Edge caching and pricing method based on mean field game

Abstract

The invention relates to the technical field of caching of edge computing, and particularly discloses an edge caching and pricing method based on mean field game, which specifically comprises the following steps: S01, respectively designing a dynamic network model and a dynamic edge caching model according to the characteristics of a network channel and content caching; s02, designing a reasonable benefit function for each data provider under the condition of considering various transactions according to the characteristics of the data providers; and S03, regarding each data provider as a player, regarding a cache strategy as an action, regarding an accumulated benefit value as a target, then modeling interaction among the data providers as a random differential game, and setting a dynamic network model and a dynamic edge cache model as game limiting conditions. The method is based on the average field game, and the optimal decision can be determined in a decentration mode.

Description

Technical Field

[0001] The present invention relates to the field of cache technology for edge computing, and in particular to an edge cache and pricing method based on mean field game. Background Art

[0002] With the popularity of smart devices and services, mobile edge caching has become an effective solution to handle the explosive growth of mobile data traffic. Mobile edge caching systems use cache nodes located at the edge of the network to store commonly used content and data close to users to reduce data transmission latency and network congestion, thereby significantly improving mobile network performance and user experience. A typical mobile edge caching system consists of many edge data providers (such as cell / microcell base stations, smartphones, edge servers, specially designed caching devices, etc.) and some content requesters. These data providers can cache appropriate content (such as articles, videos, and music, etc.) and then trade with requesters at an appropriate price. Since mobile edge caching systems can effectively improve the quality of experience of requesters and reduce bandwidth consumption, mobile edge caching has attracted the attention of various commercial platforms, such as Google Edge Network, Fastly, CacheMire, and VbrickEdge Caching.

[0003] In mobile edge caching systems, the study of content placement is crucial because it directly affects the system performance, user experience, and network resource utilization. On the one hand, due to the limited caching capacity of each data provider, how to place appropriate content to meet the needs of requesters and maximize the benefits (i.e., net profit) of data providers has become an urgent problem to be solved. On the other hand, each data provider needs to formulate a suitable pricing strategy and sell cached content to requesters in an on-demand manner. Note that when a data provider does not cache the content required by the corresponding requester, peer-to-peer content sharing will help improve caching efficiency. Therefore, it is of great significance to study the dynamic memory caching problem and pricing problem in mobile edge caching systems. However, most studies have not yet discussed the economic transactions between data providers and requesters, and have ignored the strategic behavior of multiple data providers.

[0004] Since data providers need to sell cached content through competition, firstly, there are complex interactions between caching, pricing and sharing in large-scale mobile edge caching systems, which will make it difficult for each data provider to formulate the optimal caching strategy. Specifically, under the principle of supply and demand, the caching strategy can directly affect the transaction price, and the benefits of content trading in turn affect the decision of content caching. This intricate interaction is crucial because excess content caching may lead to market saturation and reduce the profits of data providers, while insufficient caching will lead to a decline in service quality for requesters and affect future transactions. At the same time, content sharing between data providers also involves economic transaction issues, making the interaction more complicated. Secondly, it is difficult to make real-time decisions in dynamic systems. Due to the random movement of requesters and some unknown interference, the network channel may be in an unstable state. Moreover, in the dynamic trading market, time-varying content service requests reflect unpredictable content popularity and timeliness requirements. Taking these spatiotemporal dynamic factors into consideration, it is very challenging to enable each data provider to adaptively make the best caching decision. Finally, it is extremely difficult to achieve large-scale distributed optimal response in an incomplete information environment. Since data providers all exist in a common trading market, the behaviors of data providers are mutually influenced. That is, there is a complex non-cooperative game between data providers to make distributed caching decisions. More importantly, it is not a simple matter for a data provider to estimate certain information and actions of other data providers in a dynamic system, because it will consume a lot of communication and computing resources, especially in large-scale scenarios. Summary of the invention

[0005] In view of the problems mentioned in the background technology, the present invention provides an edge caching and pricing method based on mean field game. The mobile edge caching system of the present invention determines the optimal caching strategy for each data provider with the help of mean field game theory, takes the maximization of the benefits of multiple data providers as the optimization goal, and takes the network model dynamics and cache dynamics as constraints. The method effectively motivates the participation of data providers and content requesters through reasonable edge caching and pricing methods, and is suitable for online decision-making in large-scale systems.

[0006] The technical solution adopted by the present invention is: an edge caching and pricing method based on mean field game, which specifically includes the following steps:

[0007] S01: According to the characteristics of network channels and content cache, a dynamic network model and a dynamic edge cache model are designed respectively;

[0008] S02: Based on the characteristics of data providers, design a reasonable benefit function for each data provider under various transaction scenarios;

[0009] S03: Consider each data provider as a player, the cache strategy as an action, and the accumulated benefit value as the goal. Then, the interaction between data providers is modeled as a stochastic differential game, and the dynamic network model and dynamic edge cache model are set as game constraints.

