A multi-server collaborative resource allocation method based on game theory

Abstract

The present invention relates to the field of wireless communication technology, and in particular to a multi-server collaborative resource allocation method based on game theory, comprising: constructing a system model of multiple edge servers collaborating, wherein the edge servers in the system model serve as migrators or collaborators; constructing a migrator cost model, a collaborator cost model and a revenue model, and constructing a buyer's maximum revenue model and a seller's maximum revenue model based on these three models; calculating an optimal migration strategy for a migrator and an optimal dynamic quotation strategy for a collaborator to pay a quotation to a migrator; judging whether the optimal migration strategy and the optimal dynamic quotation strategy satisfy the Stackelberg equilibrium, and if so, realizing computing resource allocation according to the optimal strategy; the present invention realizes flexible control and on-demand allocation of task migration and computing resources.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a multi-server collaborative resource allocation method based on game theory. Background Art

[0002] In recent years, massive intelligent terminals such as sensors, cameras, and smart meters have been widely used in various emerging businesses, which has put forward higher requirements on existing cellular networks. Therefore, a promising local service communication mode, mobile edge computing (MEC), has been introduced to meet the growing data needs of users. MEC provides IT server environment and cloud computing capabilities at the edge of the mobile network to shorten transmission time delay, improve bandwidth efficiency, enhance location awareness, and alleviate the network's urgent need for a large number of intelligent terminal devices.

[0003] Mobile edge computing can effectively overcome the shortcomings of network congestion and delay in edge computing systems by processing data at the edge of the network. MEC servers, as indispensable devices in mobile edge computing technology, provide computing services for users. However, with the rapid increase in the number of users, the limited computing resources of MEC servers are difficult to provide fast and fair services to each user. In order to improve the efficiency of edge cloud under limited communication and computing capabilities, the collaboration between edge computing servers is considered. Due to its limited storage and computing power, a single MEC server usually cannot meet heavy computing tasks, and the cooperation of MEC servers provides an effective way to solve this problem. However, there are several problems in traditional MEC collaboration. First, when heavy tasks from multiple users arrive, the edge server has unstable service quality. Second, how to select the most suitable edge server for offloading between multiple edge servers and remote cloud servers? Third, when edge server computing resources are scarce, how to collaborate between edge servers or between edge servers and cloud servers. In addition, when considering server collaboration, its costs and benefits must also be considered. How to reasonably construct a model of MEC server collaboration and perform joint optimization of task migration and computing resource allocation based on this is a problem to be solved by the present invention. Summary of the invention

[0004] To solve the above problems, the present invention provides a multi-server collaborative resource allocation method based on game theory, comprising:

[0005] S1. Build a system model of multiple edge servers collaborating, where the edge servers in the system model act as migrators or collaborators;

[0006] S2. Construct the cost model of the migrant, the cost model of the collaborator and the benefit model;

[0007] S3. Construct a buyer's maximum profit model and a seller's maximum profit model through the three models constructed in step S2;

[0008] S4. Based on the buyer's maximization model, the optimal migration strategy of the migrators is calculated using the Lagrange multiplier method and KKT conditions;

[0009] S5. According to the seller's maximization profit model and the migrator's optimal migration strategy, the optimal dynamic bidding strategy for the collaborator to pay the migrator is obtained;

[0010] S6. Determine whether the optimal migration strategy and the optimal dynamic quotation strategy satisfy the Stackelberg equilibrium. If so, achieve the optimal computing resource allocation. Otherwise, return to step S4.

[0011] Furthermore, the amount of computing tasks arriving at each edge server in the system model is expressed as:

[0012] A i (t) = a i (t)+c i (t);

[0013] Among them, A i (t) represents the amount of computing tasks arriving at the i-th edge server, and represents the maximum amount of tasks that arrive at the i-th edge server, a i (t) represents the amount of tasks that the ith edge server can handle, c i (t) represents the amount of tasks that the i-th edge server migrates to other servers for processing.

[0014] Furthermore, each MEC server has a CPU processing frequency limit, denoted as K i (t), when A i (t)>K i At (t), MEC server i acts as a migrator, and the total computing task of the migrator is:

[0015]

[0016] in, It means that MEC server i can migrate the tasks that cannot be processed to any other MEC server in the same LAN. i0 (t) represents the task migrated from MEC server i to the remote cloud server RC.

[0017] Furthermore, when A j (t)<K j At (t), MEC server j acts as a collaborator, and the total computing task of the collaborator is:

[0018]

[0019] At this time, P j (t) is the total tasks that MEC server j needs to process, Indicates the migration tasks received by MEC server j from other MEC servers.

