Method and system for optimizing average field game in edge computing network based on content popularity

Abstract

The invention relates to an average field game optimization method and system in an edge computing network based on content popularity. The method comprises the following steps: (1) setting a system model; comprising the steps that an edge computing network is set, and the edge computing network comprises a cloud data center, a plurality of edge nodes with storage units and a plurality of users; (2) modeling a video service-oriented cache decision problem in the edge computing network as a random differential game problem, namely an SDG problem, according to a residual storage space state of each edge node and a state change of a task popularity degree based on content popularity; and (3) solving the SDG problem by using a mean field game method, obtaining Nash equilibrium oriented to a video service cache decision problem in the edge computing network, and obtaining an optimal cache strategy of each edge node. According to the method, the satisfaction of user requirements is concerned, and the caching income of the edge node is considered.

Description

Technical Field

[0001] The present invention relates to a mean field game optimization method and system in an edge computing network based on content popularity, and belongs to the technical field of wireless communication networks and game theory optimization. Background Art

[0002] With the commercialization of 5G networks and the development of 6G networks, the proportion of video services such as high-definition video and real-time streaming services in Internet traffic has increased dramatically, which has also put forward higher standards for service delay and user experience. Video service caching technology can reduce network traffic burden and service delay by caching the required video service content on multiple edge servers during non-peak network traffic periods, thereby delegating user service requests to each server for processing. Due to the constant changes in user preferences and content popularity, the demand for video services is dynamic and time-varying. How to update the video cache ratio on the edge server to match the changes in user video service demand is an urgent problem to be solved. In addition, edge servers are deployed by different operators for the purpose of obtaining revenue, so there is competition between servers of different operators. How to make edge caching decisions to ensure that while meeting user needs, the revenue of edge servers is maximized and the overall performance of the network is improved is an urgent problem to be solved.

[0003] The video service caching decision problem of multiple edge servers in edge computing networks can be modeled as a game optimization problem. However, the existing game theory modeling of content caching decisions in edge computing networks still lacks consideration of content popularity, an important factor affecting caching decisions. Most of them focus on users' demand for caching service experience such as latency, but ignore the consideration of the service benefits of the edge server itself.

[0004] Chinese patent document CN111565419A discloses a collaborative edge caching method for latency optimization in an ultra-dense network. The proposed network model is divided into three layers, namely the user device layer, the MEC layer and the cloud layer. The MEC layer includes M small base stations SBS and 1 macro base station. The small base stations communicate with each other through the macro base station and share their cache resources. In view of the edge cache decision problem of each SBS, the patent adopts a multi-agent reinforcement learning algorithm based on game theory to make the optimal cache decision for each SBS to maximize the content cache hit rate of each SBS and minimize the total content download delay of all user devices. However, the patent considers the collaborative edge cache optimization problem of the edge server SBS, and the goal of the cache decision is to only consider the delay of the user device downloading the content from the user's perspective, without considering the service competition relationship between the edge server SBS and the problem of their respective benefits. In addition, the impact of content popularity on the cache benefit of the edge server is not considered, so that when the content popularity changes, the edge server cannot make real-time dynamic adjustments to the cache decision to obtain more service benefits. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a mean field game optimization method for video service caching strategy in an edge computing network based on content popularity, which is used to solve the problems related to each edge server dynamically adjusting its own video caching strategy in real time according to the time-varying content popularity in the edge computing network, as well as the problems of complex information interaction, coupling effect and high computational complexity when the number of game participants is large.

[0006] Terminology explanation:

[0007] The Ornstein-Uhlenbeck process, or OU process for short, is a classic stochastic process, usually used to describe dynamic systems with the characteristic of "regression to the mean". It is a linear, stationary stochastic process. Specifically, the OU process is a Markov process of continuous time and continuous state space. Its most important characteristic is that it can regress to the mean, that is, the process has an equilibrium point. As time goes by, the value of the process tends to a constant mean, and the degree of deviation from the mean gradually decreases. The OU process is an important tool for describing the phenomenon of "regression to the mean". It has stationarity and regression, and is suitable for various systems that need to simulate random fluctuations but tend to a stable state. It is widely used in physics, finance, engineering, sociology and other fields.

[0008] For example, suppose X(t) is an Ornstein-Uhlenbeck process, which satisfies the following stochastic differential equation:

[0009] dX(t)=θ[μ-X(t)]dt+σdW(t)

[0010] Among them, X(t) is the value of the OU process at time t; μ is the long-term mean of the process (i.e., the regression point); θ is the regression rate, which indicates the speed at which the process regresses to the long-term mean; σ is the volatility of the process, which controls the intensity of random disturbances; W(t) is a standard Brownian motion, which is used to represent the random interference factors in the process. Therefore, the OU process will regress to the mean μ over time, and the regression speed is controlled by the parameter θ. If θ is large, the process will return to the mean faster; if θ is small, the process will regress more slowly. In addition, the OU process is stationary, that is, its statistical properties (mean, variance, etc.) are constant over time.

