CN106055425A - Method for cloud disaster recovery data backup based on game theory - Google Patents

Abstract

The cloud disaster recovery data backup method based on game theory involves the field of data backup and disaster recovery technology, and solves the problems of large resource consumption and high storage cost in existing data backup methods, while ignoring the impact of the source cloud provider's behavior on the destination cloud provider. The problem of the influence of suppliers, the optimal data backup method in the cloud disaster recovery environment based on game theory described in the present invention simulates the interaction process between the source cloud provider and the destination cloud provider as a storage resource pricing model , and model the storage resource leasing process among the backup nodes of the destination cloud provider as a game process seeking the maximum benefit. The present invention also provides a quantitative calculation method for the quantity of storage resources and the optimal solution of storage resource prices, so that the interests of both sides of the game, that is, the source-end cloud provider and the destination-end cloud provider, can be maximized at the same time.

Description

Cloud disaster recovery data backup method based on game theory

technical field

The invention relates to the technical field of data backup and disaster recovery, in particular to an optimal data backup method in a cloud environment based on game theory.

Background technique

With the development of information technology, the value of data continues to increase, and people's dependence on network data is gradually increasing, especially financial or official data. Even a small part of data loss or short-term downtime may affect the lives and property of the people. cause great harm. Therefore, data disaster recovery technology has received extensive research and attention. People usually back up data copies in different geographical locations to meet data reliability requirements. However, traditional data storage deployment methods are resource-intensive. The low cost, on-demand purchase and dynamic nature of cloud storage make it gradually become the best choice for data backup.

In recent years, cloud storage has been widely used in data disaster recovery with a pay-as-you-go pricing model. In the current data backup method, most of them focus on the parameters of the destination node, such as storage cost and data recovery time, etc., and impose strict restrictions on storage capacity, minimum bandwidth and number of copies, while ignoring the data provided by the source cloud. The impact of the provider's behavior on the destination cloud provider.

Game theory is a mathematical theory and method that studies the decision-making when the behavior of the decision-making subject interacts directly and the equilibrium problem of this decision-making, which has the nature of struggle or competition. Game theory considers the predicted and actual behavior of individuals in games and studies their optimization strategies. It has broad applications in biology, economics, international relations, computer science, political science, military strategy, and many other disciplines.

Contents of the invention

The present invention provides a cloud disaster recovery based on game theory to solve the problem that the existing data backup method has relatively large resource consumption and high storage cost, and at the same time ignores the influence of the behavior of the source-end cloud provider on the target-end cloud provider. Data backup method.

A cloud disaster recovery data backup method based on game theory, which is implemented by the following steps:

Step 1. The user backs up the data respectively to i source cloud provider SCPi, and the source cloud provider SCPi backs up the user data stored by itself to the destination cloud service provider DCP, and the destination cloud service Provider DCP includes j destination storage nodes D_nodej that store price changes; i is the number of source cloud providers, and j is the number of storage nodes of destination cloud providers;

Step 2, calculating the utility function U _scpi of the source cloud provider SCP and the utility function U _dcp of the destination cloud provider DCP; specifically expressed as:

formula one,

In the formula, U _scpi represents the utility function of the i-th source cloud provider SCPi, B _ij is the benefit obtained by SCPi after storing resources on the j-th destination storage node D_nodej of the destination cloud provider DCP, and the B _ij is expressed by formula 2 as:

Formula two,

In the formula, b _i is a positive parameter used to distinguish each source cloud provider, t _j is a positive parameter greater than 1, used to distinguish different destination storage nodes of the destination cloud provider; x _ij is the source cloud provider C _ij is the cost spent by the i-th source cloud provider SCPi for renting storage resources from the j-th destination storage node D_nodej of the destination cloud provider DCP, expressed as:

Formula 3, C _ij = p _j · x _ij

In the formula, p _j is the strategy of the storage node of the destination cloud provider, namely: the unit price of storage resources on j destination storage nodes D_nodej of the destination cloud provider DCP;

Said N _ij is network load balancing, expressed as:

Formula four,

In the formula, L _j represents the maximum load balance on the jth destination storage node D_nodej of the destination cloud provider DCP;

