CN112308279A - Multi-server fund distribution method - Google Patents

Multi-server fund distribution method Download PDF

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CN112308279A
CN112308279A CN201910713698.4A CN201910713698A CN112308279A CN 112308279 A CN112308279 A CN 112308279A CN 201910713698 A CN201910713698 A CN 201910713698A CN 112308279 A CN112308279 A CN 112308279A
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server
fund
model
allocation
cost
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张功萱
张欢欢
王添
周俊龙
徐林丽
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/50—Allocation of resources, e.g. of the central processing unit [CPU]
    • G06F9/5083—Techniques for rebalancing the load in a distributed system
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06313—Resource planning in a project environment
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/067—Enterprise or organisation modelling

Abstract

The invention discloses a multi-server fund allocation method. The method comprises the following steps: firstly, establishing a fund consumption and server request model of a multi-server system to obtain the correlation between a service request and the fund consumption; then, different fund scheduling strategies are formulated according to the current available fund state of the system: in the high available fund state, only allocation is needed according to needs; when the fund is in a low available fund state, constructing a cooperative game model conforming to the multi-server system by using a game theory; and finally, converting the constructed cooperative game model by using a Lagrange multiplier method, and calculating a corresponding Nash equilibrium solution, thereby obtaining an optimal fund allocation scheme of the multi-server system. The method is simple to operate and high in practicability, improves the efficiency of the multi-server system, and reduces the hardware requirement of the multi-server system.

Description

Multi-server fund distribution method
Technical Field
The invention relates to the technical field of system resource allocation, in particular to a multi-server fund allocation method.
Background
For applications with corresponding workloads, cloud service providers must properly allocate existing resources to achieve maximum system throughput and ensure basic performance of individual servers. In cloud computing systems, it is important for service providers to balance resource allocation among multiple servers.
Hu et al (Y.Hu, J.Wong, G.Iszlai, and M.Litoiu, "Resource provisioning for closed computing," in Proceedings of the 2009Conference of the Center for Advanced students on Collapsitive research. IBM Corp.,2009, pp.101-111.) propose an autonomous fund management algorithm based on response time distribution for determining an appropriate fund allocation policy between the shared allocation and the dedicated allocation; kenli Li et al (Li K, Mei J, Li K.A fuel-constrained approximation scheme for modifying in closed computing. IEEE Trans Serv computing.2018; 11(6):893-907.https:// doi.org/10.1109/TSC.2016.2589241.) propose a heuristic strategy to overcome the selection problem in the application field, the strategy being proposed in order to satisfy the market demands in different application fields; mazzucco et al (m.mazzucco, d.dyachuk, and r.deters, maximum closed providers' customers via energy allocation policies, International Conference on Cloud Computing, IEEE,2010, pp.131-138.) solved the economic problem of Cloud Computing to a certain extent by reducing the power cost, the idea being to improve the utilization of servers based on dynamic user demands and system behaviors. However, the existing resource management schemes maintain system functions with limited resources and do not consider the throughput of each server and the fairness between the servers.
Disclosure of Invention
The invention aims to provide the multi-server fund distribution method which is simple to operate and high in practicability, can ensure the efficiency and also can give consideration to fairness among servers.
The technical solution for realizing the purpose of the invention is as follows: a multi-server fund allocation method comprising the steps of:
step 1, establishing a fund consumption and server request model of a multi-server system to obtain a correlation between a service request and the fund consumption;
step 2, making different fund scheduling strategies according to the current available fund state of the system: in the high available fund state, only allocation is needed according to needs; when the fund is in a low available fund state, constructing a cooperative game model conforming to the multi-server system by using a game theory; the high available fund state means that the system requirement is not greater than the existing fund, and the low available fund state means that the system requirement is greater than the existing fund;
and 3, converting the constructed cooperative game model by using a Lagrange multiplier method, and calculating a corresponding Nash equilibrium solution so as to obtain an optimal fund allocation scheme of the multi-server system.