[0011] The technical solution of the present invention is:

[0012] A mean field game optimization method for video service caching strategy in an edge computing network based on content popularity, comprising:

[0013] (1) Setting a system model, including setting an edge computing network, where the edge computing network includes a cloud data center, a plurality of edge nodes (EN) with storage units, and a plurality of users;

[0014] (2) According to the remaining storage space status of each edge node and the change in the popularity of the task based on the content popularity, the video service cache decision problem in the edge computing network is modeled as a stochastic differential game (SDG) problem;

[0015] (3) The mean field game (MFG) method is used to solve the above SDG problem, obtain the Nash equilibrium of the video service caching decision problem in the edge computing network, and obtain the optimal caching strategy for each edge node.

[0016] Preferably, according to the present invention, setting a system model includes:

[0017] The edge computing network includes a cloud data center, Q edge nodes (EN) with storage units, and K users; the edge node set is represented as The user set is represented as

[0018] Each edge node deploys an edge server with a storage unit and is connected to the cloud data center via a wireless link. The video task content requested by the user is downloaded through the wireless link. All task content files are stored in the content library of the cloud data center. The cloud data center allows the edge node to cache the video task content from the content library in advance. When the user generates a video task request, if the required content file is completely cached on the edge node, the edge node directly provides the user with video service. Otherwise, the edge node downloads the uncached task content from the cloud data center via the wireless link. The edge node caches the popular video task content in its storage unit in advance. For all edge nodes, the goal is to determine the storage ratio of the task content. The qth edge node EN q The cache decision for the task content in time slot t is c q (t) indicates that c q (t)∈[0,1], means EN q The proportion of task content downloaded in advance from the cloud data center in time slot t; the qth edge node EN q The rate of downloading video task content from the cloud data center is R qc .

[0019] More preferably, R qc As shown in formula (I):

[0020]

[0021] In formula (I), B q Indicates the qth edge node EN q The allocated channel bandwidth, It represents the signal-to-noise ratio in the current network environment. S and N refer to the signal power and noise power of the edge node EN in the process of downloading the task content from the cloud data center in the current network environment.

[0022] Preferably, according to the present invention, in step (2), the video service caching decision problem in the edge computing network is modeled as an SDG problem; including:

[0023] 2-1. Obtain a dynamic model of content cache and remaining storage space of edge nodes;

[0024] 2-2. Obtain a dynamic model of edge nodes’ popularity for tasks based on content popularity;

[0025] 2-3. Evaluate the cache benefit of the video service cache decision problem in the edge computing network;

[0026] 2-4. Establish the SDG problem of video service caching decision problem in edge computing network.

[0027] Further preferably, obtaining a dynamic model of content cache and remaining storage space of edge nodes includes:

[0028] EN q The remaining storage space for the task content in time slot t is r q Indicates that r q The dynamic differential equation of is expressed as:

[0029] dr q (t)=[D q -Hc q (t)]dt+η1dB q (t) (II)

[0030] Among them, D q Indicates EN q For the available storage space of the task, H represents the size of the task content file, η1 is a positive coefficient, and B q (t) is a standard Brownian motion, dr q (t) indicates EN q The remaining storage space change, D q -Hc q (t) indicates EN q Uncached content portion, η1dB q (t) indicates EN q The volatility of remaining storage space.

[0031] Further preferably, a dynamic model of the popularity of edge nodes for tasks based on content popularity is obtained; including:

[0032] EN q The popularity of the task in time slot t is expressed as v q (t) indicates that v q The dynamic change process of (t) is described by the Ornstein-Uhlenbeck process, v q The stochastic differential equation for (t) is expressed as:

[0033] dv q (t) = θ[λ q (t)-v q (t)]dt+η2dF q (t) (III)

[0034] Among them, θ represents the mean reversion rate, θ>0, η2 represents the volatility of the Omstein-Uhlenbeck process during dynamic changes, and F q (t) is the standard Brownian motion;

[0035] λ q(t) represents EN in the Ornstein-Uhlenbeck process q The mean of the task popularity change process is determined by the recognized basic mean λ of the task popularity and the popularity l(t) of the current time slot task, expressed as λ q (t) = (1-αq)λ + α q l(t), where l(t) is the popularity of the task in time slot t, expressed as the ratio of the number of tasks generated in the current region n(t) to the maximum number of tasks generated in the region N(t) α q Indicates EN q The popularity of a task affects the confidence value of the task’s popularity. λ represents a common judgment value of the popularity of a task that is generally recognized by all edge nodes in the current network environment. The popularity of a task l(t) affects EN q Personality judgment value on the popularity of the task.

