0050] If priority n is the optimal strategy, it must satisfy... The above equation can be rewritten as:

[0051] b e -1≤n≤b e +ρ

[0052] And noting that 1+ρ<2, the Nash equilibrium exists and is... and If s1 = s2, then the Nash equilibrium is unique; otherwise, s2 = s1 + 1.

[0053] In a Nash equilibrium, all users purchase the same priority, forming an FCFS service queue. For all possible equilibria, the total expected waiting cost is the same.

[0054] Furthermore, step 5 specifically includes:

[0055] The optimal policy is described as a function of other users using pure policies rather than mixed policies. Let B(n) be the user's optimal response to policy n. If the following conditions are met:

[0056]

[0057] Then B(n) = m; If it satisfies Then B(n) = 0; Since D(m, n) is a decreasing function of m, therefore:

[0058]

[0059] Or β(n) is The solution of; Since D(β, n) is a decreasing function of β, and:

[0060]

[0061] Therefore when When, there is β(n) < n;

[0062] When β > n, there is

[0063]

[0064] Therefore The solution of is

[0065] When β < n, there is:

[0066]

[0067] From this, we get

[0068] To sum up, if s2 = 0, then for all n ≥ 0, then B(n) = 0;

[0069] If s2 > 0, then:

[0070]

[0071] Set a maximum time threshold t for the entire system max , if the cumulative time of a certain task reaches t max , then it is determined that the task has waited too long in the priority queue and the server is too busy. At this time, the transmission of tasks in the system is paused, that is, admission control is used; the 0-1 notification method is adopted, that is, when a = 0, it is not recommended that the user join the system, and the tasks generated by the user can only be processed locally. When a = 1, the user is allowed to join the priority queue for waiting.

[0072] The beneficial effects of the present invention are as follows:

[0073] 1) The present invention applies cumulative priority to the edge computing scenario to ensure that low-priority tasks can be processed within a certain time.

[0074] 2) This invention utilizes an admission control strategy to stop the transmission of a task when it reaches the maximum time threshold, thereby ensuring the quality of service for users.

[0075] 3) This invention uses game theory to derive the user's optimal strategy selection. Attached Figure Description

[0076] Figure 1 This is a scene diagram from the present invention.

[0077] Figure 2 This is a diagram illustrating the solution used in this invention. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0079] To address the aforementioned problems, this invention proposes an edge computing task offloading admission control method based on cumulative priority. This addresses the issue of selecting the optimal user strategy in multi-priority scenarios within edge computing.

[0080] An edge computing task offloading admission control method based on cumulative priority includes the following steps:

[0081] Step 1: Build an edge computing task offloading system;

[0082] Step 2: Construct the task offloading transmission model, cumulative priority model, and user cost model;

[0083] Step 3: Solve for the optimal response strategy for the hybrid strategy user;

[0084] Step 4: Introduce linear cumulative priority and solve for Nash equilibrium;

[0085] Step 5: Solve for the optimal response strategy for pure policy users and provide admission control by setting time thresholds. Specific implementation examples:

[0087] like Figure 1 and Figure 2 As shown.

[0088] Step one specifically involves: constructing an edge computing task offloading system. This system includes an edge server that serves N users. Tasks arriving in the buffer follow a Poisson distribution with parameter λ. Considering homogeneous tasks, each task has an equal average processing time, and the waiting cost per unit time is v. Users are rational; tasks in the buffer accept user admission suggestions, rejected tasks are sent to other servers for processing, and the transmission of tasks during the communication phase is suspended.

[0089] Step two,

[0090] Step 2-1: The data transmission rate model between the user and the base station is as follows:

[0091]

[0092] Among them B i represents the bandwidth resources allocated by the base station to user i, h represents the channel gain between the user and the base station, q represents the transmission power between the user and the base station, and w represents the noise power;

[0093] The transmission delay of the task is then:

[0094] Step 2-2: Model the cumulative priority. Set up K queues, where queue K has the highest priority. For tasks arriving at the same time, the server will first serve the highest priority task from queue K. Tasks in queue K-1 will only be processed when queue K is empty. Let the price of priority queue j be b. j *C, where C is the price coefficient, b j Let b be the rate coefficient, and 0 = b0 < ... k k+1 , where b k+1 If the amount is large enough, users won't make a purchase. The cumulative priority is represented as follows: assuming the task arrives at time t, the payment is b. j After C enters the priority queue j, its priority is b at time t′. j *(t′-t).

[0095] Using the M / G / 1 service model on the server side, where the arrival process follows a Poisson distribution and the service time follows a general distribution, makes it more universally applicable. The average service time for each task is... The variance is x, and the server's workload is...

