Cost and reliability-aware profit optimization method for heterogeneous multi-server systems

Abstract

This invention discloses a cost- and reliability-aware profit optimization method for a heterogeneous multi-server system. The method includes: establishing a heterogeneous multi-server system model to obtain expected service revenue and multi-server system utilization; establishing a soft error reliability model to formulate the application domain investment selection and profit maximization problem as a constrained nonlinear optimization problem; utilizing an iterative method based on a penalty function to obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain, and converting the profit and configuration optimization problem of the heterogeneous multi-server system into a 0-1 knapsack problem; and utilizing a dynamic programming-based algorithm and a greedy-based algorithm to solve the optimal application domain investment strategy and the corresponding maximum profit. This method can consider budget constraints and the soft error reliability of service requests while configuring the heterogeneous multi-server system configuration, thereby improving cloud service quality and provider profits.

Description

Technical Field

[0001] The present invention belongs to the technical field of profit maximization, and in particular to a cost- and reliability-aware profit optimization method for a heterogeneous multi-server system. Background Art

[0002] Cloud computing is a promising IT business model that has attracted widespread attention from both academia and industry over the past decade. Cloud computing is being used for a variety of application domains, such as email, virtual desktops, big data analytics, and customer-facing web applications. Cloud computing's elasticity allows for the availability of computing resources tailored to customer needs, and allows for rapid scaling of computing resources to accommodate changing service demands. To maximize profits, cloud service providers must develop an optimal application domain investment strategy, as budgets are often limited and cannot support all application domains.

[0003] In terms of increasing service revenue to improve the profit of service providers. Chaisiri et al. (Z. Yang, Y. Cui, X. Wang, Y. Liu, M. Li, and Z. Zhang, "Towards maximal service profit in geo-distributed clouds," in Proceedings of the International Conference on Distributed Computing Systems (ICDCS), pp. 442-452, 2019.) proposed a stochastic programming strategy with two-stage resources to maximize the profit of service providers, which takes into account the uncertainty of service demand. Cao et al. (J. Cao, K. Huang, K. Li, and AY Zomaya, "Optimal multiserver configuration for profit maximization in cloud computing," IEEE Transactions on Parallel and Distributed Systems, vol. 24, no. 6, pp. 1087-1096, 2013.) proposed a dynamic pricing strategy to maximize the profit of service providers by increasing service revenue and an optimal multi-server configuration with two speed models. Mei et al. (M. Jing, K. Li, A. Ouyang, and K. Li, "A profit maximization scheme with guaranteed quality of service in cloud computing," IEEE Transactions on Computing, vol. 64, no. 11, pp. 3064-3078, 2015.) designed a revenue guarantee strategy to maximize the service provider's profit by utilizing long-term leases and short-term server leasing schemes to ensure that service processing is completed within the deadline.

[0004] Several works have helped reduce the operating costs of cloud service platforms to maximize service provider profits. Ye et al. (X. Ma, S. Wang, S. Zhang, P. Yang, C. Lin, and X. Shen, "Costefficient resource provisioning for dynamic requests in cloud-assisted mobile edge computing," IEEE Transactions on Cloud Computing, vol. 9, no. 3, pp. 968-980, 2021) developed an autonomous resource management scheme that improves service provider profits by reducing server energy consumption, thereby saving electricity costs. This scheme can derive the minimum number of servers that meet service level requirements. Beloglazov et al. (A. Beloglazov, J. Abawajy, and R. Buyya, "Energy-aware resource allocation heuristics for efficient management of data centers for cloud computing," Future Generation Computer Systems, vol. 28, no. 5, pp. 755-768, 2012) also developed a resource management strategy, but reduced the monetary cost of energy consumption in cloud data centers by increasing server utilization.

[0005] While many schemes effectively improve service provider profits in various ways, few consider the adverse impact of soft errors in their work. When designing multi-server configuration schemes to maximize profits, most work assumes that all cloud service requests have the same maximum latency. This assumption fails to account for the heterogeneity of cloud service request timeliness. Furthermore, most existing work maximizes service profits and optimizes multi-server configurations, focusing on a single application domain. However, providing services to multiple application domains can improve both the quality and profits of cloud service providers. Summary of the Invention

[0006] The purpose of the present invention is to address the problems existing in the above-mentioned prior art and provide a cost- and reliability-aware heterogeneous multi-server system profit optimization method. In a multi-server configuration, under limited budget and reliability constraints, the profit of the service provider is maximized by optimizing the cloud platform configuration of the invested application domain.

[0007] The technical solution to achieve the purpose of the present invention is: a cost- and reliability-aware heterogeneous multi-server system profit optimization method, the method comprising the following steps:

[0008] Step 1: Establish a heterogeneous multi-server system model and obtain the expected service revenue and multi-server system utilization based on the probability distribution of the maximum waiting time of cloud service requests;

[0009] Step 2: Build a soft error reliability model for processing service requests on a multi-server system. Based on the service revenue and soft error reliability model, formulate the application domain investment selection and profit maximization problem as a constrained nonlinear optimization problem.

[0010] Step 3: Using an iterative method based on a penalty function, we obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, we transform the profit and configuration optimization problem of heterogeneous multi-server systems into a 0-1 knapsack problem.

[0011] Step 4: Based on the converted 0-1 knapsack problem and the preferences of cloud server providers, the optimal application domain investment strategy and the corresponding maximum profit are solved using a dynamic programming-based algorithm and a greedy-based algorithm.

[0012] Furthermore, in step 1, a heterogeneous multi-server system model is established, and the expected service revenue and multi-server system utilization are obtained based on the probability distribution of the maximum waiting time of cloud service requests, as follows:

[0013] Step 1-1, establish a heterogeneous multi-server system model, specifically: use n heterogeneous multi-server systems MS1, MS2, ..., MS n Build a cloud computing environment, the number of servers in each cloud server system is m1, m2, ..., m n ; Consider the servers in each cloud service system as M / M / m i Queuing system, by m i It consists of homogeneous servers with a running speed of s;

[0014] Step 1-2, establish a service level agreement model, specifically: the service level agreement model C is based on the service waiting time π in the queuing system i and service request processing requirements i Processing is performed, which is expressed as:

[0015]

[0016] Among them, a is a constant, which represents the service fee per unit of service, and x i It is MS iThe maximum tolerable waiting time for a service request;