Further, the step 1 of establishing a fund consumption and server request model of the multi-server system to obtain a correlation between the service request and the fund consumption includes:
step 1.1, initialize the capital requirement F of the multi-server systemdem＝0；
Step 1.2, establishing a task model of each server, and calculating the task quantity Q of each serveri,T：
Figure BDA0002154625550000021
Wherein Qi,TIs the amount of work of server i, λiIs the task arrival rate of server i, ciFor the execution cycle of the task, siThe speed of the server i is shown, and T is the working time;
step 1.3, establishing a cost model of each server, and calculating the cost C of each servertot,i：
Figure BDA0002154625550000022
Wherein C istot,iCost for server i, ρiFor server i utilization, ξ is the processor effective coefficient, ε is a constant greater than 0, Pbas,iIs the energy consumed by the server when idle, delta is the energy cost per unit time of the server, riIs the lease cost per unit time for server i;
step 1.4, establishing a fund model of each server, and calculating the total cost F of each server i for executing one taskcost,i：
Figure BDA0002154625550000023
Step 1.5, updating capital requirement F of systemdem＝Fdem+Ctot,i。
Further, step 2 of formulating different fund scheduling strategies according to the current available fund state of the system specifically includes:
step 2.1, if the system demand is not greater than the existing capital, Fdem≤FavlIn which F isavlFor existing funds, when the system is in a high-funds state, allocating funds to each server according to the requirements of that server, i.e. Ftot,i＝Ctot,i；
Step 2.2, if the system demand is greater than the current capital, Fdem＞FavlConstructing a cooperative game model according with the multi-server system by using a game theory, and calculating the fund allocated by the server
Figure BDA0002154625550000024
Figure BDA0002154625550000031
Wherein
Figure BDA0002154625550000032
Capital required to ensure initial performance of server i, α, βiIs a lagrange multiplier.
Further, the constructed cooperative game model is converted by using a lagrange multiplier method in the step 3, and a corresponding nash equilibrium solution is calculated, so that an optimal fund allocation scheme of the multi-server system is obtained, which specifically comprises the following steps:
step 3.1, converting the constructed cooperative game model into a corresponding dual problem;
step 3.2, solving the optimal solution of the dual problem, and solving the Lagrange multiplier alpha and beta through gradient projectioniA value of (d);
step 3.3, Lagrange multiplier alpha, betaiThe optimal solution of the dual problem is obtained by back substitution, namely the optimal fund allocation scheme of the multi-server system is obtained.
Compared with the prior art, the invention has the remarkable advantages that: (1) the operation is simple, and the practicability is strong: the cloud service provider only needs to calculate the cost required by each server and the fund demand of the system according to the model provided by the invention, and then allocates funds for each server according to the fund allocation scheme; the established cooperative game model is converted by using a Lagrange multiplier method, so that the optimal solution of fund allocation can be obtained more simply and conveniently; (2) the efficiency of the multi-server system is improved, the hardware requirement of the multi-server system is reduced: when the model is built, the throughput of each server and the efficiency of the server are considered, and the throughput of the server and the fairness between the servers can be considered under the condition of ensuring the system efficiency.
Drawings
FIG. 1 is a flow chart of a multi-server fund allocation method for ensuring basic operation indexes of servers according to the invention.
FIG. 2 is a schematic diagram of the structure of an M/M/M queuing system.
Detailed Description
The fund distribution strategy provided by the invention means that a load balancer distributes a user request to an application program server through a service provider. When the service provider is under-funded, the various application servers may engage in gambling to compete for limited resources with the goal of maintaining the possibility of timely completing their service requests or workloads. At the same time, service providers desire higher system throughput because there is an overall request to perform as many tasks as possible with limited funds. Obviously, in the case of shortage of funds, the allocation of funds to a multi-server system is essentially a resource sharing problem and can be solved by using a Nash bargaining method.
The Nash bargaining is a powerful technology widely applied to the problem of resource allocation, and based on the technology, the invention provides a game theory method for solving the problem of fund allocation of a multi-server system of a service provider. Modeling the distribution problem as a cooperative game among a plurality of servers, and deducing a Nash bargaining solution for distributing the shared fund source.
A multi-server fund allocation method comprising the steps of:
step 1, establishing a fund consumption and server request model of a multi-server system to obtain a correlation between a service request and the fund consumption;
step 2, making different fund scheduling strategies according to the current available fund state of the system: in the high available fund state, only allocation is needed according to needs; when the fund is in a low available fund state, constructing a cooperative game model conforming to the multi-server system by using a game theory; the high available fund state means that the system requirement is not greater than the existing fund, and the low available fund state means that the system requirement is greater than the existing fund;
and 3, converting the constructed cooperative game model by using a Lagrange multiplier method, and calculating a corresponding Nash equilibrium solution so as to obtain an optimal fund allocation scheme of the multi-server system.