[0010] S04: We estimate the unknown income and unknown expenditure of data providers based on the mean field distribution and local information. Then, we obtain the optimal caching strategy for each data provider by iteratively solving multiple coupled equations, and prove that these strategies form a Nash equilibrium.

[0011] S05: In a system equilibrium environment, each data provider sets a suitable price and then sells the cached content to the corresponding requester.

[0012] The present invention is further configured to be applied to a mobile edge cache system, wherein the mobile edge cache system includes three components: an edge data provider, multiple cloud centers, and a content requester; each edge data provider needs to simultaneously formulate a content cache strategy and a pricing strategy to maximize its own benefits;

[0013] The mobile edge cache system has three components:

[0014] (1) Data Provider It has a caching function to satisfy requesters who want to obtain certain content. In order to quickly respond to the needs of requesters through wireless communication, data providers need to cache certain content in advance and allow the cached content to be shared in a distributed point-to-point communication manner. After receiving the request, the data provider will sell its cached content at an appropriate transaction price;

[0015] (2) Multiple cloud centers store various types of content The data size of each content is Q k ,Each data provider can download the content they want from the cloud center;

[0016] (3) Content Requester Request content from data providers based on their own needs and are willing to pay the corresponding price. Different data providers only provide services to requesters within their jurisdiction. In addition, the number of requests generated by content requesters for different content will reflect its popularity, and content requesters can inform data providers of their own urgency for the content when making requests.

[0017] The present invention is further configured that the detailed network model design process in step S01 is as follows: Since the movement of requesters in the mobile edge cache system is random and uncertain, there are some interferences between requesters and the network channel conditions become unstable. Therefore, a non-steady-state time-varying channel model needs to be considered to describe this random process.

[0018] Let h i,j (t) represents the channel fading coefficient between provider i and requester j, h i,j The dynamics of (t) can be described by a mean-reverting Ornstein-Uhlenbeck process, whose dynamic differential equation is:

[0019]

[0020] in, υ h and are all positive parameters, the random diffusion term W i,j (t) characterizes the standard Brownian motion, capturing the randomness of the system (e.g., requester mobility and channel fluctuations).

[0021] The present invention is further configured such that the detailed cache model design process in step S01 is as follows: In the content placement phase, each data provider requires a cache strategy to optimize its own benefits.

[0022] Let vector x i (t) = [x i,1 (t),…,x i,K (t)] represents the cache strategy of data provider i, where x i,k (t)∈[0,1] represents the instantaneous cache rate of content k. Correspondingly, the time-varying remaining storage capacity of all content of data provider i is given by q i (t) = [q i,1 (t),…,q i,K (t)] represents, where q i,k (t) represents the remaining space of data provider i for content k. Meanwhile, considering the popularity of the content, if content k is rarely requested, data provider i will discard it. On the other hand, from the perspective of response delay, when content k is urgently requested, data provider i tends to increase its storage space to avoid additional communication with other data providers i or the center. Therefore, the dynamics of the cache state can be described as:

[0023]

[0024] Among them, w1, w2 and w3 are parameters used to adjust the ratio. i,k (t) and Li,k (t) represent the popularity and timeliness of content k detected by data provider i, respectively.

[0025] The present invention is further configured that, in the content transaction stage, each data provider sells its own content to the corresponding requester, so that p i,k (t) represents the unit price customized by data provider i for selling content k at time t. It is worth noting that according to the cache strategy x determined by it i,k (t), data provider i may not cache all the data of content k. When requesting uncached data from the center or other data providers, each data provider will give priority to neighboring providers to reduce transmission delay. A common usage-based pricing scheme is adopted, in which each data provider needs to pay a uniform unit price (usage denoted) to obtain content k from other providers.

[0026] The present invention is further configured such that the benefit function design process in step S02 is:

[0027] Each data provider may encounter three situations when serving a requester:

[0028] Case 1: Data provider i has cached enough content k for the requester. Due to the continuity of the cache state, some content may not be completely cached, that is, only a relatively small part α is not stored. In this case, the content basically meets the requester's needs;

[0029] Case 2: Data provider i does not cache enough content k for the requester, but some neighboring providers have cached the content. Then, data provider i will contact other providers who provide enough content k and pay the corresponding compensation.

[0030] Case 3: Data provider i and its neighbors cannot cache enough content k for the requester, so data provider i needs to download the uncached part of content k from the cloud center;

[0031] use Respectively represent the probability of occurrence of three situations;

[0032] The benefit of each data provider i is the transaction income paid by the requester and shared revenue from other providers Subtract its total cost, which includes the cost of content placement Delay Cost and shared costs The benefit function U of data provider i i,k (t) can be defined as follows:

[0033]

[0034] The present invention is further configured such that the detailed mean field game design process in step S03 is as follows:

[0035] The competitive content placement problem among large-scale data providers is formalized as an incomplete information stochastic differential game in a finite time horizon, where each data provider is a player and the state of each player is Each player's action is a cached strategy, and the cumulative benefit of each player is In this game, the goal is to maximize the benefit function of each data provider, namely:

[0036]

[0037] limit:

[0038]

[0039] Where S -i,k represents the state of the other M-1 providers. The solution to this optimization problem needs to achieve a Nash equilibrium, that is, it needs to ensure that no participant can improve its own utility by unilaterally deviating from its optimal strategy.