[0017] Cloud service requests have soft real-time requirements. The soft real-time requirements of service requests are usually specified by two metrics, namely, deadline and maximum waiting time;

[0018] Multi-server system MS i The slack x of the service request with soft real-time requirements follows a uniform distribution and is expressed as S(x i ):

[0019]

[0020] Among them, S min,i and S max,i are the minimum and maximum values ​​of relaxation, respectively;

[0021] Let C i For application domain A i The expected cost of a service request is derived as:

[0022]

[0023] in, is the average value of service request processing demand; μ i is the average service rate of the server, denoted as μ i =s i / r i ρ i It is a multi-server system MS i System utilization; represents the probability that there are exactly m tasks in the queue system;

[0024] Steps 1-3, establishing a cost model, specifically include: the cost of cloud service providers consists of two parts, infrastructure usage costs and utility costs for energy consumption;

[0025] The cost of renting a server per unit time is v, so the construction includes m i Multi-server system MS i Cost rent,i :

[0026] Cost rent,i =m i v (4)

[0027] Heterogeneous multi-server system MS i The utility cost per unit time is Cost utility,i :

[0028]

[0029] Among them, ξs 3 is the dynamic power of the server, where ξ is a hardware-related coefficient related to the processor; For heterogeneous multi-server system MS i At a rate s per unit time i Dynamic energy consumption during operation; E * represents the energy consumption per unit time when the server is idle, and assumes that the energy price is δ per watt;

[0030] Multi-server system MS i The total cost per unit time is Cost i :

[0031]

[0032] Furthermore, in step 2, a soft error reliability model for processing service requests on a multi-server system is established. Based on the service revenue and soft error reliability model, the application domain investment selection and profit maximization problem is formulated as a constrained nonlinear optimization problem, specifically including:

[0033] Step 2-1: Establish a soft error reliability model, specifically:

[0034] The soft error rate follows an exponential distribution, denoted as λ se (s i ):

[0035]

[0036] Among them, s l,i is the lower bound of server speed, λ 0,i Is the server at maximum speed s u,i Soft error rate during runtime, d 0,i is a hardware-dependent constant that reflects the sensitivity of the server to soft errors; i It is the server system MS i The running speed of; e is a natural constant;

[0037] Calculations from application domain A i The expected soft error reliability SER of the service request i :

[0038]

[0039] Calculate MS per unit time i The expected number of service requests processed in Q,i :

[0040]

[0041] Among them, λ i Is application domain A i service arrival rate;

[0042] Thus, the multi-server system MS i The system service utilization of is re-derived as:

[0043]

[0044] Step 2-2, express the profit maximization problem as:

[0045]

[0046] st:ρ i <1, (12)

[0047] I i (1-I i )=0, (13)

[0048] s l ≤s i ≤s u , (14)

[0049] m l ≤m i ≤m u , (15)

[0050]

[0051]

[0052] Among them, Profit represents profit, 0-1 variable I i Indicates whether the CSP is application domain A i Building a multi-server system; l and s u are the lower and upper limits of the server rate, m l and m u are the lower and upper bounds of the number of servers, respectively, and B represents a limited budget.

[0053] Furthermore, in step 3, an iterative method based on a penalty function is used to obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, the profit and configuration optimization problem of the heterogeneous multi-server system is converted into a 0-1 knapsack problem, which specifically includes:

[0054] Step 3-1, calculate application domain A i Maximum profit:

[0055] Max:Profit i =λ i ·C i -Cost i (18)

[0056]

[0057] s l ≤s i ≤s u ,i=1,2,...,n, (20)

[0058] m l ≤m i ≤m u ,i=1,2,...,n, (21)

[0059] Cost i -B≤0,i=1,2,...,n. (22)

[0060] Among them, Profit i To serve application domain A i profits;

[0061] Step 3-2, calculate the penalty function:

[0062] Convert the constraint problem in step 3-1 into standard form:

[0063] Min:O(m i ,s i )=-Profit i =-(λ i ·C i -Cost i ) (twenty three)

[0064]

[0065] g2(m i ,s i )=m l -m i ≤0, (25)

[0066] g3(m i ,s i )=m i -m u ≤0, (26)

[0067] g4(m i ,s i )=s l -s i ≤0, (27)

[0068] g5(m i ,s i )=s i -s u ≤0. (28)

[0069] Among them, g j (m i ,s i ) represents the constraint on the equation, j = 1, 2, ..., 5;

[0070] The penalty function is thus expressed as F(m i ,s i ):

[0071] F(m i ,s i )=O(m i ,s i )+φ(m i ,s i ) (29)

[0072] Among them, φ(m i ,s i ) is the external penalty period, specifically:

[0073]

[0074] Among them, σ is the penalty coefficient;

[0075] Step 3-3, calculate the partial derivative of the penalty function:

[0076] 1)O(m i ,s i ) is:

[0077]

[0078] (3) Solve C i The partial derivative of

[0079] Applying Taylor series expansion, C i Rewritten as:

[0080]

[0081] Let D1, D2 and D3 be expressed as:

[0082]

[0083] Then C i About m i The partial derivative of is expressed as:

[0084]

[0085] C i About s i The partial derivative of is:

[0086]

[0087] Export as:

[0088]

[0089] in,

[0090]

[0091] λ se (s i ) is given by formula (7);

[0092] (4) Calculate Cost i The partial derivative of

[0093] Cost i To m i and s i The partial derivative of is:

[0094]

[0095] C i Partial derivatives and Cost i Add the partial derivatives of O(m i ,s i ) of the partial derivative; 2) φ(m i ,s i ) is rewritten as:

[0096]

[0097] Then φ(m i ,s i ) for m i and s i The partial derivative of is:

[0098]

[0099]

[0100] Step 3-4, calculate the optimal numerical solution based on the iterative method of penalty function, specifically: use the penalty term φ(m i ,s i ), iteratively obtain F(m i ,s i ) is the optimal numerical solution m i* and s i * ; The input of the algorithm is the threshold L of the number of iterations and the amplification rate of the penalty coefficient η.