Further, the step 1 of establishing a fund consumption and server request model of the multi-server system to obtain a correlation between the service request and the fund consumption includes:
step 1.1, initialize the capital requirement F of the multi-server systemdem＝0；
Step 1.2, establishing a task model of each server, and calculating the task quantity Q of each serveri,T：
Figure BDA0002154625550000041
Wherein Qi,TIs the amount of work of server i, λiIs the task arrival rate of server i, ciFor the execution cycle of the task, siThe speed of the server i is shown, and T is the working time;
step 1.3, establishing a cost model of each server, and calculating the cost C of each servertot,i：
Figure BDA0002154625550000042
Wherein C istot,iCost for server i, ρiFor server i utilization, ξ is the processor effective coefficient, ε is a constant greater than 0, Pbas,iIs the energy consumed by the server when idle, delta is the energy cost per unit time of the server, riIs the lease cost per unit time for server i;
step 1.4, establishing a fund model of each server, and calculating the total cost F of each server i for executing one taskcost,i：
Figure BDA0002154625550000043
Step 1.5, updating capital requirement F of systemdem＝Fdem+Ctot,i。
Further, step 2 of formulating different fund scheduling strategies according to the current available fund state of the system specifically includes:
step 2.1, if the system demand is not greater than the existing capital, Fdem≤FavlIn which F isavlFor existing funds, when the system is in a high-funds state, allocating funds to each server according to the requirements of that server, i.e. Ftot,i＝Ctot,i；
Step 2.2, if the system demand is greater than the current capital, Fdem＞FavlConstructing a cooperative game model according with the multi-server system by using a game theory, and calculating the fund allocated by the server
Figure BDA0002154625550000051
Figure BDA0002154625550000052
Wherein
Figure BDA0002154625550000053
Capital required to ensure initial performance of server i, α, βiIs a lagrange multiplier.
Further, the constructed cooperative game model is converted by using a lagrange multiplier method in the step 3, and a corresponding nash equilibrium solution is calculated, so that an optimal fund allocation scheme of the multi-server system is obtained, which specifically comprises the following steps:
step 3.1, converting the constructed cooperative game model into a corresponding dual problem;
step 3.2, solving the optimal solution of the dual problem, and solving the Lagrange multiplier alpha and beta through gradient projectioniA value of (d);
step 3.3, Lagrange multiplier alpha, betaiThe optimal solution of the dual problem is obtained by back substitution, namely the optimal fund allocation scheme of the multi-server system is obtained.
The invention is described in further detail below with reference to the figures and the embodiments.
Examples
Referring to fig. 1, the multi-server fund allocation method of the embodiment includes the following steps:
step 1, establishing a fund consumption and server request model of a multi-server system, and deriving the correlation between a service request and the fund consumption, which is as follows:
step 1.1, initialize the capital requirement F of the multi-server systemdem＝0；
Step 1.2, establishing a task model of each server:
referring to fig. 2, a server in the cloud computing system is regarded as an M/M queuing system, and is composed of N heterogeneous servers, and the task arrival rate of each server is λi。
Because the cloud computing system is a capital-sensitive system, the limited capital resources cannot support continuous operation of the servers. Therefore, the number of task executions on the server i is the smaller value between the number of tasks reached and the number of tasks that the server can handle during the Tjob, which is:
Figure BDA0002154625550000054
wherein
Figure BDA0002154625550000061
For the number of tasks reached during the Twork,
Figure BDA0002154625550000062
server i at rate s during operation for TiThe number of tasks that can be processed.