Substitute Formula 2, Formula 3, and Formula 4 into Formula 1 to obtain Formula 5:

Formula five,

In the formula, m is a positive integer greater than j, and n is a positive integer greater than i;

The utility function of the destination cloud provider DCP is expressed as:

Formula six,

In the formula, U _dcp is the utility function of the selected destination cloud provider DCP, B _j ' is the storage resource obtained by the jth destination storage node D_nodej of the destination cloud provider DCP leasing the storage resource to the source cloud provider Income, expressed by Formula 7:

Formula seven,

The C _j ' is the consumption cost of the jth destination storage node D_nodej of the destination cloud provider DCP, expressed as:

Formula eight,

In the formula, p _j ' represents the unit consumption cost of storage resources on the jth destination storage node D_nodej of the destination cloud provider DCP, where p _j '<p _j ;

Substitute Formula 7 and Formula 8 into Formula 6 to obtain Formula 9:

formula nine,

Using formula 5 and formula 9 to calculate the initial value of the utility function U _scpi of the SCP of the source cloud provider and the initial value of the utility function U _dcp of the destination cloud provider DCP;

Step 3, using an iterative algorithm to achieve Nash equilibrium;

Specifically: use iterative algorithm to calculate the policy x _ij of the source-end cloud provider; use formula ten to express as:

formula ten,

In the formula, x _ij (τ ₁ ) is the number of resources that the i-th source cloud provider SCPi plans to store in the j-th destination storage node D_nodej of the destination cloud provider DCP after the τ ₁ iteration, and τ ₁ represents the resources provided by the source cloud The number of iterations of the quotient, x _ij (τ ₁ +1) represents the next iteration result of x _ij (τ ₁ ); δ is the step factor when the i-th source cloud provider SCPi performs resource quantity iteration;

Step 4: The source cloud provider SCPi corrects the quantity of its own storage resources, and the j storage nodes D_nodej of the destination cloud provider DCP continuously adjust the unit price of storage resources according to the changes in the quantity of i source cloud provider SCPi storage resources p _j , the adjustment method is expressed by Formula 11 as:

formula eleven,

In the formula, τ ₂ is the number of iterations of the source cloud provider, p _j (τ ₂ ) is the storage resource unit price of the jth storage node D_nodej of the destination cloud provider DCP after the τ ₂ iteration, p _j (τ ₂ + 1) Indicates the next iteration result of p _j (τ ₂ ); θ is the step size factor when the jth storage node D_nodej of the destination cloud provider DSP performs resource storage unit price iteration;

Step 5. According to the policy x _ij of the source cloud provider obtained in step 3 and the policy p _j of the storage node of the destination cloud provider obtained in step 4, use formula 9 to calculate the utility function U _dcp of the destination cloud provider DCP New iterative result, and judge whether U _dcp is the maximum value, if not, then return to step four; if yes, perform step six;

Step 6. Calculate the utility function U _scpi of the i-th source cloud provider SCPi according to formula 5, and judge whether U _scpi is the maximum value. If not, return to step 3. If yes, the source cloud provider SCPi and The destination cloud provider DCP reaches the Nash equilibrium, obtains the optimal xij and pj values, and realizes the final Nash equilibrium.

Beneficial effects of the present invention: the optimal data backup method in the cloud disaster recovery environment based on game theory in the present invention simulates the interaction process between the source cloud provider and the destination cloud provider as a storage resource pricing model , and model the storage resource leasing process among the backup nodes of the destination cloud provider as a game process seeking the maximum benefit. The present invention also provides a quantitative calculation method for the quantity of storage resources and the optimal solution of storage resource prices, so that the interests of both sides of the game, that is, the source-end cloud provider and the destination-end cloud provider, can be maximized at the same time.