[0101] Furthermore, the iterative method based on the penalty function described in steps 3-4 calculates the optimal numerical solution, and the specific process includes:

[0102] Step 3-4-1, randomly generate the initial solution (m i (0) ,s i (0) ), and initialize the penalty coefficient σ and iteration counter l;

[0103] Step 3-4-2, determine whether the solution is less than a preset threshold between the penalty function shown in Formula 29 and the constraint problems shown in Formulas 23 to 28, that is, ||φ(m i (l) ,s i (l) )||<ε, if so, the obtained solution is an acceptable solution to the constraint problem;

[0104] Step 3-4-3, obtain the optimal solution from the acceptable solutions (m i * ,s i * ), calculate the total cost corresponding to the optimal solution according to Formula 6 and Formula 11 respectively i * and maximum profit i * ;

[0105] Step 3-4-4: Determine whether the current number of iterations reaches the set iteration threshold. If so, execute step 3-4-6; otherwise, execute step 3-4-5.

[0106] Step 3-4-5: If the optimal solution to the constraint problem is not found during the iteration, update the penalty coefficient σ and return to step 3-4-2 to continue execution;

[0107] Step 3-4-6, return the optimal solution and the maximum profit and total cost, that is, [Profit i * ,Cost i * ,m i * ,s i * ].

[0108] Furthermore, in steps 3-4, GD-Solver is used to obtain the optimal numerical solution of the penalty function. When obtaining the optimal solution of Formula 11, the penalty term only needs to be changed to:

[0109]

[0110] Furthermore, based on the converted 0-1 knapsack problem in step 4, according to the preferences of the cloud server provider, the optimal application domain investment strategy and the corresponding maximum profit are solved using a dynamic programming-based algorithm and a greedy-based algorithm, specifically including:

[0111] Step 4-1: When the cloud service provider prefers to prioritize efficiency, a knapsack problem based on a greedy algorithm is used to solve the optimal application domain investment strategy and the corresponding maximum profit. The input of the algorithm is the budget of the CSP, the cost consumed, and the application domain A. i maximum profit;

[0112] In step 4-2, when the cloud service provider prefers to prioritize profit, a knapsack problem based on dynamic programming is used to solve the optimal application domain investment strategy and the corresponding maximum profit. The input of the algorithm is the same as that of the greedy algorithm.

[0113] Step 4-3, based on the best application domain investment strategy and the corresponding maximum profit obtained above, use the corresponding algorithm to calculate the multi-server investment application domain configuration solution based on the backpack; the input of the algorithm includes application domain A 1:n The maximum profit array is Profit 1:n , application domain A 1:n Cost array * 1:n ,MS 1:n The optimal server size array is m * 1:n , and MS 1:n The best server speed array is s * 1:n .

[0114] Furthermore, the specific process of step 4-1 includes:

[0115] Step 4-1-1, Initialize the optimal application domain investment strategy I 1:n , I i =0, and the accumulated usage cost Cost temp and the total maximum profit totProfit is set to 0;

[0116] Step 4-1-2, according to Profiti Arrange the values ​​of the Profit array in descending order 1:n and from the maximum profit array Profit 1:n Search for the maximum profit Profit i , add the cost of this item to Cost temp Middle; judge the accumulated cost at this time temp Less than the limited budget B, record that the item has been selected, that is, let I i =1, add the maximum profit of this item to totProfit, and delete Profit in the maximum profit array i ;

[0117] Step 4-1-3, repeat step 4-1-2 until there is no element that makes the cumulative cost Cost temp If the condition that the budget is less than B is met, the algorithm ends and the optimal application domain investment strategy I is returned. 1:n And the total maximum profit value totProfit.

[0118] Furthermore, the specific process of step 4-2 includes:

[0119] Step 4-2-1, recursively derive the optimal application domain investment strategy and the corresponding maximum profit. The recursive process algorithm is expressed as:

[0120]

[0121] This is a dynamic programming algorithm. f(i,B) is the decision of the 0th to the i-th application domain A i The maximum total profit when f(i,B) is the final value of the budget and the application domain A i Cost decision for building a multi-server system. When the budget is larger than the application domain A i When building a multi-server system, there are two cases: when application domain A i When a multi-server system is not built, f(i,B) will be directly equal to the decision of application domain A from 0th to i+1th. i+1 The maximum total profit f(i+1,B) when the budget B will not be reduced; when the application domain A i When a multi-server system is built, f(i,B) will be equal to the decision of application domain A from 0th to i+1th i+1 The maximum total profit when adding the application domain A i The maximum profit f(i+1,B-Cost i * )+Profit i * , budget B is reduced by the amount for application domain Ai Cost of building a multi-server system i * When the budget is less than the application domain A i When building a multi-server system, the cost of f(i,B) will be directly equal to the cost of deciding the 0th to i+1th application domain A. i+1 The maximum total profit f(i+1,B) at this time.

[0122] Step 4-2-2, ends when the recursion reaches the boundary, and returns the best application domain investment strategy I 1:n And the total maximum profit value totProfit is obtained.

[0123] Furthermore, the specific process of step 4-3 includes:

[0124] Step 4-3-1, set the total cost of the server system MS, i.e., totCost, to 0, and initialize the array newArrM of the optimal server size and the array newArrS of the optimal server speed to two empty arrays;

[0125] Step 4-3-2, based on the algorithm selected by the cloud service provider's preference, the best application domain investment strategy and the maximum profit, calculate the total cost of configuring MS, and put the corresponding optimal configuration into newArrM and newArrS respectively;

[0126] In step 4-3-3, after putting all elements into newArrM and newArrS, the results are returned, including the best application domain investment strategy, total profit, total cost, and optimal configuration.

[0127] Compared with the prior art, the present invention has the following significant advantages:

[0128] This paper achieves cost- and reliability-aware profit optimization for heterogeneous multi-server systems by establishing a heterogeneous multi-server system model and a soft error reliability model, and utilizing penalty function-based iterative methods and other technical means. A novel analytical method can derive the soft error reliability of an average strategy, further exploring the adverse impact of soft errors on multi-server system utilization. Furthermore, the profit and configuration optimization problem for heterogeneous multi-server systems is converted into a 0-1 knapsack problem, and dynamic programming and greedy algorithms are used to solve the optimal application domain investment strategy and maximize profit.

[0129] The technical approach of this invention can help cloud service providers configure heterogeneous multi-server systems while considering budget constraints and soft error reliability of service requests, thereby improving cloud service quality and provider profits. Compared with existing technologies, the method of this invention can increase profits by up to 8.38%. The details are as follows:

[0130] 1) Considering the adverse effects of soft errors on the utilization of multi-server systems, the quality of cloud services and the profits of providers are improved;

[0131] 2) Using an iterative method based on penalty functions, we can efficiently obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain;

[0132] 3) Converting the profit and configuration optimization problem of heterogeneous multi-server systems into a 0-1 knapsack problem makes the problem easier to solve;

[0133] 4) Dynamic programming and greed-based algorithms can efficiently solve the optimal application domain investment strategy and maximize profits;

[0134] 5) It improves the economic benefits and user experience of cloud services and has high application value and business prospects.