[0020] Furthermore, the total cost in the migrator cost model is expressed as:

[0021] C m_cost (t) = α(T m_cp (t)+T m_qe (t)+1·T mg (t)+1·T bl (t))+β(E m_cp (t)+E m_mg (t));

[0022] Among them, T m_cp (t) is the delay for migrating, T c_cp Calculate the delay for the collaborator, T mg (t) is the migration delay, T bl (t) is the return link delay, E m_cp (t) Calculate the energy consumption of the migrant, E m_mg (t) is the migration energy consumption of the migrator, α is the unit time cost required for the server to process the task, and β is the unit energy cost required for the server to process the task.

[0023] Furthermore, the total cost in the collaborator cost model is expressed as:

[0024] C c_cost (t) = α(T c_cp (t)+T c_qe (t))+βE c_cp (t);

[0025] Among them, α is the unit time cost required for the server to process the task, β is the unit energy cost required for the server to process the task, T c_cp (t) is the delay calculated by the collaborator, T c_qe (t) is the queuing delay of the collaborator, E c_cp (t) Calculate the energy consumption for the collaborators.

[0026] Furthermore, the buyer's maximum profit model is constructed through the migration cost model and the profit model. The buyer's maximum profit problem is expressed as:

[0027]

[0028] Among them, C m_cost (t) is the total cost in the migrating cost model, v ij (t) represents the cost paid by the migrator to purchase computing tasks from the collaborator.

[0029] Furthermore, the total cost in the collaborator cost model is expressed as:

[0030] C c_cost (t) = α(T c_cp (t)+T c_qe (t))+βE c_cp (t);

[0031] Among them, α is the unit time cost required for the server to process the task, β is the unit energy cost required for the server to process the task, T c_cp (t) is the delay calculated by the collaborator, T c_qe (t) is the queuing delay of the collaborator, E c_cp (t) Calculate the energy consumption for the collaborators.

[0032] Furthermore, the seller's maximum profit model is constructed through the collaborator cost model and the profit model. The seller's maximum profit problem is expressed as:

[0033] maxU c (p ij (t)) = v ji (t)-C c_cost (t);

[0034] Among them, C c_cost (t) is the total cost in the collaborator cost model, v ji (t) represents the profit model.

[0035] Beneficial effects of the present invention:

[0036] The present invention proposes a multi-server collaborative resource allocation method based on game theory, puts forward the concepts of migrator and collaborator, and based on the knowledge of game theory, regards the MEC server as the migrator as the buyer and the MEC server as the collaborator as the seller, establishes a buying and selling model, and achieves the profit balance of the buyer and the seller by seeking elastic allocation of computing resources. A multi-server resource dynamic quotation mechanism is studied, and a multi-server collaborative resource allocation algorithm is proposed. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flowchart of a multi-server collaborative resource allocation method based on game theory of the present invention;

[0038] Figure 2 This is a system model diagram of the multi-server collaborative resource allocation method based on game theory of the present invention. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] The present invention proposes a multi-server collaborative resource allocation method based on game theory, such as Figure 1 , specifically including the following steps:

[0041] S1. Build a system model with multiple edge servers collaborating. The edge servers in the system model can act as migrators or collaborators.

[0042] Specifically, the system model includes a task migration model, a delay model and an energy consumption model; the task migration model is divided into a task migration mode and a task collaboration mode; the delay model includes the migrant computing delay, the collaborator computing delay, the migrant queuing delay, the collaborator queuing delay, the migration delay and the return link delay; the energy consumption model includes the migrant computing energy consumption, the collaborator computing energy consumption and the migrant migration energy consumption.

[0043] S2. Construct the cost model of the migrant, the cost model of the collaborator and the benefit model;

[0044] S3. Construct a buyer's maximum profit model and a seller's maximum profit model through the three models constructed in step S2;

[0045] S4. Based on the buyer's maximization model, the optimal migration strategy of the migrators is calculated using the Lagrange multiplier method and KKT conditions;

[0046] S5. According to the seller's maximization profit model and the migrator's optimal migration strategy, the optimal dynamic bidding strategy for the collaborator to pay the migrator is obtained;

[0047] S6. Determine whether the optimal migration strategy and the optimal dynamic quotation strategy satisfy the Stackelberg equilibrium. If so, achieve the optimal computing resource allocation. Otherwise, return to step S4.