[0040] The present invention is further configured such that the game solving process in step S04 includes:

[0041] The original game is transformed into a new mean field game, and two modules are designed: a universal player who takes rational actions and a mean field estimator that represents the collective actions of all other players. Initially, each universal data provider formulates a strategy set containing all feasible states to optimize its utility. Subsequently, by approximating the probability density function (PDF) of the states, the mean field estimator calculates the cumulative impact of all data providers on the universal data provider in terms of content caching, trading, and sharing.

[0042] Here, the mean field estimator is composed of a cache strategy for each data provider determined only by its own current state and the mean field estimate. That is, any permutation of the data provider indexes does not change the determination of the optimal strategy. Therefore, we can focus on studying a common data provider by removing index i, which interacts with the mean field estimator instead of communicating with all other data providers individually. Given a state S k (t), the mean field estimator needs to estimate the statistical distribution of the state at time t. The probability density of the data provider associated with content k in a specific state is expressed as follows:

[0043]

[0044] Among them, λ(S k (t)) indicates that it is in state S k The indicator function returns 1 when the given condition is met, otherwise it returns 0. When all data providers in the system implement the derived optimal strategy, the FPK equation can be used to describe the channel state h(t) and the remaining buffer state q k The evolution of the dynamic mean field distribution of (t) is as follows:

[0045]

[0046] Based on the mean field distribution, we can approximate the unknown income and costs involving other data providers’ strategies and states. First, we use the mean field probability density function λ(S k (t)) and the optimal strategy To determine the dynamic price p k (t), that is:

[0047]

[0048] in, represents the maximum price per unit of data that the data provider can charge. η1 is used to convert the average content supply into a monetary value. In addition to the dynamic price, the transaction revenue also needs to know q -i,k (t), which can be approximated by the average state of all other data providers, defined as represents the average value of the remaining cache storage space of other data providers, given the mean field distribution, and λ(S k The average cache state associated with (t) can be expressed as:

[0049]

[0050] We then estimate the sharing benefits to analyze the impact of content sharing. At time t, the number of data providers M who are eligible to share their content k is k (t) can be published by the center. At the same time, the center will also observe the number of data providers who encounter situation 3, denoted as M' k (t), in addition, the average transmission volume between data providers can be approximately calculated, and the average shared benefit is obtained as:

[0051]

[0052] Based on the above approximation, the general provider can further optimize its utility by calling the mean field estimator and determine the optimal caching strategy under the current state information. The specific strategy determination process is as follows;

[0053] General Player Strategies

[0054] With the establishment of the mean field estimator, the optimization problem of each data provider can be transformed into a general problem that only involves local state information and the mean field distribution, namely: It should be emphasized that here we only need to use the mean field estimator to quickly obtain p k (t), and Then they are directly substituted into the transaction revenue, shared benefits, delay costs, and shared costs; thus, the value objective function It depends only on the individual cache strategy, the current state and the mean field distribution; to solve the optimization problem, the HJB equation can be rewritten as:

[0055]

[0056] By solving the above equation, we can get the optimal caching strategy as follows:

[0057]

[0058] Among them, the function [x] + Defined as: When x>1, [x] + =1; when x<0 [x] + =0; otherwise [x] + = x. The solution of the HJB equation has a great influence on the FPK equation, which is used to update the mean field. Conversely, the solution of the FPK equation is also needed by the HJB equation to estimate the utility of the general player and update the strategy. The two modules, the general player and the mean field estimator, interact with each other and constitute the whole of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flow chart of the edge caching and pricing method based on mean field game of the present invention;

[0060] Figure 2 The present invention is in different initial states q k (0) Schematic diagram of the change of cache amount under the value;

[0061] Figure 3 The present invention is in different initial states q k (0) Schematic diagram of the change of benefit value under different values;

[0062] Figure 4 It is a schematic diagram of the change of benefit value under different distribution means of the present invention;

[0063] Figure 5 It is a schematic diagram of the change of benefit value under different parameter η1 values ​​of the present invention.

[0064] The beneficial effects of the present invention are:

[0065] (1) The present invention provides an edge caching and pricing method based on mean field game, which can determine the optimal decision in a decentralized manner based on mean field game.