[0135] The present invention is further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0136] Figure 1 This is a flow chart of the cost- and reliability-aware heterogeneous multi-server system profit optimization method of the present invention. DETAILED DESCRIPTION

[0137] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0138] It should be noted that if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or suggesting their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of such features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the fact that they can be implemented by ordinary technicians in this field. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0139] In one embodiment, combined Figure 1 , provides a cost and reliability-aware profit optimization method for a heterogeneous multi-server system, the method comprising the following steps:

[0140] Step 1: Establish a heterogeneous multi-server system model and obtain the expected service revenue and multi-server system utilization based on the probability distribution of the maximum waiting time of cloud service requests;

[0141] Step 2: Build a soft error reliability model for processing service requests on a multi-server system. Based on the service revenue and soft error reliability model, formulate the application domain investment selection and profit maximization problem as a constrained nonlinear optimization problem.

[0142] Step 3: Using an iterative method based on a penalty function, we obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, we transform the profit and configuration optimization problem of heterogeneous multi-server systems into a 0-1 knapsack problem.

[0143] Step 4: Based on the converted 0-1 knapsack problem and the preferences of cloud server providers, the optimal application domain investment strategy and the corresponding maximum profit are solved using a dynamic programming-based algorithm and a greedy-based algorithm.

[0144] Furthermore, in one embodiment, a heterogeneous multi-server system model is established in step 1, and the expected service revenue and multi-server system utilization are obtained based on the probability distribution of the maximum waiting time of cloud service requests, as follows:

[0145] Step 1-1, establish a heterogeneous multi-server system model, specifically: use n heterogeneous multi-server systems MS1, MS2, ..., MS n Build a cloud computing environment, the number of servers in each cloud server system is m1, m2, ..., m n ; Consider the servers in each cloud service system as M / M / m i Queuing system, by m i The processing demand of service requests is determined by the number of executed instructions r. i To quantify, r i is a mean An exponential random variable. i The probability distribution function of The running time of a service request is also an exponential random variable, that is, t i =r i / s i , the mean is Let μ i is the average service rate of the server (in terms of the speed at which the server can provide data per unit time s i The average number of service requests processed is measured), denoted as μ i =s i / ri .

[0146] Let P k i For MS i The probability of waiting for or processing k service requests in a multi-server system:

[0147]

[0148] P0 i is the probability that there is no task in the queueing system, P b i Indicates that when all servers are busy, the newly arrived service request is i The probability of waiting in a queue system is represents the probability that there are exactly m tasks in the queue system, P0 i 、P b i 、 Respectively expressed as:

[0149]

[0150]

[0151]

[0152] f w (x i ) indicates MS i The waiting time x for a service request in the queuing system i The probability distribution function is expressed as:

[0153]

[0154] u(x i ) is the unit pulse function, expressed as:

[0155]

[0156] u(x i )=lim z→∞ u z (x i ) is established. z (x i ) also satisfies the following two properties:

[0157]

[0158] Step 1-2, establish a service level agreement model, specifically: the service level agreement model C is based on the service waiting time π in the queuing system i and service request processing requirementsi Processing is performed, which is expressed as:

[0159]

[0160] Among them, a is a constant, which represents the service fee per unit of service, and x i It is MS i The maximum tolerable waiting time for a service request;

[0161] Cloud service requests have soft real-time requirements. The soft real-time requirements of service requests are usually specified by two metrics, namely, deadline and maximum waiting time;

[0162] Multi-server system MS i The slack x of the service request with soft real-time requirements follows a uniform distribution and is expressed as S(x i ):

[0163]

[0164] Among them, S min,i and S max,i are the minimum and maximum values ​​of relaxation, respectively;

[0165] Let C i For application domain A i The expected cost of a service request is derived as:

[0166]

[0167] in, is the average value of service request processing demand; μ i is the average service rate of the server, denoted as μ i =s i / r i ρ i It is a multi-server system MS i System utilization;

[0168] Steps 1-3, establishing a cost model, specifically include: the cost of cloud service providers consists of two parts, infrastructure usage costs and utility costs for energy consumption;

[0169] The cost of renting a server per unit time is v, so the construction includes m i Multi-server system MS i Cost rent,i :

[0170] Cost rent,i =m i v (54)

[0171] Heterogeneous multi-server system MS i The utility cost per unit time is Cost utility,i :

[0172]

[0173] Among them, ξs 3 is the dynamic power of the server, where ξ is a hardware-related coefficient related to the processor; For heterogeneous multi-server system MS i At a rate s per unit time i Dynamic energy consumption during operation; E * represents the energy consumption per unit time when the server is idle, and assumes that the energy price is δ per watt;

[0174] Multi-server system MS i The total cost per unit time is Cost i :

[0175]

[0176] Furthermore, in one embodiment, step 2 establishes a soft error reliability model for processing service requests on a multi-server system; based on the service revenue and soft error reliability model, the application domain investment selection and profit maximization problem is formulated as a constrained nonlinear optimization problem, specifically including:

[0177] Step 2-1: Establish a soft error reliability model, specifically:

[0178] The soft error rate is the average number of transient failures that occur when a service request is running on the server. The soft error rate follows an exponential distribution, denoted by λ se (s i ):

[0179]

[0180] Among them, s l,i is the lower bound of server speed, λ 0,i Is the server at maximum speed s u,i Soft error rate during runtime, d 0,i is a hardware-dependent constant that reflects the sensitivity of the server to soft errors;

[0181] Soft Error Reliability (SER) is defined as the probability of completing a service request in a multi-server system without encountering any transient failures, calculated from application domain A. i The expected soft error reliability SER of the service request i :

[0182]

[0183] Calculate MS per unit time i The expected number of service requests processed in Q,i :

[0184]

[0185] Among them, λ i Is application domain A i service arrival rate;

[0186] Thus, the multi-server system MS i The system service utilization of is re-derived as:

[0187]

[0188] Step 2-2, express the profit maximization problem as:

[0189]

[0190] st:ρ i <1, (62)

[0191] I i (1-I i )=0, (63)

[0192] s l ≤s i ≤s u , (64)

[0193] m l ≤m i ≤m u , (65)

[0194]

[0195]

[0196] Among them, Profit represents profit, 0-1 variable I i Indicates whether the CSP is application domain A i Building a multi-server system; l and s u are the lower and upper limits of the server rate, m l and m u are the lower and upper bounds of the number of servers, respectively, and B represents a limited budget.