[0096] The goal is to minimize user costs while ensuring service provider revenue. User costs primarily consist of the cost of purchasing priority accumulation rates and the latency cost of waiting for computing services. Server revenue mainly comes from the fees charged for priority queues. The server cannot set the price of priorities too high, otherwise users will not choose to uninstall tasks or only uninstall tasks to the lowest priority queue. Conversely, the price of priorities cannot be set too low, otherwise the server's own revenue cannot be guaranteed.

[0097] The user's goal is to achieve the following:

[0098]

[0099] Among them, W i K represents the expected waiting time for user i. i ​​The cost paid by a user for selecting the cumulative priority queue k, where b0 ≤ k i ≤b k+1 .

[0100] For users, there is a balance: higher speeds can reduce average waiting time, but at a higher cost. At the same time, when a user purchases a higher speed, other users face the same choice, resulting in a non-cooperative game between users.

[0101] Suppose that the user's choice of each priority is a set of strategies, P = {p0, p1, ..., p2}. k} represents the probability of choosing a certain priority, and If p j =1 indicates that the user chooses priority j. Let W(j, p) represent the waiting time for a user to choose priority j when all users follow policy set P. Based on the existing formula, we can derive...

[0102]

[0103] Furthermore, W(j, p) can be calculated recursively.

[0104]

[0105] Where W0 is the expected service time of the server, and

[0106] In step three, when all other users are using policy set P, the cost function for the user using pure policy j is:

[0107] M i =C*W(j,P)+v*j (5)

[0108] Therefore, the optimal strategy for the policy set is argmin. 0≤j≤k (M(j, P)}.

[0109] If not purchasing is the optimal strategy, then G(0, P) ≤ G(1, P). Therefore, if strategy j * ≥1 is the optimal response strategy, which must satisfy...

[0110] G(j * -1, P)≥G(j * ,P)≤G(j * +1, P) (6)

[0111] Due to G(j) * If P is a convex function of j, then only one of the above two inequalities holds. If neither holds, then j *For a unique optimal response strategy, if the first inequality holds, then both 0 and 1 are optimal response strategies; if the second inequality holds, then j... * and j * -1 represents the optimal response strategy. Therefore, the set of optimal strategies for any mixed strategy P contains at most two strategies, which are two consecutive integers if they exist.

[0112] Suppose D(m, P) = W(m-1, P) - W(m, P) represents the reduced latency when the user chooses priority m instead of m-1. Therefore, j * ≥1 is also required for the optimal response strategy.

[0113]

[0114] If priority 0 is the optimal strategy, then it must satisfy... This means the system's priority pricing is too high, and the user's optimal strategy is not to purchase priority.

[0115] In step four, to prove the existence of the Nash equilibrium, a linear cumulative priority is first introduced, where users can choose any value b, b > 0, and the user's purchase cost is C*b. Existing literature has proven that in a unique symmetric Nash equilibrium, the optimal cumulative rate of purchase priority for all users is...

[0116] According to the recursive formula of W(j, p), we have

[0117]

[0118] And because

[0119]

[0120]

[0121] If priority 0 is the optimal strategy, then it must satisfy...

[0122] If priority n is the optimal strategy, it must satisfy... Rewrite the above equation as follows:

[0123] b e -1≤n≤b e +ρ

[0124] And noting that 1+p<2, the Nash equilibrium exists and is... and If s1 = s2, then the Nash equilibrium is unique; otherwise, s2 = s1 + 1.

[0125] In the Nash equilibrium, all users purchase the same priority, forming a FCFS service queue. For all possible equilibria, the total expected waiting cost is the same, which is

[0126] In step five, the best strategy is described as a function of other users using pure strategies rather than mixed strategies. Let B(n) be the best response of a user to strategy n. From the previous argument, if

[0127]

[0128] then B(n) = m; if then B(n) = 0. Since D(m, n) is a decreasing function of m, thus

[0129]

[0130] or β(n) is the solution of. Since D(β, n) is a decreasing function of β, and

[0131]

[0132] Therefore, when there is β(n) < n.

[0133] When β > n, there is

[0134]

[0135] So the solution of is

[0136] When β < n, there is

[0137]

[0138] From this, it can be obtained that

[0139] To sum up, if s2 = 0, then for all n ≥ 0, B(n) = 0

[0140] If s2 > 0, then

[0141]

[0142] Set a maximum time threshold t for the entire system max , if the cumulative time of a certain task reaches t maxIf the task has been waiting in the priority queue for too long and the server is too busy, the transmission of tasks in the system is suspended. This is called admission control, which uses a 0-1 notification method. When a=0, it is not recommended for the user to join the system, and the tasks generated by the user can only be processed locally. When a=1, the user is allowed to join the priority queue and wait. By controlling the threshold, the quality of service for users can be better guaranteed.