[0066] (2) In the present invention, based on game theory, the cache optimization problem is modeled as a non-cooperative stochastic differential game between multiple data providers. By designing a mean field estimator, this method can approximate the effects of caching, trading, and sharing without the need for a large amount of information exchange, so that each data provider can customize the optimal caching strategy and pricing strategy using only its local information. At the same time, the present invention takes into account the impact of sharing and pricing on caching, which can be more in line with practical applications. DETAILED DESCRIPTION

[0067] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0068] Reference Figure 1-5 ,In order to solve the problems existing in the background technology, the present application proposes the following technical solutions: ,An edge caching and pricing method based on mean field game, ,The edge caching and pricing method based on mean field game in this embodiment, ,is mainly applied to a mobile edge caching system, ,which includes three components: an edge data provider, ,a plurality of cloud centers, and a content requester; ,Each edge data provider needs to formulate content caching strategy and pricing strategy at the same time to maximize its own benefits;

[0069] The mobile edge cache system has three components:

[0070] (1) Data Provider It has a caching function to satisfy requesters who want to obtain certain content. In order to quickly respond to the needs of requesters through wireless communication, data providers need to cache certain content in advance and allow the cached content to be shared in a distributed point-to-point communication manner. After receiving the request, the data provider will sell its cached content at an appropriate transaction price;

[0071] (2) Multiple cloud centers store various types of content The data size of each content is Q k ,Each data provider can download the content they want from the cloud center;

[0072] (3) Content Requester Request content from data providers based on their own needs and are willing to pay the corresponding price. Different data providers only provide services to requesters within their jurisdiction. In addition, the number of requests generated by content requesters for different content will reflect its popularity, and content requesters can inform data providers of their own urgency for the content when making a request. For example, the urgency can be set to non-urgent, urgent, relatively urgent, etc.

[0073] The edge caching and pricing method based on mean field game specifically includes the following steps:

[0074] S01: According to the characteristics of network channels and content cache, a dynamic network model and a dynamic edge cache model are designed respectively;

[0075] S02: Based on the characteristics of data providers, design a reasonable benefit function for each data provider under various transaction scenarios;

[0076] S03: Consider each data provider as a player, the cache strategy as an action, and the accumulated benefit value as the goal. Then, the interaction between data providers is modeled as a stochastic differential game, and the dynamic network model and dynamic edge cache model are set as game constraints.

[0077] S04: We estimate the unknown income and unknown expenditure of data providers based on the mean field distribution and local information. Then, we obtain the optimal caching strategy for each data provider by iteratively solving multiple coupled equations, and prove that these strategies form a Nash equilibrium.

[0078] S05: In a system equilibrium environment, each data provider sets a suitable price and then sells the cached content to the corresponding requester.

[0079] The detailed network model design process in step S01 is as follows: Since the movement of requesters in the mobile edge cache system is random and uncertain, there are some interferences between requesters and the network channel conditions become unstable. Therefore, a non-steady-state time-varying channel model needs to be considered to describe this random process.

[0080] Let h i,j (t) represents the channel fading coefficient between provider i and requester j, h i,j The dynamics of (t) can be described by a mean-reverting Ornstein-Uhlenbeck process, whose dynamic differential equation is:

[0081]

[0082] in, υh and are all positive parameters, the random diffusion term W i,j (t) characterizes the standard Brownian motion, capturing the randomness of the system (e.g., requester mobility and channel fluctuations).

[0083] The detailed cache model design process in step S01 is as follows: In the content placement phase, each data provider needs a cache strategy to optimize its own benefits.

[0084] Let vector x i (t) = [x i,1 (t),…,x i,K (t)] represents the cache strategy of data provider i, where x i,k (t)∈[0,1] represents the instantaneous cache rate of content k. Correspondingly, the time-varying remaining storage capacity of all content of data provider i is given by q i (t) = [q i,1 (t),…,q i,K (t)] represents, where q i,k (t) represents the remaining space of data provider i for content k. Meanwhile, considering the popularity of the content, if content k is rarely requested, data provider i will discard it. On the other hand, from the perspective of response delay, when content k is urgently requested, data provider i tends to increase its storage space to avoid additional communication with other data providers i or the center. Therefore, the dynamics of the cache state can be described as:

[0085]

[0086] Among them, w1, w2 and w3 are parameters used to adjust the ratio. i,k (t) and L i,k (t) represent the popularity and timeliness of content k detected by data provider i, respectively.

[0087] In the content transaction phase, each data provider sells its content to the corresponding requester, allowing p i,k (t) represents the unit price customized by data provider i for selling content k at time t. It is worth noting that according to the cache strategy x determined by it i,k (t), data provider i may not cache all the data of content k. When requesting uncached data from the center or other data providers, each data provider will give priority to neighboring providers to reduce transmission delay. A common usage-based pricing scheme is adopted, in which each data provider needs to pay a uniform unit price (usage denoted) to obtain content k from other providers.

[0088] The benefit function design process in step S02 is as follows:

[0089] Each data provider may encounter three situations when serving a requester:

[0090] Case 1: Data provider i has cached enough content k for the requester. Due to the continuity of the cache state, some content may not be completely cached, that is, only a relatively small part α is not stored. In this case, the content basically meets the requester's needs;

[0091] Case 2: Data provider i does not cache enough content k for the requester, but some neighboring providers have cached the content. Then, data provider i will contact other providers who provide enough content k and pay the corresponding compensation.