[0197] Furthermore, in one embodiment, step 3 utilizes an iterative method based on a penalty function to obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, the profit and configuration optimization problem of the heterogeneous multi-server system is converted into a 0-1 knapsack problem, specifically including:

[0198] Step 3-1, calculate application domain A i maximum profit.

[0199] First, we formulate the relationship between profit and multi-server configuration when CSP has sufficient budget. Let Profit i To serve application domain A i Profit. Then formulate the relationship between multi-server configuration with budget constraints and profit. i It can be expressed as:

[0200] Max:Profit i =λ i ·C i -Cost i (68)

[0201]

[0202] s l ≤s i ≤s u ,(i=1,2,...,n), (70)

[0203] m l ≤m i ≤m u ,(i=1,2,...,n), (71)

[0204] Then, the relationship between multi-server configuration and profit under the limited budget constraint is formulated, and we can obtain:

[0205] Max:Profit i =λ i ·C i -Cost i (72)

[0206]

[0207] s l ≤s i ≤s u ,(i=1,2,...,n), (74)

[0208] m l ≤m i ≤mu ,(i=1,2,...,n), (75)

[0209] Cost i -B≤0,(i=1,2,...,n). (76)

[0210] Among them, B represents a limited budget.

[0211] Step 3-2, calculate the penalty function. Here, a penalty function-based method is used to transform this constrained nonlinear optimization problem into an unconstrained problem by constructing a penalty function.

[0212] Convert the constraint problem in step 3-1 into standard form:

[0213] Min:O(m i ,s i )=-Profit i =-(λ i ·C i -Cost i ) (77)

[0214]

[0215] g2(m i ,s i )=m l -m i ≤0, (79)

[0216] g3(m i ,s i )=m i -m u ≤0, (80)

[0217] g4(m i ,s i )=s l -s i ≤0, (81)

[0218] g5(m i ,s i )=s i -s u ≤0. (82)

[0219] Among them, g j (m i ,s i ) represents the constraint on the equation, j = 1, 2, ..., 5;

[0220] The penalty function is thus expressed as F(m i ,s i ):

[0221] F(m i ,s i )=O(m i ,s i )+φ(m i ,s i ) (83)

[0222] Among them, φ(m i ,s i ) is the external penalty period, specifically:

[0223]

[0224] Among them, σ is the penalty coefficient;

[0225] Step 3-3, calculate the partial derivative of the penalty function:

[0226] 1)O(m i ,s i ) is:

[0227]

[0228] (1) Solve C i The partial derivative of

[0229] Applying Taylor series expansion, C i Rewritten as:

[0230]

[0231] Let D1, D2 and D3 be expressed as:

[0232]

[0233] Then C i About m i The partial derivative of is expressed as:

[0234]

[0235] in

[0236]

[0237] C i About s i The partial derivative of is:

[0238]

[0239] in,

[0240]

[0241] Export as:

[0242]

[0243] in,

[0244]

[0245] λ se (s i ) is given by formula (57);

[0246] (2) Find the cost i The partial derivative of

[0247] Cost i To m i and s i The partial derivative of is:

[0248]

[0249] C i Partial derivatives and Cost i Add the partial derivatives of O(m i ,s i )’s partial derivatives;

[0250] φ(m i ,s i ) is rewritten as:

[0251]

[0252] Then φ(m i ,s i ) for m i and s i The partial derivative of is:

[0253]

[0254]

[0255] Step 3-4, calculate the optimal numerical solution based on the iterative method of penalty function, specifically: use the penalty term φ(m i ,s i ), iteratively obtain F(m i ,s i ) is the optimal numerical solution m i * and s i * ; The input of the algorithm is the threshold L of the number of iterations and the amplification rate of the penalty coefficient η.

[0256] Furthermore, in one embodiment, the iterative method based on the penalty function in steps 3-4 calculates the optimal numerical solution, and the specific process includes:

[0257] Step 3-4-1, randomly generate the initial solution (m i (0) ,s i (0) ), and initialize the penalty coefficient σ and iteration counter l;

[0258] Step 3-4-2, determine whether the solution is less than a preset threshold between the penalty function shown in Formula 83 and the constraint problems shown in Formulas 77 to 82, that is, ||φ(m i (l) ,s i (l) )||<ε, if so, the obtained solution is an acceptable solution to the constraint problem;

[0259] Step 3-4-3, obtain the optimal solution from the acceptable solutions (m i * ,s i * ), calculate the total cost corresponding to the optimal solution according to formula 56 and formula 61 respectively i * and maximum profit i * ;

[0260] Step 3-4-4: Determine whether the current number of iterations reaches the set iteration threshold. If so, execute step 3-4-6; otherwise, execute step 3-4-5.

[0261] Step 3-4-5: If the optimal solution to the constraint problem is not found during the iteration, update the penalty coefficient σ and return to step 3-4-2 to continue execution;

[0262] Step 3-4-6, return the optimal solution and the maximum profit and total cost, that is, [Profit i * ,Cost i * ,m i * ,s i * ].

[0263] Furthermore, in one embodiment, in steps 3-4, GD-Solver is used to obtain the optimal numerical solution of the penalty function; when obtaining the optimal solution of Formula 61, the penalty term only needs to be changed to:

[0264]

[0265] Furthermore, in one embodiment, step 4 is based on the converted 0-1 knapsack problem and, according to the cloud server provider's preference, utilizes a dynamic programming-based algorithm and a greedy-based algorithm to solve the optimal application domain investment strategy and the corresponding maximum profit, specifically including:

[0266] Step 4-1: When the cloud service provider prefers to prioritize efficiency, a knapsack problem based on a greedy algorithm is used to solve the optimal application domain investment strategy and the corresponding maximum profit. The input of the algorithm is the budget of the CSP, the cost consumed, and the application domain A. i Maximum profit;

[0267] In step 4-2, when the cloud service provider prefers to prioritize profit, a knapsack problem based on dynamic programming is used to solve the optimal application domain investment strategy and the corresponding maximum profit. The input of the algorithm is the same as that of the greedy algorithm.