Description of drawings

Fig. 1 is the functional block diagram of the cloud disaster recovery data backup method based on game theory of the present invention;

Fig. 2 is the flow chart of the cloud disaster recovery data backup method based on game theory of the present invention;

Fig. 3 is a schematic diagram of changes in the quantity of storage resources of three storage nodes of the destination cloud provider in the game theory-based cloud disaster recovery data backup method of the present invention;

Fig. 4 is a schematic diagram of changes in storage resource prices of three storage nodes of the destination cloud provider in the game theory-based cloud disaster recovery data backup method of the present invention;

Fig. 5 is a schematic diagram of the resource quantity distribution of five source-end cloud providers respectively stored in three storage nodes of the destination-end cloud provider in the game theory-based cloud disaster recovery data backup method of the present invention;

Fig. 6 is a schematic diagram of the change trend of utility functions of five source cloud providers in the game theory-based cloud disaster recovery data backup method of the present invention;

Fig. 7 is a schematic diagram of the change trend of the utility function of the source cloud provider SCP1 in the game theory-based cloud disaster recovery data backup method of the present invention;

Fig. 8 is a schematic diagram of the change trend of the utility functions of the three storage nodes of the destination cloud provider in the game theory-based cloud disaster recovery data backup method of the present invention;

FIG. 9 is a schematic diagram of the change trend of the total utility function of the three storage nodes of the destination cloud provider in the game theory-based cloud disaster recovery data backup method of the present invention.

detailed description

Specific embodiments one, illustrate this embodiment in conjunction with Fig. 1 and Fig. 2, the cloud disaster recovery data backup method based on game theory, this method is realized by the following steps:

A. The user backs up the data to different source cloud providers SCPi, i=1,2,...n, n represents the number of available source cloud providers; for data security and integrity requirements And considering economic factors, the source-end cloud provider SCP needs to back up its own user data to another cloud service provider, that is, the destination-end cloud provider DCP. The destination cloud provider DCP includes multiple destination storage nodes D_nodej with variable storage prices (j=1, 2, . . . , m, where m represents the number of available storage nodes included in the destination cloud provider DCP). The destination storage node D_nodej dynamically adjusts the storage price according to the amount of data backed up by the source cloud provider SCP, and continuously adjusts the resource price and resource quantity of the backup data to maximize the benefits of both parties.

B. Model the dynamic interaction process between the source cloud provider SCP and the destination storage node D_nodej of the destination cloud provider DCP as a storage resource pricing model. The specific process is as follows:

When the source cloud provider SCP rents storage resources on the destination storage node D_nodej of the destination cloud provider DCP, it hopes to obtain a maximum benefit: including a lower unit storage price than D_nodej's current bid, and higher network load balancing.

The utility function for calculating the SCP of the source cloud provider is expressed as:

formula one,

where U _scpi represents the utility function of the i-th source cloud provider SCPi. B _ij represents the benefit that SCPi hopes to obtain after storing resources on the jth destination storage node D_nodej of the destination cloud provider DCP, that is, the fee paid by the user after SCPi completes the data backup, expressed in Formula 2 as:

Formula two,

In the formula, _bi is a positive parameter to distinguish each source cloud provider. t _j is a positive parameter greater than 1, which is used to distinguish different destination storage nodes of the destination cloud provider. x _ij represents the policy of the source cloud provider, that is, the amount of storage resources that the i-th source cloud provider SCPi wants to rent on the j-th destination storage node D_nodej of the destination cloud provider DCP.

C _ij represents the cost of renting storage resources by the i-th source cloud provider SCPi from the j-th destination storage node D_nodej of the destination cloud provider DCP, expressed as:

Formula 3, C _ij =p _j x _ij (i=1,2,3,4,5 j=1,2,3)

In the formula, p _j represents the policy of the destination storage node, that is, the storage resource unit price on the jth destination storage node D_nodej of the destination cloud provider DCP.

N _ij in Formula 1 represents network load balancing, expressed by Formula 4:

Formula four,

In the formula, L _j represents the maximum load balance on the jth destination storage node D_nodej of the destination cloud provider DCP, that is, the maximum storage capacity.