[0092] Case 3: Data provider i and its neighbors cannot cache enough content kk for the requester, so data provider i needs to download the uncached part of content k from the cloud center;

[0093] use Respectively represent the probability of occurrence of three situations;

[0094] The benefit of each data provider i is the transaction income paid by the requester and shared revenue from other providers Subtract its total cost, which includes the cost of content placement Delay Cost and shared costs The benefit function U of data provider i i,k (t) can be defined as follows:

[0095]

[0096] The above technical solution is explained as follows:

[0097] Transaction income: When M=1, the transaction price is: Otherwise the transaction price is: At this point, the transaction income is calculated by the following formula:

[0098]

[0099] Share the revenue: here, represents the set of other providers that request content k from data provider i at time t.

[0100] Content placement costs: Here, w4 and w5 are two adjustable parameters.

[0101] Latency Cost: Since latency directly affects the requester’s user experience quality, this function needs to be non-decreasing and non-negative to measure the impact of latency.

[0102] For simplicity, we adopt a linear penalty function to describe the delay cost as follows:

[0103]

[0104] Among them, η2 is used to convert the total request service delay into delay cost, H c Represents the transfer rate between the hub and any data provider.

[0105] The first item is generated by data provider i downloading content k from the center according to the determined caching strategy.

[0106] The second item corresponds to case 1, that is, data provider i can directly transmit content k to the requester.

[0107] The third term corresponds to case 2 and represents the delay when the data provider purchases content from its neighboring providers and transmits it to the requester. The transmission time between data provider i and its neighboring providers is ignored here because it is much smaller than the communication delay between data provider i and the center / requester.

[0108] The fourth term corresponds to case 3, that is, data provider i will download the uncached content from the data center and transmit the entire content k to the requester. After accumulating the delays of all corresponding requesters, the delay cost of data provider i can be obtained.

[0109] Shared costs:

[0110] Based on the above definition, the benefit function U of data provider i can be obtained: i,k (t) is:

[0111]

[0112] The detailed mean field game design process in step S03 is as follows:

[0113] The competitive content placement problem among large-scale data providers is formalized as an incomplete information stochastic differential game in a finite time horizon, where each data provider is a player and the state of each player is Each player's action is a cached strategy, and the cumulative benefit of each player is In this game, the goal is to maximize the benefit function of each data provider, namely:

[0114]

[0115] limit:

[0116]

[0117] Where S -i,k represents the state of the other M-1 providers. The solution to this optimization problem needs to achieve a Nash equilibrium, that is, it needs to ensure that no participant can improve its own utility by unilaterally deviating from its optimal strategy.

[0118] The above technical solution is explained as follows: Players: a group of data providers, denoted as

[0119] State: Let the two-tuple represents the state of data provider i at time t relative to a given content k. Then, the state space is

[0120] Policy: The set of all possible cache controls {x i,k (t)}.

[0121] Cumulative utility: The cumulative utility of player i with respect to content k in a finite time horizon t can be defined as

[0122] In this game, the goal is to maximize the cumulative benefit value, and the dynamic network model and dynamic edge cache model are set as game constraints;

[0123] The game solving process in step S04 includes:

[0124] The basic idea of ​​the solution is to approximate the collective influence of large-scale data providers on content caching, trading, and sharing without a large number of interactions, and then determine the optimal caching strategy for each data provider by iteratively solving multiple coupled equations. More specifically, the original stochastic differential game is first converted into a mean field game, in which the interaction of multiple players can be regarded as a universal player representation based on statistical distribution.

[0125] Next, a mean-field estimator is designed to approximate the cumulative impact of all providers on caching, trading, and sharing, where the Fokker-Planck-Kolmogorov (FPK) equation is used to show the evolution of the mean-field distribution.

[0126] In the process, the unknown revenue and costs of each data provider are cleverly estimated without the need for frequent information exchange.

[0127] Then, a general player is designed to adjust its caching strategy according to the feedback from the HJB equation and the mean field estimator. Finally, in order to obtain the Nash equilibrium of the game for each data provider in a distributed scenario, an iterative best response learning algorithm is designed to solve the coupled HJB and FPK equations.

[0128] In this way, the optimal caching strategy can be determined within the time horizon by only utilizing the local information and the mean field distribution.

[0129] According to the above design ideas, we first convert the original game into a new mean field game and design two modules: a universal player who takes rational actions and a mean field estimator that represents the collective actions of all other players. Initially, each universal data provider formulates a strategy set containing all feasible states to optimize its utility. Since all data providers are symmetric and equally rational in possible states, they share a universal strategy set. Subsequently, by approximating the probability density function (PDF) of the state, the mean field estimator calculates the cumulative impact of all data providers on the universal data provider in terms of content caching, trading, and sharing. In this way, the universal data provider adjusts its strategy set based on the feedback of the mean field estimator, and the mean field estimator recalculates the impact based on the updated strategy set. This iterative process continues until a Nash equilibrium is reached.