[0268] Step 4-3, based on the best application domain investment strategy and the corresponding maximum profit obtained above, use the corresponding algorithm to calculate the multi-server investment application domain configuration solution based on the backpack; the input of the algorithm includes application domain A 1:n The maximum profit array is Profit 1:n , application domain A 1:n Cost array * 1:n ,MS 1:n The optimal server size array is m * 1:n , and MS 1:n The best server speed array is s * 1:n .

[0269] Here, the greedy algorithm is simple to implement and can quickly find the local optimal solution. However, it may not be able to find the global optimal solution. Therefore, the present invention also uses a dynamic programming algorithm to find the global optimal solution with a time complexity of O(2n). The greedy algorithm outperforms the dynamic programming algorithm in terms of runtime, and the dynamic programming algorithm achieves a higher maximum profit than the greedy algorithm. These two algorithms can address both efficiency- and profit-first scenarios for cloud service providers.

[0270] Furthermore, in one embodiment, the specific process of step 4-1 includes:

[0271] Step 4-1-1, Initialize the optimal application domain investment strategy I 1:n , I i=0, and the accumulated usage cost Cost temp and the total maximum profit totProfit is set to 0;

[0272] Step 4-1-2, according to Profit i Arrange the values ​​of the Profit array in descending order 1:n and from the maximum profit array Profit 1:n Search for the maximum profit Profit i , add the cost of this item to Cost temp Middle; judge the accumulated cost at this time temp Less than the limited budget B, record that the item has been selected, that is, let I i =1, add the maximum profit of this item to totProfit, and delete Profit in the maximum profit array i ;

[0273] Step 4-1-3, repeat step 4-1-2 until there is no element that makes the cumulative cost Cost temp If the condition that the budget is less than B is met, the algorithm ends and the optimal application domain investment strategy I is returned. 1:n And the total maximum profit value totProfit.

[0274] Furthermore, in one embodiment, the specific process of step 4-2 includes:

[0275] Step 4-2-1, recursively derive the optimal application domain investment strategy and the corresponding maximum profit. The recursive process algorithm is expressed as:

[0276]

[0277] Step 4-2-2, ends when the recursion reaches the boundary, and returns the best application domain investment strategy I 1:n And the total maximum profit value totProfit is obtained.

[0278] Furthermore, in one embodiment, the specific process of step 4-3 includes:

[0279] Step 4-3-1, set the total cost of the server system MS, i.e., totCost, to 0, and initialize the array newArrM of the optimal server size and the array newArrS of the optimal server speed to two empty arrays;

[0280] Step 4-3-2, based on the algorithm selected by the cloud service provider's preference, the best application domain investment strategy and the maximum profit, calculate the total cost of configuring MS, and put the corresponding optimal configuration into newArrM and newArrS respectively;

[0281] In step 4-3-3, after putting all elements into newArrM and newArrS, the results are returned, including the best application domain investment strategy, total profit, total cost, and optimal configuration.

[0282] In one embodiment, a cost and reliability-aware multi-server system profit optimization system is provided, the system comprising:

[0283] The first module is used to establish a heterogeneous multi-server system model and obtain the expected service revenue and multi-server system utilization based on the probability distribution of the maximum waiting time of cloud service requests;

[0284] The second module is used to establish a soft error reliability model for processing service requests on a multi-server system. Based on the service revenue and soft error reliability model, the application domain investment selection and profit maximization problem is formulated as a constrained nonlinear optimization problem.

[0285] The third module is used to obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain using an iterative method based on a penalty function. Based on this, the profit and configuration optimization problem of a heterogeneous multi-server system is converted into a 0-1 knapsack problem.

[0286] The fourth module is used to solve the optimal application domain investment strategy and the corresponding maximum profit based on the converted 0-1 knapsack problem and the preferences of cloud server providers using dynamic programming-based algorithms and greedy-based algorithms.

[0287] Regarding the specific definition of the cost- and reliability-aware heterogeneous multi-server system profit optimization system, please refer to the definition of the cost- and reliability-aware heterogeneous multi-server system profit optimization method above, which will not be repeated here. Each module in the above-mentioned cost- and reliability-aware heterogeneous multi-server system profit optimization system can be implemented in whole or in part through software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in hardware form, or can be stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above modules.

[0288] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the following steps are performed:

[0289] Step 1: Establish a heterogeneous multi-server system model and obtain the expected service revenue and multi-server system utilization based on the probability distribution of the maximum waiting time of cloud service requests;

[0290] Step 2: Build a soft error reliability model for processing service requests on a multi-server system. Based on the service revenue and soft error reliability model, formulate the application domain investment selection and profit maximization problem as a constrained nonlinear optimization problem.

[0291] Step 3: Using an iterative method based on a penalty function, we obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, we transform the profit and configuration optimization problem of heterogeneous multi-server systems into a 0-1 knapsack problem.

[0292] Step 4: Based on the converted 0-1 knapsack problem and the preferences of cloud server providers, the optimal application domain investment strategy and the corresponding maximum profit are solved using a dynamic programming-based algorithm and a greedy-based algorithm.

[0293] For the specific limitations of each step, please refer to the limitations of the profit optimization method for heterogeneous multi-server systems based on cost and reliability awareness above, which will not be repeated here.

[0294] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the following steps are implemented:

[0295] Step 1: Establish a heterogeneous multi-server system model and obtain the expected service revenue and multi-server system utilization based on the probability distribution of the maximum waiting time of cloud service requests;

[0296] Step 2: Build a soft error reliability model for processing service requests on a multi-server system. Based on the service revenue and soft error reliability model, formulate the application domain investment selection and profit maximization problem as a constrained nonlinear optimization problem.

[0297] Step 3: Using an iterative method based on a penalty function, we obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, we transform the profit and configuration optimization problem of heterogeneous multi-server systems into a 0-1 knapsack problem.

[0298] Step 4: Based on the converted 0-1 knapsack problem and the preferences of cloud server providers, the optimal application domain investment strategy and the corresponding maximum profit are solved using a dynamic programming-based algorithm and a greedy-based algorithm.

[0299] For the specific limitations of each step, please refer to the limitations of the profit optimization method for heterogeneous multi-server systems based on cost and reliability awareness above, which will not be repeated here.

[0300] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention, and such changes and modifications fall within the scope of the invention as claimed.