Substituting Formula 2, Formula 3, and Formula 4 into Formula 1, Formula 5 can be expressed as follows:

Formula five,

In this embodiment, the utility function for calculating the destination cloud provider DCP is expressed as:

Formula six,

In the formula, U _dcp represents the utility function of the selected destination cloud provider DCP, that is, the maximum benefit obtained by the DCP, including the benefits and costs of leasing storage resources to the source cloud provider SCP. B _j 'represents the income obtained by the jth destination storage node D_nodej of the destination cloud provider DCP from leasing storage resources to the source cloud provider, expressed by formula 7:

Formula seven,

C _j ' in Formula 6 represents the consumption cost of the jth destination storage node D_nodej of the destination cloud provider DCP, including maintenance cost and power loss. Expressed in formula eight:

Formula eight,

In the formula, p _j ' represents the unit consumption cost of storage resources on the jth destination storage node D_nodej of the destination cloud provider DCP, p _j '<p _j .

Substitute Formula 7 and Formula 8 into Formula 6 to get Formula 9, as follows:

formula nine

Calculate the initial value of the utility function U _scpi of the SCP of the source cloud provider and the initial value of the utility function U _dcp of the DCP of the destination cloud provider by using Formula 5 and Formula 9 respectively.

C. Use an iterative algorithm to achieve Nash equilibrium.

τ ₁ represents the number of iterations of the source cloud provider. The i-th source cloud provider SCPi uses the method of formula 10 to iteratively calculate the number of resources to be stored in the j-th destination storage node D_nodej of the destination cloud provider DCP.

formula ten,

in the formula x _ij (τ ₁ ) represents the number of resources that the i-th source cloud provider SCPi plans to store in the j-th destination storage node D_nodej of the destination cloud provider DCP after the τ ₁ iteration, x _ij (τ ₁ +1 ) represents the next iteration result of x _ij (τ ₁ ). δ>0, which is a constant, represents the step size factor when SCPi, the i-th source cloud provider, iterates the number of resources.

D. While the source-end cloud provider SCPi is constantly revising the amount of its own storage resources, each storage node D_nodej of the destination-end cloud provider is constantly adjusting the amount of its own storage resources according to the changes in the number of storage resources of all source-end cloud providers SCPi unit price. The adjustment method is performed iteratively in the form of formula eleven.

formula eleven,

formula τ ₂ represents the number of iterations of the source cloud provider.

p _j (τ ₂ ) represents the storage resource unit price of the jth storage node D_nodej of the destination cloud provider DCP after the τ ₂ iteration, and p _j (τ ₂ +1) represents the next iteration of p _j (τ ₂ ) Iterate over the results. θ>0, which is a constant, represents the step size factor when the jth storage node D_nodej of the destination cloud provider DSP performs resource storage unit price iteration.

E. According to the source cloud provider SCPi calculated in the above step C, the number of resources x _ij stored in the jth destination storage node D_nodej of the destination cloud provider DCP and the destination cloud calculated in step D The storage resource unit price p _j of the jth storage node D_nodej of the provider DCP uses the method described in formula 9 to calculate the new iterative result of the utility function U _dcp of the destination cloud provider DCP. Judging whether U _dcp is the maximum value, if yes, then proceed to step F, if not return to step D;

F. Calculate the utility function U _scpi of the i-th source cloud provider SCPi according to formula 5, and judge whether U _scpi is the maximum value, if not, return to step C; if yes, it is the final Nash equilibrium, so that Both game participants: the source-end cloud provider SCP and the destination-end cloud provider DCP maximize the benefits.

G. The source-end cloud provider SCPi backs up the data with the size of xij to the storage node D_nodej of the destination-end cloud provider at the price pj respectively.

Specific embodiment two, in conjunction with Fig. 1 to Fig. 9 illustrate this embodiment, this embodiment is the embodiment of the cloud disaster recovery data backup method based on game theory described in specific embodiment one:

a. The user backs up data to different source cloud providers SCP1, SCP2, SCP3, SCP4, SCP5 respectively. Referring to Figure 1, each source cloud provider SCP1, SCP2, SCP3, SCP4, and SCP5 needs to back up their own user data to another cloud service provider, that is, the destination cloud provider DCP. DCP contains three destination storage nodes D_node1, D_node2 and D_node3 with variable storage prices. The destination storage nodes D_node1, D_node2, and D_node3 dynamically adjust the storage price according to the amount of data backed up by the source cloud providers SCP1, SCP2, SCP3, SCP4, and SCP5.