Step 1.3, establishing a cost model of each server:
the lease cost of server i is r in units of timeiThe energy cost is δ per watt cost, and the dynamic power per unit time of server i is expressed as:
Figure BDA0002154625550000063
where xi is the processor effective coefficient, ε is a constant having a value of
Figure BDA0002154625550000064
The total energy consumption of server i is the base power, expressed as:
Figure BDA0002154625550000065
wherein P isbas,iEnergy consumed when the server is idle;
due to the limited utilization rate of the servers in the cloud computing system, the speed of the server i is siThe utilization rate is as follows:
Figure BDA0002154625550000066
thus, the dynamic power consumption for the Ton time is:
Figure BDA0002154625550000067
the total consumption cost of the server i during the T work period is obtained as follows:
Figure BDA0002154625550000068
the total cost of a server i to perform a task is:
Figure BDA0002154625550000069
step 1.4, establishing a fund model of each server:
setting FavlFor funds available during the period of T work, Falloc,iThe fund distributed to each server in the system, wherein i is more than or equal to 1 and less than or equal to N, satisfies the following conditions:
Falloc,1+Falloc,2+…+Falloc,N＝Favl
the fund state of the system can be divided into a high fund state and a low fund state, and the low fund state is digitally represented as Favl≤Fdem；
Step 1.5, updating the fund requirement of the system: fdem＝Fdem+Ctot,i
Step 2, making different fund scheduling strategies according to the current available fund state of the system: in the high available fund state, only allocation is needed according to needs; and when the low available fund state is realized, a cooperative game model conforming to the multi-server system is constructed by using a game theory, and the specific steps are as follows:
the service provider needs two fund allocation strategies to allocate the fund in two system states, and when the system is in a high fund state, the service provider only needs to allocate the fund to each server according to fund requests of different servers; when the system is in a low-funded state, the individual servers need to compete again for funding to maximize their respective performance. At the same time, service providers need to maximize the throughput of the entire system, i.e., the revenue of the entire system through cooperation between the various servers.
The system distributes limited funds to each server, maximizes the throughput of the system on the premise of ensuring the performance of each server, namely maximizes the throughput of the whole system and a single server under the condition of limited funds, and provides a fund distribution scheme which can ensure the fairness among the servers and also can give consideration to the efficiency.
Step 2.1, if the system demand is not greater than the existing capital, Fdem≤FavlIn which F isavlFor existing funds, when the system is in a high-funds state, allocating funds to each server according to the requirements of that server, i.e. Ftot,i＝Ctot,i；
Step 2.2, if the system demand is greater than the current capital, Fdem＞FavlAnd constructing a cooperative game model conforming to the multi-server system by using a game theory, and calculating the fund distributed by the server.
And 3, converting the constructed cooperative game model by using a Lagrange multiplier method, and calculating a corresponding Nash equilibrium solution, so as to obtain an optimal fund allocation scheme of the multi-server system, wherein the method specifically comprises the following steps:
step 3.1, converting the constructed cooperative game model into a corresponding dual problem:
the problem of allocating available funds to multiple servers can create a model for cooperative gaming. To take efficiency and fairness into account, the problem is solved by Nash bargaining.
A cooperative game may be described in which N players (N servers) compete for the limited resources (funds) of their owners (service providers),
Figure BDA0002154625550000073
a space vector representing the allocation policy of the N servers.
Wherein R isNFor the set of allocation policies, X is a non-empty, closed, convex set.
A pair of (U, U)0) The problem is called cooperative gaming, the solution of which is called the Nash bargaining solution, which is to define a mapping that satisfies the Nash bargaining:
Map：(U,u0)→RN，Map(U,u0)∈U (8)
wherein
Figure BDA0002154625550000071
For the initial performance of each of the servers,
Figure BDA0002154625550000072
as a function of the server, fi(x) As a function of the performance of server i.
There is a unique Nash bargained solution u*And solution x*＝f-1(u*) I.e. solving the following problem:
Figure BDA0002154625550000081
in the cooperative game problem, at least two players enter the game with the performance function and initial performance requirements. The game also guarantees a minimum investment guarantee due to the initial performance agreement, which complies with the design requirements of capital-sensitive cloud computing systems, requiring maximum throughput of the system and lower investment limits for individual servers. For easier solution of the problem, (9) is equivalent to:
Figure BDA0002154625550000082
wherein P'JIs a convex optimization problem and has a unique solution which is the Nash bargained solution of (9).
Calculate server i to allocate fund F in its budgetalloc,iThe following performance functions:
Figure BDA0002154625550000083
in the invention, N servers can realize the performance strictly higher than the initial performance.