Claims

1. A cost- and reliability-aware profit optimization method for a heterogeneous multi-server system, characterized by: The method comprises the following steps: Step 1: Establish a heterogeneous multi-server system model and obtain the expected service revenue and multi-server system utilization based on the probability distribution of the maximum waiting time of cloud service requests; Step 2: Build a soft error reliability model for processing service requests on a multi-server system. Based on the service revenue and soft error reliability model, formulate the application domain investment selection and profit maximization problem as a constrained nonlinear optimization problem. Step 3: Using an iterative method based on a penalty function, we obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, we transform the profit and configuration optimization problem of heterogeneous multi-server systems into a 0-1 knapsack problem. Step 4: Based on the converted 0-1 knapsack problem and the preferences of cloud server providers, the optimal application domain investment strategy and the corresponding maximum profit are solved using a dynamic programming-based algorithm and a greedy-based algorithm.

2. The cost and reliability-aware heterogeneous multi-server system profit optimization method according to claim 1, characterized in that: In step 1, a heterogeneous multi-server system model is established. Based on the probability distribution of the maximum waiting time of cloud service requests, the expected service revenue and multi-server system utilization are obtained as follows: Step 1-1, establish a heterogeneous multi-server system model, specifically: use n heterogeneous multi-server systems MS1, MS2, ..., MS n Build a cloud computing environment, the number of servers in each cloud server system is m1, m2, ..., m n ; Consider the servers in each cloud service system as M / M / m i Queuing system, by m i It consists of homogeneous servers with a running speed of s; Step 1-2, establish a service level agreement model, specifically: the service level agreement model C is based on the service waiting time π in the queuing system i and service request processing requirements i Processing is performed, which is expressed as: Among them, a is a constant, which represents the service fee per unit of service, and x i It is MS i The maximum tolerable waiting time for a service request; Cloud service requests have soft real-time requirements. The soft real-time requirements of service requests are usually specified by two metrics, namely, deadline and maximum waiting time; Multi-server system MS i The slack x of the service request with soft real-time requirements follows a uniform distribution and is expressed as S(x i ): Among them, S min,i and S max,i are the minimum and maximum values ​​of relaxation, respectively; Let C i For application domain A i The expected cost of a service request is derived as: in, is the average value of service request processing demand; μ i is the average service rate of the server, denoted as μ i =s i / r i ρ i It is a multi-server system MS i System utilization; represents the probability that there are exactly m tasks in the queue system; Steps 1-3, establishing a cost model, specifically include: the cost of cloud service providers consists of two parts, infrastructure usage costs and utility costs for energy consumption; The cost of renting a server per unit time is v, so the construction includes m i Multi-server system MS i Cost rent,i : Cost rent,i =m i v (4) Heterogeneous multi-server system MS i The utility cost per unit time is Cost utility,i : Among them, ξs 3 is the dynamic power of the server, where ξ is a hardware-related coefficient related to the processor; For heterogeneous multi-server system MS i At a rate s per unit time i Dynamic energy consumption during operation; E * represents the energy consumption per unit time when the server is idle, and assumes that the energy price is δ per watt; Multi-server system MS i The total cost per unit time is Cost i :

3. The cost and reliability-aware profit optimization method for heterogeneous multi-server systems according to claim 1 or 2, characterized in that: In step 2, a soft error reliability model for processing service requests on a multi-server system is established. Based on the service revenue and soft error reliability model, the application domain investment selection and profit maximization problem is formulated as a constrained nonlinear optimization problem, specifically including: Step 2-1: Establish a soft error reliability model, specifically: The soft error rate follows an exponential distribution, denoted as λ se (s i ): Among them, s l,i is the lower bound of server speed, λ 0,i Is the server at maximum speed s u,i Soft error rate during runtime, d 0,i is a hardware-dependent constant that reflects the sensitivity of the server to soft errors; i It is the server system MS i The running speed of; e is a natural constant; Calculations from application domain A i The expected soft error reliability SER of the service request i : Calculate MS per unit time i The expected number of service requests processed in Q,i : Among them, λ i Is application domain A i service arrival rate; Thus, the multi-server system MS i The system service utilization of is re-derived as: Step 2-2, express the profit maximization problem as: st:r i <1, (12) I i (1-I i )=0, (13) s l ≤s i ≤s u , (14) m l ≤m i ≤m u , (15) Among them, Profit represents profit, 0-1 variable I i Indicates whether the CSP is application domain A i Building a multi-server system; l and s u are the lower and upper limits of the server rate, m l and m u are the lower and upper bounds of the number of servers, respectively, and B represents a limited budget.

4. The cost and reliability-aware heterogeneous multi-server system profit optimization method according to claim 3, characterized in that: In step 3, we use an iterative method based on a penalty function to obtain the optimal multi-server system configuration, minimum cost, and maximum profit for any single application domain. Based on this, we transform the profit and configuration optimization problem of the heterogeneous multi-server system into a 0-1 knapsack problem, which specifically includes: Step 3-1, calculate application domain A i Maximum profit: Max:Profit i =λ i ·C i -Cost i (18) s l ≤s i ≤s u ,i=1,2,...,n, (20) m l ≤m i ≤m u ,i=1,2,...,n, (21) Cost i -B≤0,i=1,2,...,n. (22) Among them, Profit i To serve application domain A i profits; Step 3-2, calculate the penalty function: Convert the constraint problem in step 3-1 into standard form: Min:O(m i ,s i )=-Profit i =-(λ i ·C i -Cost i ) (23) g2(m i ,s i )=m l -m i ≤0, (25) g3(m i ,with i )=m i -m u ≤0, (26) g4(m i ,s i )=s l -s i ≤0, (27) g5(m i ,s i )=s i -s u ≤0. (28) Among them, g j (m i ,s i ) represents the constraint on the equation, j = 1, 2, ..., 5; The penalty function is thus expressed as F(m i ,s i ): F(m i ,s i )=O(m i ,s i )+φ(m i ,s i ) (29) Among them, φ(m i ,s i ) is the external penalty period, specifically: Among them, σ is the penalty coefficient; Step 3-3, calculate the partial derivative of the penalty function: 1) O(m i ,s i ) is: (1) Solve C i The partial derivative of is expanded using Taylor series, then C i Rewritten as: Let D1, D2 and D3 be expressed as: Then C i About m i The partial derivative of is expressed as: C i About s i The partial derivative of is: Export as: in, λ se (s i ) is given by formula (7); (2) Find the cost i The partial derivative of Cost i To m i and s i The partial derivative of is: C i Partial derivatives and Cost i Add the partial derivatives of O(m i ,s i )’s partial derivatives; 2) φ(m i ,s i ) is rewritten as: Then φ(m i ,s i ) for m i and s i The partial derivative of is: Step 3-4, calculate the optimal numerical solution based on the iterative method of penalty function, specifically: use the penalty term φ(m i ,s i ), iteratively obtain F(m i ,s i ) is the optimal numerical solution m i * and s i * ; The input of the algorithm is the threshold L of the number of iterations and the amplification rate of the penalty coefficient η.