[0130] Here, the mean field estimator is composed of a cache strategy for each data provider determined only by its own current state and the mean field estimate. That is, any permutation of the data provider indexes does not change the determination of the optimal strategy. Therefore, we can focus on studying a common data provider by removing index i, which interacts with the mean field estimator instead of communicating with all other data providers individually. Given a state S k (t), the mean field estimator needs to estimate the statistical distribution of the state at time t. The probability density of the data provider associated with content k in a specific state is expressed as follows:

[0131]

[0132] Among them, λ(S k (t)) indicates that it is in state S k The indicator function returns 1 when the given condition is met, otherwise it returns 0. When all data providers in the system implement the derived optimal strategy, the FPK equation can be used to describe the channel state h(t) and the remaining buffer state q k The evolution of the dynamic mean field distribution of (t) is as follows:

[0133]

[0134] Based on the mean field distribution, we can approximate the unknown income and costs involving other data providers’ strategies and states. First, we use the mean field probability density function λ(S k (t)) and the optimal strategy To determine the dynamic price p k (t), that is:

[0135]

[0136] in, represents the maximum price per unit of data that the data provider can charge. η1 is used to convert the average content supply into a monetary value. In addition to the dynamic price, the transaction revenue also needs to know q -i,k (t), which can be approximated by the average state of all other data providers, defined as represents the average value of the remaining cache storage space of other data providers, given the mean field distribution, and λ(S k The average cache state associated with (t) can be expressed as:

[0137]

[0138] We then estimate the sharing benefits to analyze the impact of content sharing. At time t, the number of data providers M who are eligible to share their content k is k (t) can be published by the center. At the same time, the center will also observe the number of data providers who encounter situation 3, denoted as M' k (t), in addition, the average transmission volume between data providers can be approximately calculated, and the average shared benefit is obtained as:

[0139]

[0140] Based on the above approximation, the general provider can further optimize its utility by calling the mean field estimator and determine the optimal caching strategy under the current state information. The specific strategy determination process is as follows;

[0141] The specific method of establishing the universal player strategy is as follows: With the establishment of the mean field estimator, the optimization problem of each data provider can be transformed into a universal problem that only involves local state information and the mean field distribution, namely: It should be emphasized that here we only need to use the mean field estimator to quickly obtain p k (t), and Then they are directly substituted into the transaction revenue, shared benefits, delay costs, and shared costs; thus, the value objective function It depends only on the individual cache strategy, the current state and the mean field distribution; to solve the optimization problem, the HJB equation can be rewritten as:

[0142]

[0143] By solving the above equation, we can get the optimal caching strategy as follows:

[0144]

[0145] Here, the function [x] + Defined as: When x>1, [x] + =1; when x<0 [x] + =0; otherwise [x] + =x. The solution of the HJB equation has a great influence on the FPK equation, which is used to update the mean field. Conversely, the solution of the FPK equation is also needed by the HJB equation to estimate the utility of the general player and update the strategy. The two modules, the general player and the mean field estimator, interact with each other and constitute the whole of the method.

[0146] Among them, the above solution is almost equivalent to the solution of the stochastic differential game when dealing with a large number of players, ensuring the consistency of the optimization problem. In addition, the mean field approximation method designed above shows lower complexity than the original game. The two modules of the universal player and the mean field estimator interact with each other to form the whole method.

[0147] More specifically, the solution of the HJB equation has a great influence on the FPK equation, which is used to update the mean field. Conversely, the solution of the FPK equation is also needed by the HJB equation to estimate the utility of the general player and update the strategy. These interrelated modules comprehensively construct the core structure of the method.

[0148] In order to determine the optimal caching strategy for each data provider, the state of each data provider and the data size of each content are initialized first.

[0149] By leveraging parallel processing, each data provider uses a limited time horizon T as an optimization period. Specifically, each data provider initially records the requester's requirements And determine the set of content that needs to be cached and

[0150] Here, it is assumed that the change speed of the requester's demand is slow relative to the time scale of the optimization cycle. Therefore, some content does not need to be considered in the subsequent optimization. Perform edge caching and content trading. After each data provider calculates the popularity and freshness of the content, provider i gives the best response, that is, customizes its optimal caching strategy.

[0151] The iterative process for each data provider to learn the best response is as follows:

[0152] When ψ<ψ th or When is greater than a preset threshold, we iteratively solve the coupled HJB and FPK equations: the backward HJB model describes the induction process of each individual optimization, while the forward FPK model describes the evolution of the mean field as a whole. Subsequently, we solve the HJB equation to obtain

[0153]

[0154] Based on the solution of the above equation, the cache strategy can be further updated as follows:

[0155]

[0156] Then, the FPK equation can be calculated based on the current strategy:

[0157]

[0158] The solution of the above FPK equation can be used to update the mean field estimator. At the same time, the benefit function is updated to be used to solve the HJB equation in the next iteration.