[0048] In one embodiment, if Figure 2 As shown in Figure 2, consider an edge network consisting of several BSs, several users, and a remote cloud server. Each BS is equipped with a MEC server within its coverage area, and the set of MEC servers is represented as It is stipulated that all collaborative MEC servers are in the same LAN, and each MEC server has a CPU processing frequency limit, denoted as K i (t), the remote cloud server is denoted as RC. Meanwhile, the network model runs in discrete time slots In each time slot t, each MEC server receives computing tasks from the users it serves. Assume that the amount of computing tasks arriving at MEC server i is in, represents the maximum amount of tasks arriving at MEC server i, A i (t) is subject to the arrival rate λ i (t) is an independent and identically distributed Poisson process, at this time A i (t) = a i (t)+c i (t), a i (t) represents the part of the tasks that the server can handle, c i (t) indicates tasks that are migrated to other servers for processing.

[0049] Specifically, when A i (t)>K i (t), the task migration mode is triggered. MEC server i, as the migrator, needs to migrate the tasks that cannot be processed within its capacity to other MEC servers for processing. At this time, the task A received by MEC server i in time slot t i (t) is converted into three parts:

[0050]

[0051] Among them, c i0 (t) represents the task of migrating MEC server i to the remote cloud server RC. In particular, when the MEC server clusters all act as migrators, that is, N servers all satisfy A i (t)>K i At (t), there is no server with sufficient resources to receive the migrated task. At this time, the task needs to be migrated to the remote cloud server RC. It means that MEC server i can migrate the tasks that it cannot handle to any other MEC server in the same LAN.

[0052] Specifically, when A j (t)<K j At (t), the task collaboration mode is triggered. MEC server j, as a collaborator, needs to process the tasks migrated by the migrator on its own server. At this time, the amount of tasks that MEC server j needs to process is divided into two parts:

[0053]

[0054] in, Indicates tasks migrated from any other MEC server in the same LAN. It should be noted that c ji (t) and c ij (t) is the same size. MEC server j is a collaborator, indicating that its server resources are idle and can help other servers process. Therefore, the present invention has a ji The size of (t) is constrained, namely:

[0055] 0≤c ji (t)≤K j (t)-A j (t);

[0056] The research goal of this invention is to optimize the overall performance of the MEC cluster system. Therefore, in this invention, the following four delays are mainly considered, namely, the calculation delay of the MEC server, the queuing delay when the MEC server task is waiting for processing, the migration delay between MEC servers, and the return link delay of the MEC server migrating to the remote cloud server. Since this invention focuses on the performance of the MEC cluster, the upload delay of the user task and the processing delay of the remote cloud server are not considered. At the same time, the calculation result is very small, and the return delay of the calculation result is also ignored.

[0057] In one embodiment, when the MEC server acts as a migrator, the calculation delay T of the MEC server is mainly considered. m_cp (t), task queuing delay T m_qe (t), task migration delay T mg (t), backhaul link delay T bl (t), calculate the energy consumption E m_cp (t), migration energy consumption E m_mg (t), and when the MEC server acts as a collaborator, the main consideration is the calculation delay T of the MEC server c_cp (t), task queuing delay T c_qe (t), calculate the energy consumption E c_cp (t);

[0058] Specifically, after completing the task migration, f(t) is used to represent the computing resources allocated to the task by the MEC server, and f min (t)≤f(t)≤f max (t), the calculation formulas of each delay parameter are:

[0059] Migrator calculation delay:

[0060] Collaborator calculation delay:

[0061] Migrator queue delay:

[0062] Collaborator queuing delay:

[0063] Migration delay:

[0064] Backhaul link delay:

[0065] where γ is the computational density (in cycles / bit), s i (t) represents the constant transmission rate of optical fiber communication between base stations, s i0 (t) represents the transmission rate between the MEC server and the remote cloud server, a i (t) represents the amount of tasks that the ith edge server can handle, c i (t) represents the amount of tasks that the ith edge server migrates to other servers for processing, P j (t) is the total tasks that MEC server j needs to process.

[0066] The present invention mainly considers computing energy consumption and migration energy consumption, but the server is divided into migrators and collaborators, so the computing energy consumption is divided into migrators computing energy consumption and collaborators computing energy consumption. At the same time, the migration energy consumption is mainly generated by the migration server, so the energy consumption parameters are expressed as:

[0067] E m_cp (t) = ξ(f(t)) 2 T m_cp ;

[0068] E c_cp (t) = ξ(f(t)) 2 T c_cp ;

[0069] E m_mg (t) = 1·θc i (t)T mg (t)+1·θc i0 (t)T bl (t);

[0070] Among them, ξ represents the weighted parameter of the CPU energy consumption of the MEC server, and θ represents the energy consumption per unit task migration.