b. Model the dynamic interaction process between the source cloud provider SCP1, SCP2, SCP3, SCP4, and SCP5 and the destination storage nodes D_node1, D_node2, and D_node3 of the destination cloud provider DCP as a storage resource pricing model. The specific process is as follows :

1. Calculate the utility function of the SCP of the source cloud provider:

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

where U _scpi represents the utility function of the i-th source cloud provider SCPi. B _ij represents the benefit that SCPi hopes to obtain after storing resources on the jth destination storage node D_nodej of the destination cloud provider DCP, that is, the fee paid by the user after SCPi completes data backup:

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

In formula (2), b _i is a positive parameter to distinguish each source cloud provider. In this embodiment, b ₁ =2.5, b ₂ =2.6, b ₃ =2.7, b ₄ =2.8, b ₅ = 2.9. t _j is a positive parameter greater than 1, which is used to distinguish different destination storage nodes of the destination cloud provider. In this embodiment, t ₁ =4, t ₂ =3, and t ₃ =2. x _ij represents the strategy of the source cloud provider, that is, the number of storage resources that the i-th source cloud provider SCPi wants to lease on the j-th destination storage node D_nodej of the destination cloud provider DCP, and the initial value is 0.

C _ij represents the cost of renting storage resources by the i-th source cloud provider SCPi from the j-th destination storage node D_nodej of the destination cloud provider DCP:

C _ij =p _j x _ij (i=1,2,3,4,5 j=1,2,3) (3)

In formula (3), p _j represents the policy of the destination storage node, that is, the unit price of storage resources on the jth destination storage node D_nodej of the destination cloud provider DCP, which in this embodiment are respectively p ₁ =0.1, p ₂ =0.2, p ₃ =0.3.

N _ij in formula (1) represents network load balancing:

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

L _j represents the maximum load balancing on the jth destination storage node D_nodej of the destination cloud provider DCP, that is, the maximum storage capacity, which are respectively L ₁ =35, L ₂ =20, and L ₃ =11 in this embodiment.

Substituting formula (2), formula (3) and formula (4) into formula (1) can get:

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span>& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

2. Calculating the utility function of the destination cloud provider DCP:

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

U _dcp in formula (6) represents the utility function of the selected destination cloud provider DCP, that is, the maximum benefit obtained by DCP, including the benefits and costs of leasing storage resources to the source cloud provider SCP.

B _j 'indicates the revenue obtained by the jth destination storage node D_nodej of the destination cloud provider DCP from leasing storage resources to the source cloud provider:

$\begin{array}{cc}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 5</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In formula (6), C _j ' represents the consumption cost of the jth destination storage node D_nodej of the destination cloud provider DCP, including maintenance costs and power consumption, as shown in formula (8):

$\begin{array}{cc}{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 5</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

In formula (8), p _j ' represents the unit consumption cost of storage resources on the jth destination storage node D_nodej of the destination cloud provider DCP, p _j '<p _j , in this embodiment p _j '=0.7p _j .

Substitute formula (7) and formula (8) into formula (6) to get:

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 5</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 5</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&rsqb;</span>& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

The initial value of the utility function U _scpi of the source cloud provider SCP and the initial value of the utility function U _dcp of the destination cloud provider DCP are calculated by formula (5) and formula (9) respectively.

c. Use an iterative algorithm to achieve Nash equilibrium. τ ₁ represents the number of iterations of the source cloud provider, and the i-th source cloud provider SCPi uses formula (10) to iteratively calculate the number of resources to be stored in the jth destination storage node D_nodej of the destination cloud provider DCP .

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&lsqb;</span>\frac{<span\; class="notranslate">\; \&part;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; \&part;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; \&rsqb;</span>& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 5</span>}& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}\end{array}\right)\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

in the formula

x _ij (τ ₁ ) represents the number of resources that the i-th source cloud provider SCPi plans to store in the j-th destination storage node D_nodej of the destination cloud provider DCP after the τ ₁ iteration, x _ij (τ ₁ +1 ) represents the next iteration result of x _ij (τ ₁ ). δ>0 is a constant, representing the step size factor when the i-th source cloud provider SCPi performs resource number iteration, and in this embodiment, δ=0.1.

d. While the source-end cloud provider is constantly revising its own storage resource quantity, each storage node D_nodej (j=1,2,3) of the destination-end cloud provider is based on all source-end cloud provider SCPi(i=1, 2, 3, 4, 5) Changes in the quantity of storage resources constantly adjust the unit price of its own storage resources.