[0159] Among them, in step S05: after each data provider determines its own cache strategy, the transaction process between the data provider and the corresponding requester will be executed, and the data provider needs to take different actions in different situations. Specifically, in situation 1, the data provider charges a unit price p i,k (t) Selling content; in case 2, the data provider uses p k Purchase uncached content from neighboring data providers and sell it to requesters; in case three, data providers download uncached content from the center and sell it to requesters;

[0160] The present invention not only enables data providers to flexibly charge prices and cache, but also brings better service quality to content requesters, effectively saves resources, and has high use value and wide application background.

[0161] In summary,

[0162] This paper provides an edge caching and pricing method based on mean field game, which can determine the optimal decision in a decentralized manner. This is the first attempt to explore the complex interaction between strategic caching and monetary transactions in large-scale dynamic mobile edge caching systems.

[0163] In addition, based on game theory, the present invention models the cache optimization problem as a non-cooperative stochastic differential game between multiple data providers. By designing a mean field estimator, this method can approximate the effects of caching, trading, and sharing without the need for a large amount of information exchange, so that each data provider can customize the optimal caching strategy and pricing strategy using only its local information. At the same time, the present invention takes into account the impact of sharing and pricing on caching, which can be more in line with practical applications.

[0164] While the embodiments of the present invention have been shown and described, it will be apparent to those skilled in the art that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An edge caching and pricing method based on mean field game, characterized in that: The specific steps include: S01: According to the characteristics of network channels and content cache, a dynamic network model and a dynamic edge cache model are designed respectively; S02: Based on the characteristics of data providers, design a reasonable benefit function for each data provider under various transaction scenarios; S03: Consider each data provider as a player, the cache strategy as an action, and the accumulated benefit value as the goal. Then, the interaction between data providers is modeled as a stochastic differential game, and the dynamic network model and dynamic edge cache model are set as game constraints. S04: We estimate the unknown income and unknown expenditure of data providers based on the mean field distribution and local information. Then, we obtain the optimal caching strategy for each data provider by iteratively solving multiple coupled equations, and prove that these strategies form a Nash equilibrium. S05: In a system equilibrium environment, each data provider sets a suitable price and then sells the cached content to the corresponding requester.

2. The edge caching and pricing method based on mean field game according to claim 1, characterized in that: Applied to the mobile edge caching system, the mobile edge caching system consists of three components: edge data providers, multiple cloud centers, and content requesters; each edge data provider needs to formulate content caching strategies and pricing strategies at the same time to maximize its own benefits; The three components of the mobile edge cache system are as follows: (1) Data Provider It has a cache function to satisfy the requesters who want to obtain certain content. It can quickly respond to the requesters' needs through wireless communication. The data provider needs to cache certain content in advance and allow the cached content to be shared in a distributed point-to-point communication manner. After receiving the request, the data provider will sell its cached content at an appropriate transaction price. (2) Multiple cloud centers store various types of content The data size of each content is Q k ,Each data provider downloads the content it wants from the cloud center; (3) Content Requester Request content from data providers based on their own needs and are willing to pay the corresponding price. Different data providers only provide services to requesters within their jurisdiction. The number of requests generated by content requesters for different content will reflect its popularity, and content requesters will inform data providers of their own urgency for the content when making requests.

3. The edge caching and pricing method based on mean field game according to claim 1, characterized in that: The detailed network model design process in step S01 is as follows: Let h i,j (t) represents the channel fading coefficient between provider i and requester j, h i,j The dynamics of (t) is described by a mean-reverting Ornstein-Uhlenbeck process, whose dynamic differential equation is: in, υ h and are all positive parameters, the random diffusion term W i,j (t) characterizes standard Brownian motion and captures the randomness of the system.

4. The edge caching and pricing method based on mean field game according to claim 1, characterized in that: The detailed cache model design process in step S01 is as follows: Let vector x i (t) = [x i,1 (t),…,x i,K (t)] represents the cache strategy of data provider i, where x i,k (t)∈[0,1] represents the instant cache rate of content k; The time-varying remaining storage capacity of data provider i for all content is given by q i (t) = [q i,1 (t),…,q i,K (t)] indicates; Among them, q i,k (t) represents the remaining space of data provider i for content k. At the same time, considering the popularity of the content, if content k is rarely requested, data provider i will discard it. On the other hand, from the perspective of response delay, when content k is urgently requested, data provider i tends to increase its storage space to avoid additional communication with other data providers i or the center. Therefore, the dynamic description of the cache state is: Among them, w1, w2 and w3 are parameters used to adjust the ratio; i,k (t) and L i,k (t) represent the popularity and timeliness of content k detected by data provider i, respectively.