[0071] In one embodiment, a migrator cost model, a collaborator cost model, and a revenue model are constructed. Since this embodiment mainly considers latency cost and energy consumption cost, the sum of the migrator communication overhead in the migrator cost model and the sum of the collaborator communication overhead in the collaborator cost model are respectively expressed as:

[0072] Migrant: C m_cost (t) = α(T m_cp (t)+T m_qe (t)+1·T mg (t)+1·T bl (t))+β(E m_cp (t)+E m_mg (t));

[0073] Collaborator: C c_cost (t) = α(T c_cp (t)+T c_qe (t))+βE c_cp (t);

[0074] Among them, α is the unit time cost required for the server to process the task, and β is the unit energy consumption cost required for the server to process the task.

[0075] Define the cost that the migrator pays for purchasing computing tasks from the collaborator at time slot t as:

[0076] v ij (t) = p ij (t)c ij (t);

[0077] Among them, p ij (t) represents the unit task resource payment price.

[0078] According to game theory, the migrators and collaborators can also be called buyers and sellers. When the buyer migrates the task to the seller, he not only needs to pay a certain fee to the seller, but also needs to pay the communication overhead. Therefore, the buyer's maximum profit problem can be defined as:

[0079]

[0080] Based on the buyer's maximum profit problem, the relevant constraints are expressed as:

[0081] C1:0≤c ji (t)≤K j (t)-A j (t);

[0082] C2:A i (t)>K i (t);

[0083] C3:f min (t)≤f(t)≤f max (t);

[0084] Among them, C1 means that the size of the migrated task cannot exceed the remaining computing resources of the collaborator, otherwise, the migration task is offloaded to the remote cloud server; C2 means that in this state, server i is the migrator; C3 means that the computing resources of the MEC server cannot be less than the minimum f min (t), nor can it exceed the maximum f max (t).

[0085] The seller obtains a certain amount of income by selling his own remaining computing resources, and the seller's income is the fee paid by the buyer v ji (t) = v ij (t), but because the collaborators help to jointly process the migration task, the migration task will incur certain communication overhead, so the seller's maximum profit problem is:

[0086] maxU c (p ij (t)) = v ji (t)-C c_cost (t);

[0087] Based on the seller's maximization problem, the relevant constraints are expressed as:

[0088] C1:A i (t)<K i (t);

[0089] C2:p ij (t)>0;

[0090] Among them, C1 means that only when this condition is met can the server become a collaborator; C2 means that the unit price must be greater than 0 and the profit cannot become a negative value.

[0091] In order to maximize their own benefits, the buyer will decide the purchase strategy based on the buyer's payment costs. Taking the second-order derivative of the buyer's maximum benefit function, we can get Therefore U m (t) is about c i (t) is a convex function. Since the constraint condition is an affine function, the buyer optimization problem can be solved using the Lagrange multiplier method, and the Lagrange function is defined as:

[0092]

[0093] Using the KKT condition, the optimal value can be obtained The necessary and sufficient conditions are:

[0094]

[0095]

[0096] c ji* (t)-(K j (t)-A j (t))≤0;

[0097] λ * ≥0,μ * ≥0,π * ≥0;

[0098] when , find the optimal migration task amount for:

[0099]

[0100] in,

[0101] For collaborators, the higher the buyer pays, the higher its profit will be. However, for migrators, paying too high a fee means that it needs to pay a higher cost to purchase resources from collaborators. Therefore, there is an optimal bid that can optimize the profits of both collaborators and migrators. It can be seen that the profit of collaborators is about p ij (t) is a convex function, and the constraint condition is an affine function. Therefore, the seller optimization problem can also be solved by the Lagrange multiplier method, and the Lagrange function is constructed as follows:

[0102] L(p ij (t),ρ)=U c (p ij (t))-ρp ij (t);

[0103] Using the KKT condition, the necessary and sufficient conditions for the existence of the optimal value are:

[0104]

[0105]

[0106]

[0107] The optimal bidding strategy of the collaborator is:

[0108]

[0109] When the collaborator's offer ij (t) is fixed, the condition is met At the same time, when the task c migrated by the migrating i (t) is fixed, the condition is met but is the SE equilibrium solution, that is