$\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&lsqb;</span>\frac{<span\; class="notranslate">\; \&part;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; p</span>}}}{<span\; class="notranslate">\; \&part;</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; \&rsqb;</span>& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In formula (11) τ ₂ represents the number of iterations of the source cloud provider.

p _j (τ ₂ ) represents the storage resource unit price of the jth storage node D_nodej of the destination cloud provider DCP after the τ ₂ iteration, and p _j (τ ₂ +1) represents the next iteration of p _j (τ ₂ ) Iterate over the results. θ>0 is a constant, indicating the step size factor when the jth storage node D_nodej of the destination cloud provider DSP performs resource storage unit price iteration. In this embodiment, θ=0.001.

e. According to the source cloud provider SCPi calculated in the above step 3, the number of resources x _ij stored in the jth destination storage node D_nodej of the destination cloud provider DCP, and the destination calculated in step 4 The storage resource unit price p _j of the jth storage node D_nodej of the cloud provider DCP uses the method described in Formula 9 to calculate the new iterative result of the utility function U _dcp of the destination cloud provider DCP. Determine whether U _dcp is the maximum value, if not return to step d, if yes, continue to execute step f.

f. According to the source cloud provider SCPi calculated in the above step c, the number of resources x _ij stored in the jth destination storage node D_nodej of the destination cloud provider DCP and the destination cloud calculated in step d For the storage resource unit price p _j of the jth storage node D_nodej of the provider DCP, calculate the utility function U _scpi of the i-th source cloud provider SCPi according to formula 5, and judge whether U _scpi is the maximum value, if not, then Return to step c, if it is, then combine Figure 3 to Figure 9, U _SCPi and U _dcp reach the maximum value, both sides of the game reach the Nash equilibrium, and obtain the optimal xij and pj values, which is the final Nash equilibrium, so that both game participants : The benefits of source-end cloud provider SCP and destination-end cloud provider DCP are maximized.

g. The source-end cloud providers SCP1, SCP2, SCP3, SCP4, and SCP5 respectively back up the data with the size of xij to the storage nodes D_node1, D_node2, and D_node3 of the destination-end cloud provider at a price pj.

Claims (3)

1. based on game theoretic cloud disaster tolerance data back up method, it is characterized in that, the method is realized by following steps:

Data are backed up on i source cloud provider SCPi by step one, user respectively, and described source cloud provider SCP will be from The user data backup of body storage is in destination cloud service provider DCP, and described destination cloud service provider DCP comprises j The purpose memory node D_nodej of individual storage price change；I is the number of source cloud provider, Duan Yun provider for the purpose of j The number of memory node；

Step 2, utility function U of calculating source cloud provider SCP_scpiUtility function U with destination cloud provider DCP_dcp； Specifically it is expressed as with following formula:

Formula one,

In formula, U_scpiRepresent the utility function of i-th source cloud provider SCPi, B_ijFor SCPi at destination cloud provider DCP Jth purpose memory node D_nodej on store interests acquired after resource, described B_ijIt is expressed as with formula two:

Formula two,

In formula, b_iFor positive parameter, it is used for distinguishing each source cloud provider, t_jFor the positive parameter more than 1, it is used for distinguishing destination The different purpose memory nodes of cloud provider；x_ijStrategy for source cloud provider；C_ijFor i-th source cloud provider SCPi The cost that storage resource is spent is rented, by public affairs from the jth purpose memory node D_nodej of destination cloud provider DCP Formula three is expressed as:

Formula three, C_ij=p_j·x_ij

In formula, p_jFor the purpose of the strategy of Duan Yun provider memory node, it may be assumed that j the purpose storage joint of destination cloud provider DCP The unit price of the storage resource on some D_nodej；