Claims

1.A cumulative priority based edge computing task offloading admission control method, characterized in that, Includes the following steps: Step 1: Build an edge computing task offloading system; Step 2: Construct the task offloading transmission model, cumulative priority model, and user cost model; Step 2 specifically involves: Step 2-1: The data transmission rate model between the user and the base station is as follows: （1） in Indicates that the base station is assigned to the user i bandwidth resources, This represents the channel gain between the user and the base station. For the transmission power between the user and the base station, Noise power; The transmission delay of the task is: ; Step 2-2: Model the cumulative priority; K priority queues are set up, with the Kth priority queue having the highest priority. For tasks arriving at the same time, the server first processes the highest priority task from the Kth priority queue; only when the Kth priority queue is empty will the server process the tasks in the (K-1)th priority queue. Let the price of priority queue j be . ,in For price coefficients, For the rate coefficient, and ,in If the amount is large enough, users won't make a purchase; the cumulative priority is represented as follows: assuming the task arrives at time t, the fee is paid. After entering the j-priority queue, in Its priority is at any given time. ; The server uses the M / G / 1 service model, meaning the arrival process follows a Poisson distribution, and the service time follows a general distribution; the average service time for each task is... The variance is x, and the server's workload is... ; The user's costs consist of the cost of purchasing the priority cumulative rate and the cost of waiting for computing services; the server's revenue comes from the fees charged for the priority queue. The user's goal is to achieve the following: （2） in, Indicates user Total cost For users i Expected waiting time Select a cumulative priority queue for the user k The fees paid , This represents the unit time delay cost coefficient. Indicates the price coefficient; Assume that the user's choice for each priority level is a set of strategies. , representing the probability of choosing a certain priority, and ,like =1 indicates that the user selects priority j; using This represents the waiting time for a user to choose priority j when all users follow the policy set P; based on the existing formula, we can derive: （3） By recursion : （4） in, This is the expected service time of the server, and ; Step 3: Solve for the optimal response strategy for the hybrid strategy user; Step 3 specifically involves: When all other users are using policy set P, the cost function for a user using pure policy j is: （5） Therefore, the best strategy for the strategy set is ; If the purchase priority is not the best strategy, then the following must be satisfied ; so if the strategy is the best response strategy, then the following must be satisfied: （6） because Since j is a convex function, only one of the above two inequalities holds; if neither holds, then... Assuming a unique optimal response strategy, if the first inequality holds, then both 0 and 1 are optimal response strategies; if the second inequality holds, then... and All are optimal response strategies; therefore, the set of optimal strategies for any mixed strategy P contains at most two strategies, which are two consecutive integers if two strategies exist. Assumption This indicates that the user selected priority m instead of the reduced latency of m-1. The optimal response strategy must also satisfy: （7） If priority 0 is the optimal strategy, then it must satisfy... This means that the system's priority pricing is too high, and the user's optimal strategy is not to purchase priority. Step 4: Introduce linear cumulative priority and solve for Nash equilibrium; Step 4 specifically involves: Introducing a linear cumulative priority, where a user can choose any value b, b > 0, the user's purchase cost is... In a unique symmetric Nash equilibrium, the optimal priority cumulative rate of purchases by all users is: ; According to the recurrence formula of there is:​ （8） And because （9） If priority 0 is the best strategy, to meet ; If the priority n is the best strategy, the following must be satisfied The above equation can be rewritten as: And noted Therefore, the Nash equilibrium exists and is and ,like If so, then the Nash equilibrium is unique; otherwise... ; In a Nash equilibrium, all users purchase the same priority, forming an FCFS service queue. For all possible equilibria, the total expected waiting cost is the same. ; Step 5: Solve for the optimal response strategy for pure policy users and provide admission control by setting time thresholds. 2.The cumulative priority-based edge computing task offloading admission control method of claim 1, wherein, Step 1 specifically involves: Construct an edge computing task offloading system. This system includes an edge server serving N users. Tasks arriving at the buffer follow a Poisson distribution with parameter λ. Considering homogeneous tasks, each task has an equal average processing time, and the waiting cost per unit time is [value missing]. Tasks in the buffer accept user admission suggestions, rejected tasks are sent to other servers for processing, and the transmission of rejected tasks is suspended during the communication phase. 3.The cumulative priority based edge computing task offloading admission control method of claim 2, wherein, Step 5 specifically involves: The optimal strategy is described as a function of other users using a pure strategy instead of a mixed strategy. It is a user-targeted strategy n The best response, if it satisfies: （10） Then If then Since is a decreasing function of m , we have: or , for The solution; because for A decreasing function, and: Therefore when Sometimes, ; When there is （11） Therefore the solution is ; When there is: （12） Thus obtained ; In summary, if then for all then ; If then: （13） Set a maximum time threshold for the entire system. If the accumulated time for a certain task reaches If the task has been waiting in the priority queue for too long, the server is too busy. In this case, the transmission of tasks in the system is suspended, i.e., admission control is used. The 0-1 notification method is adopted, that is, when a=0, it is not recommended for users to join the system. At this time, the tasks generated by users can only be processed locally. When a=1, users are allowed to join the priority queue to wait.

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