According to the cooperative game model, the problem of meeting the initial requirement of a single server through the overall throughput maximization system benefit is as follows:
Figure BDA0002154625550000084
Figure BDA0002154625550000085
Figure BDA0002154625550000086
Figure BDA0002154625550000087
wherein, the formula (13), the formula (14) and the formula (15) are three constraints which respectively represent: all available funds may be allocated to the server to perform the system's tasks; the funds allocated to each server cannot exceed the cost of the task performed on each server; the throughput achieved by each server is higher than its initial requirements.
Will PGThe problem is equivalent to:
Figure BDA0002154625550000088
solving the optimization problem with lagrange multipliers further translates equation (16) into:
Figure BDA0002154625550000091
the lagrangian expression of equation (17) is:
Figure BDA0002154625550000092
wherein
Figure BDA0002154625550000093
α、βi、γiIs the Lagrange multiplier related in the constraints of the equations (13) to (15), and obtains the optimal solution when the derivative of the function is zero, and the digital expression is as follows:
Figure BDA0002154625550000094
wherein
Figure BDA0002154625550000095
Is the capital required to ensure initial performance of server i, and the following KKT condition should be met:
Figure BDA0002154625550000096
Figure BDA0002154625550000097
Figure BDA0002154625550000098
the optimal solution for (17) can therefore be derived as:
Figure BDA0002154625550000099
wherein alpha, betai,γiIs a function of the lagrange multiplier and,
Figure BDA00021546255500000910
is a problem PGEnsuring initial performance
Figure BDA00021546255500000911
The optimal solution of (1).
To obtain the optimal solution, it is necessary to obtain the values of the lagrange multipliers that satisfy the KKT condition, in equation (22)
Figure BDA00021546255500000912
Indicating that the server i performance is equal to its initial performance
Figure BDA00021546255500000913
For profitability, in the invention
Figure BDA0002154625550000101
Thus, γ can be obtainedi＝0。
In summary, the key of solving the optimal solution of the equation (17) is to obtain the value of the lagrangian multiplier, and the lagrangian multiplier is independent of other servers, so that the optimization problem is converted into a corresponding dual problem to solve the optimal solution.
Step 3.2, solving the optimal solution of the dual problem, and solving the Lagrange multiplier alpha and beta through gradient projectioniThe value of (c):
due to PGIs a convex optimization problem with 3N constraint, has corresponding dual problem, the solution of the dual problem provides a lower bound solution for the original problem, the difference between the two solutions is dual gap, under the special condition that the dual gap is zeroThe optimal solution of the dual problem is the optimal solution of the original problem.
The lagrange problem of upper complaints
Figure BDA0002154625550000102
Corresponding dual problem d (alpha, beta)i,γi) The expression of (a) is:
Figure BDA0002154625550000103
the original problem has a unique optimal solution, and the Lagrangian function has a unique optimal solution for each of the optimal solutions of (17)
Figure BDA0002154625550000104
The upper has a lower bound for any
Figure BDA0002154625550000105
βi,γiNot less than 0 is
Figure BDA0002154625550000106
Wherein
Figure BDA0002154625550000107
Is that
Figure BDA0002154625550000108
An infimum limit; the derivative of the Lagrangian function is equal to zero when the lower bound exists, thus obtaining equation (23), and equation (23) and gammaiFormula (18) is substituted by 0, and the expression (24) for the dual function can be further derived as:
Figure BDA0002154625550000109
when (25) there is an optimal solution Falloc,iWhen, the inequality is strictly satisfied
Figure BDA00021546255500001010
And
Figure BDA00021546255500001011
Figure BDA00021546255500001012
this indicates that the inequalities of constraint equation (14) and equation (15) are strictly satisfied, and the slaite condition is satisfied; because of the problem PGConvex, satisfying both the sllate condition and the KKT condition, it can be deduced that the problem has strong duality, i.e. the duality gap is zero, and there is at least one optimal solution, so the only optimal solution of the duality problem is the only optimal solution of the original problem, and the original problem P can be obtainedGCorresponding dual problem, and no dual gap, expressed as:
Figure BDA00021546255500001013
step 3.3, Lagrange multiplier alpha, betaiThe value of (2) is substituted back to obtain the optimal solution of the dual problem, namely the optimal fund allocation scheme of the multi-server system:
to obtain the original problem PGThe optimal solution of (2) needs to be obtained first. Solving lagrange multipliers alpha, beta by gradient projectioniAnd then lagrange multipliers α, βiThe values of (a) are back-substituted to obtain the optimal solution to the dual problem. For ease of solution, equation (26) is converted to:
Figure BDA0002154625550000111
s.t.βi≥0 (28)
Figure BDA0002154625550000112
wherein d (α, β)i)*＝-d(α,βi) Equation (27) represents that the funds allocated to server i cannot exceed the maximum funds constraint it requires.