Described N_ijFor Network Load Balance, it is expressed as with formula four:

Formula four,

In formula, L_jRepresent the maximum load equilibrium on the jth purpose memory node D_nodej of destination cloud provider DCP；

Formula two, formula three, formula four are substituted into formula one, it is thus achieved that formula five:

Formula five,

In formula, m is the positive integer more than j, and n is the positive integer more than i；

The utility function formula six of described destination cloud provider DCP is expressed as:

Formula six,

In formula, U_dcpThe utility function of the destination cloud provider DCP by being chosen, B_jThe jth of Duan Yun provider DCP for the purpose of ' Storage resource is leased to the income acquired in source cloud provider by individual purpose memory node D_nodej, represents with formula seven:

Formula seven,

Described C_jThe consuming cost of the jth purpose memory node D_nodej of Duan Yun provider DCP for the purpose of ', with formula eight table It is shown as:

Formula eight,

In formula, p_j' represent that the storage resource units on the jth purpose memory node D_nodej of destination cloud provider DCP disappears Consumption cost, described p_j' ＜ p_j；

By formula seven, formula eight substitutes into formula six, it is thus achieved that formula nine:

Formula nine,

Formula five and formula nine is used to calculate utility function U obtaining described source cloud provider SCP_scpiInitial value and described mesh Utility function U of Duan Yun provider DCP_dcpInitial value；

Step 3, employing iterative algorithm realize Nash Equilibrium；

Particularly as follows: use iterative algorithm to calculate the tactful x of source cloud provider_ij；It is expressed as with formula ten:

Formula ten,

In formula,x_ij(τ₁) it is τ₁I-th source cloud provider after secondary iteration SCPi plan is stored in the resource quantity of the jth purpose memory node D_nodej of destination cloud provider DCP, τ₁Expression source The iterations of Duan Yun provider, x_ij(τ₁+ 1) x is represented_ij(τ₁) next iteration result；δ is i-th source cloud provider SCPi carries out step factor during resource quantity iteration；

Step 4, source cloud provider SCP revise self storage resource quantity, j the memory node of destination cloud provider DCP D_nodej then constantly adjusts the unit valency of storage resource according to the change of i source cloud provider SCPi storage resource quantity Lattice p_j, method of adjustment formula 11 is expressed as:

Formula 11,

In formula,τ₂For the iterations of source cloud provider, p_j(τ₂) it is τ₂After secondary iteration, destination cloud provides The storage resource units price of the jth memory node D_nodej of business DCP, p_j(τ₂+ 1) p is represented_j(τ₂) next iteration knot Really；Step-length when the jth memory node D_nodej of Duan Yun provider DSP carries out resource storage cell price iteration for the purpose of θ The factor；

Step 5, the tactful x of the source cloud provider obtained according to step 3_ijThe destination cloud provider obtained with step 4 deposits The tactful p of storage node_j, use formula nine to calculate utility function U of destination cloud provider DCP_dcpNew iteration result, and Judge U_dcpWhether it is maximum, if it is not, then return step 4；If it is, execution step 6；

Step 6, calculate utility function U of i-th source cloud provider SCPi according to formula five_scpi, and judge U_scpiIt is whether Maximum, performs step 3 if it is not, then return, if it is, source cloud provider SCP reaches with destination cloud provider DCP Nash Equilibrium, it is thus achieved that optimum xij value and pj value, it is achieved final Nash Equilibrium.

The most according to claim 1 based on game theoretic cloud disaster tolerance data back up method, it is characterised in that described purpose is deposited The size of the data volume that storage node D_nodej is backed up according to source cloud provider SCP dynamically adjusts storage price, by not The disconnected resource price adjusting Backup Data and resource quantity make source cloud provider SCP and destination cloud service provider DCP Benefit.

The most according to claim 1 and 2 based on game theoretic cloud disaster tolerance data back up method, it is characterised in that also to include Step 7, described source cloud provider SCP respectively by the data of the tactful xij of source cloud provider according to destination cloud provider The tactful pj of memory node backs up in the memory node D_nodej of destination cloud provider.