5. The cost and reliability-aware heterogeneous multi-server system profit optimization method according to claim 4, characterized in that: The iterative method based on the penalty function described in steps 3-4 calculates the optimal numerical solution. The specific process includes: Step 3-4-1, randomly generate the initial solution (m i (0) ,s i (0) ), and initialize the penalty coefficient σ and iteration counter l; Step 3-4-2, determine whether the solution is less than a preset threshold between the penalty function shown in Formula 29 and the constraint problems shown in Formulas 23 to 28, that is, ||φ(m i (l) ,s i (l) )||<ε, if so, the obtained solution is an acceptable solution to the constraint problem; Step 3-4-3, obtain the optimal solution from the acceptable solutions (m i * ,s i * ), calculate the total cost corresponding to the optimal solution according to Formula 6 and Formula 11 respectively i * and maximum profit i * ; Step 3-4-4: Determine whether the current number of iterations reaches the set iteration threshold. If so, execute step 3-4-6; otherwise, execute step 3-4-5. Step 3-4-5: If the optimal solution to the constraint problem is not found during the iteration, update the penalty coefficient σ and return to step 3-4-2 to continue execution; Step 3-4-6, return the optimal solution and the maximum profit and total cost, that is, [Profit i * ,Cost i * ,m i * ,s i * ].

6. The cost and reliability-aware heterogeneous multi-server system profit optimization method according to claim 5, characterized in that: In steps 3-4, GD-Solver is used to obtain the optimal numerical solution of the penalty function. To obtain the optimal solution of Formula 11, the penalty term only needs to be changed to:

7. The cost and reliability-aware profit optimization method for heterogeneous multi-server systems according to claim 1, characterized in that: Based on the converted 0-1 knapsack problem described in step 4, according to the preferences of cloud server providers, the optimal application domain investment strategy and the corresponding maximum profit are solved using dynamic programming-based algorithms and greedy-based algorithms. Specifically, the following are involved: Step 4-1: When the cloud service provider prefers to prioritize efficiency, a knapsack problem based on a greedy algorithm is used to solve the optimal application domain investment strategy and the corresponding maximum profit. The input of the algorithm is the budget of the CSP, the cost consumed, and the application domain A. i maximum profit; In step 4-2, when the cloud service provider prefers to prioritize profit, a knapsack problem based on dynamic programming is used to solve the optimal application domain investment strategy and the corresponding maximum profit. The input of the algorithm is the same as that of the greedy algorithm. Step 4-3, based on the best application domain investment strategy and the corresponding maximum profit obtained above, use the corresponding algorithm to calculate the multi-server investment application domain configuration solution based on the backpack; the input of the algorithm includes application domain A 1:n The maximum profit array is Profit 1:n , application domain A 1:n Cost array * 1:n ,MS 1:n The optimal server size array is m * 1:n , and MS 1:n The best server speed array is s * 1:n .

8. The cost and reliability-aware profit optimization method for heterogeneous multi-server systems according to claim 7, characterized in that: The specific process of step 4-1 includes: Step 4-1-1, Initialize the optimal application domain investment strategy I 1:n , And the accumulated usage cost temp and the total maximum profit totProfit is set to 0; Step 4-1-2, according to Profit i Arrange the values ​​of the Profit array in descending order 1:n and from the maximum profit array Profit 1:n Search for the maximum profit Profit i , add the cost of this item to Cost temp Middle; judge the accumulated cost at this time temp Less than the limited budget B, record that the item has been selected, that is, let I i =1, add the maximum profit of this item to totProfit, and delete Profit in the maximum profit array i ; Step 4-1-3, repeat step 4-1-2 until there is no element that makes the cumulative cost Cost temp If the condition that the budget is less than B is met, the algorithm ends and the optimal application domain investment strategy I is returned. 1:n And the total maximum profit value totProfit.

9. The cost and reliability-aware profit optimization method for heterogeneous multi-server systems according to claim 7, characterized in that: The specific process of step 4-2 includes: Step 4-2-1, recursively derive the optimal application domain investment strategy and the corresponding maximum profit. The recursive process algorithm is expressed as: Where f(i,B) is the decision of the 0th to the i-th application domain A i The maximum total profit when f(i,B) is finally determined by the budget and the application domain A i Cost decision for building a multi-server system; when the budget is larger than the application domain A i When building a multi-server system, there are two cases: when application domain A i When a multi-server system is not built, f(i,B) will be directly equal to the decision of application domain A from 0th to i+1th. i+1 The maximum total profit f(i+1,B) when the budget B will not be reduced; when the application domain A i When a multi-server system is built, f(i,B) will be equal to the decision of application domain A from 0th to i+1th i+1 The maximum total profit when adding the application domain A i The maximum profit f(i+1,B-Cost i * )+Profit i * , budget B is reduced by the amount for application domain A i Cost of building a multi-server system i * When the budget is less than the application domain A i When building a multi-server system, the cost of f(i,B) will be directly equal to the cost of deciding the 0th to i+1th application domain A. i+1 The maximum total profit f(i+1,B); Step 4-2-2, ends when the recursion reaches the boundary, and returns the best application domain investment strategy I 1:n And the total maximum profit value totProfit is obtained.

10. The cost and reliability-aware heterogeneous multi-server system profit optimization method according to claim 7, characterized in that: The specific process of step 4-3 includes: Step 4-3-1, set the total cost of the server system MS, i.e., totCost, to 0, and initialize the array newArrM of the optimal server size and the array newArrS of the optimal server speed to two empty arrays; Step 4-3-2, based on the algorithm selected by the cloud service provider's preference, the best application domain investment strategy and the maximum profit, calculate the total cost of configuring MS, and put the corresponding optimal configuration into newArrM and newArrS respectively; In step 4-3-3, after putting all elements into newArrM and newArrS, the results are returned, including the best application domain investment strategy, total profit, total cost, and optimal configuration.

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