Gradient projection is widely usedThe use of a greedy search in the gradient project may be trapped in local optima for solving the constrained optimization problem. Therefore, it is necessary to verify that the solution obtained by the gradient method is a globally optimal solution by analysis. Dual function d (alpha, beta)i)*Is convex and has a hessian matrix with each element not less than zero as follows:
Figure BDA0002154625550000113
in summary, the function d (α, β)i)*Is convex, so the solution obtained by the gradient method is the globally optimal solution, which is also the original problem PGThe optimal Nash bargaining solution.

Claims (4)

1. A multi-server fund allocation method, comprising the steps of:
step 1, establishing a fund consumption and server request model of a multi-server system to obtain a correlation between a service request and the fund consumption;
step 2, making different fund scheduling strategies according to the current available fund state of the system: in the high available fund state, only allocation is needed according to needs; when the fund is in a low available fund state, constructing a cooperative game model conforming to the multi-server system by using a game theory; the high available fund state means that the system requirement is not greater than the existing fund, and the low available fund state means that the system requirement is greater than the existing fund;
and 3, converting the constructed cooperative game model by using a Lagrange multiplier method, and calculating a corresponding Nash equilibrium solution so as to obtain an optimal fund allocation scheme of the multi-server system.
2. The method for allocating funds of multiple servers according to claim 1, wherein the step 1 of establishing a fund consumption and server request model of the multiple server system to obtain the correlation between the service request and the fund consumption comprises the following steps:
step 1.1, initialize the multi-serverCapital requirement of the system Fdem＝0；
Step 1.2, establishing a task model of each server, and calculating the task quantity Q of each serveri，T：
Figure FDA0002154625540000011
Wherein Qi，TIs the amount of work of server i, λiIs the task arrival rate of server i, ciFor the execution cycle of the task, siThe speed of the server i is shown, and T is the working time;
step 1.3, establishing a cost model of each server, and calculating the cost C of each servertot，i：
Figure FDA0002154625540000012
Wherein C istot，iCost for server i, ρiFor server i utilization, ξ is the processor effective coefficient, ε is a constant greater than 0, Pbas，iIs the energy consumed by the server when idle, delta is the energy cost per unit time of the server, riIs the lease cost per unit time for server i;
step 1.4, establishing a fund model of each server, and calculating the total cost F of each server i for executing one taskcost，i：
Figure FDA0002154625540000013
Step 1.5, updating capital requirement F of systemdem＝Fdem+Ctot，i。
3. The method for multi-server fund allocation according to claim 1, wherein the step 2 of formulating different fund scheduling policies according to the current available fund status of the system comprises the following specific steps:
step 2.1, if the system demand is not greater than the existing capital, Fdem≤FavlIn which F isavlFor existing funds, when the system is in a high-funds state, allocating funds to each server according to the requirements of that server, i.e. Ftot，i＝Ctot，i；
Step 2.2, if the system demand is greater than the current capital, Fdem＞FavlConstructing a cooperative game model according with the multi-server system by using a game theory, and calculating the fund allocated by the server
Figure FDA0002154625540000021
Figure FDA0002154625540000022
Wherein
Figure FDA0002154625540000023
Capital required to ensure initial performance of server i, α, βiIs a lagrange multiplier.
4. The method for multi-server fund allocation according to claim 1, wherein the Lagrange multiplier method is used for transforming the constructed cooperative game model in the step 3, and a corresponding Nash equilibrium solution is calculated, so as to obtain an optimal fund allocation scheme of the multi-server system, which is specifically as follows:
step 3.1, converting the constructed cooperative game model into a corresponding dual problem;
step 3.2, solving the optimal solution of the dual problem, and solving the Lagrange multiplier alpha and beta through gradient projectioniA value of (d);
step 3.3, Lagrange multiplier alpha, betaiThe optimal solution of the dual problem is obtained by back substitution, namely the optimal fund allocation scheme of the multi-server system is obtained.
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