5. The edge caching and pricing method based on mean field game according to claim 1, characterized in that: In the content transaction phase, each data provider sells its content to the corresponding requester, allowing p i,k (t) represents the unit price customized by data provider i for selling content k at time t, according to the cache strategy x determined by it i,k (t), data provider i will not cache all the data of content k. When requesting uncached data from the center or other data providers, each data provider will give priority to neighboring providers to reduce transmission delays. A common usage-based pricing scheme is adopted, in which each data provider needs to pay a uniform unit price (usage denoted) to obtain content k from other providers.

6. The edge caching and pricing method based on mean field game according to claim 1, characterized in that: The benefit function design process in step S02 is: Each data provider encounters three situations when serving a requester: Case 1: Data provider i has cached enough content k for the requester. Due to the continuity of the cache state, some content is not completely cached, that is, only a relatively small part α is not stored. In this case, the content basically meets the requester's needs. Case 2: Data provider i does not cache enough content k for the requester, but some neighboring providers have cached the content. Data provider i will contact other providers who provide enough content k and pay the corresponding compensation. Case 3: Data provider i and its neighbors cannot cache enough content k for the requester, and data provider i needs to download the uncached part of content k from the cloud center; use Respectively represent the probability of occurrence of three situations; The benefit of each data provider i is the transaction income paid by the requester and shared revenue from other providers Subtract its total cost, which includes the content placement cost Delay Cost and shared costs The benefit function U of data provider i i,k (t) is defined as follows:

7. The edge caching and pricing method based on mean field game according to claim 1, characterized in that: The detailed mean field game design process in step S03 is as follows: The competitive content placement problem among large-scale data providers is formalized as an incomplete information stochastic differential game in a finite time horizon, where each data provider is a player and the state of each player is Each player’s action is a cached strategy; The cumulative benefit for each player is expressed as follows: In this game, the goal is to maximize the benefit function of each data provider, namely: limit: Where S -i,k Indicates the status of the other M-1 providers.

8. The edge caching and pricing method based on mean field game according to claim 1, characterized in that: The game solving process in step S04 includes the following methods: First, the original game is converted into a new mean-field game, and two modules are designed: a universal player who takes rational actions and a mean-field estimator that represents the collective actions of all other players. Initially, each universal data provider formulates a strategy set containing all feasible states to optimize its utility; Subsequently, by approximating the probability density function (PDF) of the states, the mean field estimator calculates the cumulative impact of all data providers on the common data provider in terms of content caching, trading, and sharing; The mean field estimator is composed of a cache strategy for each data provider determined only by its own current state and mean field estimate. Any permutation of the data provider index does not change the determination of the optimal strategy. By removing index i, we focus on a common data provider that interacts with the mean field estimator instead of communicating with all other data providers individually. Given a state S k (t), the mean field estimator needs to estimate the statistical distribution of the state at time t. The probability density of the data provider associated with content k in a specific state is expressed as follows: Among them, λ(S k (t)) indicates that it is in state S k The indicator function returns 1 when the given condition is met, otherwise it returns 0. When all data providers in the system implement the derived optimal strategy, the FPK equation is used to describe the channel state h(t) and the remaining buffer state q k The evolution of the dynamic mean field distribution of (t) is as follows: Based on the mean field distribution, we approximate the unknown income and costs involving the strategies and states of other data providers. First, we use the mean field probability density function λ(S k (t)) and the optimal strategy To determine the dynamic price p k (t), that is: in, represents the highest price per unit of data charged by the data provider, η1 is used to convert the average content supply into a monetary value. In addition to the dynamic price, the transaction revenue also needs to know q -i,k (t), approximated by the average state of all other data providers, defined represents the average value of the remaining cache storage space of other data providers, given the mean field distribution, and λ(S k The average cache state associated with (t) is expressed as: We then estimate the sharing benefits to analyze the impact of content sharing. At time t, the number of data providers M who are eligible to share their content k is k (t) is published by the center. At the same time, the center will also observe the number of data providers who encounter situation 3, denoted as M' k (t), in addition, the average transmission volume between data providers is approximately calculated, and the average shared benefit is obtained as: Based on the above approximation, the general provider further optimizes its utility by calling the mean field estimator and determines the optimal caching strategy under the current state information. The specific strategy determination process is as follows; Among them, the specific method for establishing a general player strategy is as follows: With the establishment of the mean field estimator, the optimization problem of each data provider is transformed into a general problem that only involves local state information and the mean field distribution, namely: Use the mean field estimator to quickly obtain p k (t and Substitute them directly into the transaction revenue, shared benefits, delay costs, and shared costs; therefore, the value objective function Depends only on individual cache strategies, current states, and average field distribution; To solve the optimization problem, the HJB equation is rewritten as: By solving the above equation, the optimal caching strategy is as follows: Among them, the function [x] + Defined as: When x>1, [x] + =1; when x<0 [x] + =0; otherwise [x] + =x; used to update the mean field.

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