[0110] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-server collaborative resource allocation method based on game theory, characterized in that: include: S1. Build a system model of multiple edge servers collaborating, where the edge servers in the system model act as migrators or collaborators; S2. Construct the cost model of the migrant, the cost model of the collaborator and the benefit model; The sum of the costs in the migrator cost model is expressed as: C m_cost (t)=α(T m_cp (t)+T m_qe (t)+1·T mg (t)+1·T bl (t))+β(E m_cp (t)+E m_mg (t)); Among them, T m_cp (t) is the delay for migrating, T m_qe is the queuing delay of the migrants, T mg (t) is the migration delay, T bl (t) is the return link delay, E m_cp (t) Calculate the energy consumption of the migrant, E m_mg (t) is the migration energy consumption of the migrator, α is the unit time cost required by the server to process the task, and β is the unit energy cost required by the server to process the task; The sum of the costs in the collaborator cost model is expressed as: C c_cost (t)=α(T c_cp (t)+T c_qe (t))+βE c_cp (t); Among them, α is the unit time cost required for the server to process the task, β is the unit energy cost required for the server to process the task, T c_cp (t) is the delay calculated by the collaborator, T c_qe (t) is the queuing delay of the collaborator, E c_cp (t) Calculate energy consumption for collaborators; Define the cost that the migrator pays for purchasing computing tasks from the collaborator at time slot t as: v ij (t)=p ij (t)c ij (t); Among them, p ij (t) represents the unit task resource payment price, c ij It means that MEC server i will migrate the tasks that it cannot process to MEC server j in the same LAN; S3. Construct a buyer's maximum profit model and a seller's maximum profit model through the three models constructed in step S2; The buyer's maximum profit model is constructed through the migration cost model and the profit model. The buyer's maximum profit problem is expressed as: Among them, C m_cost (t) is the total cost in the migrating cost model, v ij (t) represents the revenue model, i.e., the cost paid by the migrator to purchase computing tasks from the collaborator; Based on the buyer's maximum profit problem, the relevant constraints are expressed as: C1:0≤c ji (t)≤K j (t)-A j (t); C2:A i (t)>K i (t); C3:f min (t)≤f(t)≤f max (t); Among them, C1 means that the size of the migrated task cannot exceed the remaining computing resources of the collaborator, otherwise, the migration task is offloaded to the remote cloud server; C2 means that in this state, server i is the migrator; C3 means that the computing resources of the MEC server cannot be less than the minimum f min (t), nor can it exceed the maximum f max (t); K i (t) represents the CPU processing frequency limit of MEC server i, K j (t) represents the CPU processing frequency limit of MEC server j, A i (t) represents the amount of computing tasks arriving at the i-th edge server, A j (t) represents the amount of computing tasks arriving at the jth edge server, c ji represents the task of migrating from MEC server j to MEC server i in the same LAN; f(t) represents the computing resources allocated to the task by the MEC server; The seller's maximum profit model is constructed through the collaborator cost model and the profit model. The seller's maximum profit problem is expressed as: max U c (p ij (t))=v ji (t)-C c_cost (t); Among them, C c_cost (t) is the total cost in the collaborator cost model, v ji (t) represents the revenue model; Based on the seller's maximization problem, the relevant constraints are expressed as: C1:A i (t)<K i (t); C2:p ij (t)>0; Among them, C1 means that only if this condition is met, the server can become a collaborator; C2 means that the unit price must be greater than 0, and the profit cannot become a negative value; p ij (t) represents the unit task resource payment price; S4. Based on the buyer's maximization model, the optimal migration strategy of the migrators is calculated using the Lagrange multiplier method and KKT conditions; S5. According to the seller's maximum profit model and the optimal migration strategy, the optimal dynamic bidding strategy for the collaborator to pay the migrator is obtained; S6. Determine whether the optimal migration strategy and the optimal dynamic quotation strategy satisfy the Stackelberg equilibrium. If so, achieve optimal computing resource allocation.

2. A multi-server collaborative resource allocation method based on game theory according to claim 1, characterized in that: The amount of computing tasks arriving at each edge server in the system model is expressed as: A i (t)=a i (t)+c i (t); Among them, A i (t) represents the amount of computing tasks arriving at the i-th edge server, and represents the maximum amount of tasks that arrive at the i-th edge server, a i (t) represents the amount of tasks that the ith edge server can handle, c i (t) represents the amount of tasks that the i-th edge server migrates to other servers for processing.

3. The multi-server collaborative resource allocation method based on game theory according to claim 2 is characterized in that: Each MEC server has a CPU processing frequency limit, denoted as K i (t), when A i (t)>K i At (t), MEC server i acts as a migrator, and the total computing task of the migrator is: in, It means that MEC server i can migrate the tasks that cannot be processed to any other MEC server in the same LAN. i0 (t) represents the task migrated from MEC server i to the remote cloud server RC.

4. The multi-server collaborative resource allocation method based on game theory according to claim 3 is characterized in that: When A j (t)<K j At (t), MEC server j acts as a collaborator, and the total computing task of the collaborator is: At this time, P j (t) is the total tasks that MEC server j needs to process, Indicates the migration tasks received by MEC server j.

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