[0036] Further preferably, a cache benefit evaluation is performed on the video service cache decision problem in the edge computing network; including:

[0037] a. Obtaining the waiting advantage delay benefit: Define EN q Compared with other edge nodes, the benefit of waiting for the advantage delay for the task is the waiting advantage delay benefit The formula is:

[0038]

[0039] Among them, v q (t) is EN q The popularity of the task in time slot t, v q′ (t) is the difference between EN q The popularity of other edge nodes to the task, ε t is the waiting delay corresponding to the unit task popularity, assuming that the waiting delay is linearly related to the popularity of the edge node to the task;

[0040] b. Seeking service advantage delay benefits: EN q Service Advantages Delay It comes from the cache strategy c q The task service delay after (t) is compared with the expected average task service delay P after other edge nodes in the region adopt their own caching strategies mean The difference of (t) is expressed as P mean (t) can be expressed as: Among them, H represents the size of the task content file, R q Indicates ENq The rate at which content is downloaded from the cloud via the wireless link; c mean (t) represents the average size of cached content files of other edge nodes in the region, which can be expressed as c q′ (t) is the difference between EN q The cache strategy adopted by other edge nodes other than P q (t) is EN q The download delay caused by downloading the uncached part of the task content file from the cloud through the wireless link is expressed as

[0041] c. Calculate the storage space occupation cost: the occupied storage space φ q (t) is expressed as φ q (t) = D q -r q (t);

[0042] d. Obtain instantaneous cache benefit evaluation: EN q The instantaneous profit function J at time slot t q (t) is expressed as:

[0043]

[0044] Among them, ω represents the penalty coefficient of storage space occupancy.

[0045] Further preferably, the SDG problem of video service cache decision problem in edge computing network is established; including:

[0046] Definition q At time slot t, the state of the video task cache is s q (t)=(r q (t), v q (t)); The SDG problem defines a four-tuple representation: in, represents the set of players, Indicates EN q The state space of Indicates EN q A collection of cache strategies, Indicates EN q The profit function in a limited time horizon T Finally, the video task caching problem within a limited time range is modeled as a SDG problem as follows:

[0047]

[0048] dr q (t)=[D q-Hc q (t)]dt+η1dB q (t) (VI)

[0049] dv q (t) = θ[λ q (t)-v q (t)]dt+η2dF q (t)

[0050] Among them, c q (t) is the caching strategy within a limited time range, c q′ (t) is the difference between EN q The cache strategy of other edge nodes other than s q′ Indicates except EN q The state of other edge nodes other than t; define the profit objective function O in the time period [t, T] q (t) is:

[0051]

[0052] The solution to the above SDG problem is obtained by solving the following Q coupled Hamilton-Jacobi-Bellman (HJB) equations using the inverse solution method:

[0053]

[0054] Preferably, in step (3), the mean field game method is used to solve the optimal cache strategy for the SDG problem; comprising:

[0055] 3-1. The SDG problem is transformed into the MFG problem: By defining an empirical distribution M(t, r(t), v(t)) under a single task type, the probability distribution m(t) of the edge node state is given; the empirical distribution M(t, r(t), v(t)) is the probability distribution of the edge node state at time slot t. q (t), v q The statistical distribution density of edge nodes under the (t) state is expressed as follows:

[0056]

[0057] Among them, δ is an indicator function. When the edge node is in the state of (r(t), v(t)), δ = 1, otherwise, δ = 0. The Fokker-Planck-Kolmogorov (FPK) equation is used to describe the evolution of the mean field distribution m(t) under the dynamic changes of the remaining storage space state and the popularity of the task, which is expressed as follows:

[0058]

[0059] definition As the average popularity of other edge nodes for the task, given the average field distribution m(t, r(t), v(t)), The distribution is approximately expressed as follows:

[0060]

[0061] The mean value c of the cached content file size of other edge nodes in the service advantage delay benefit mean (t), is approximately converted into:

[0062]

[0063] When the number of edge nodes participating in the game Q approaches infinity, then:

[0064] c mean (t)=H∫∫m(t, r(t), v(t))c q (t)drdv (XIII)

[0065] Assume m * (t, r(t), v(t)) represents the solution of the FPK equation (XIII). Under the commutativity of the mean field distribution, we get the waiting advantage delay benefit: and service advantages delay benefits The approximate formula is as follows:

[0066]

[0067] By establishing the average field, the optimal cache strategy is obtained according to the local state information of each edge node and the average field distribution;

[0068] Therefore, for each player, the SDG problem is transformed into the following MFG problem:

[0069]

[0070] In this MFG problem, the HJB equation is decoupled as follows:

[0071]

[0072] 32. MFG problem solution: For edge nodes, if the optimal cache strategy c*(t) satisfies J(c*(t), m*(t, r(t), v(t))≥J(c(t), m*(t, r(t), v(t)), then the MFE state of the MFG cache decision problem is reached;

[0073] The HJB equation and the FPK equation are iteratively solved until the difference between the average field distributions m(t, r(t), v(t)) obtained twice is within a certain threshold range. The average field distribution is considered to converge. At this time, the average field distribution at convergence is m*(t, r(t), v(t)). When the average field distribution converges, the optimal cache strategy c*(t) is calculated by the following formula:

[0074]

[0075] Using the average field distribution m*(t, r(t), v(t)) at convergence and the obtained optimal caching strategy c*(t), solve equation (XVII) and calculate the optimal caching strategy benefit O*(t) of the edge node in the current time slot.

[0076] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, steps of a mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity are implemented.

[0077] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity.

[0078] A mean field game optimization system for video service caching strategy in an edge computing network based on content popularity, comprising:

[0079] The system model setting module is configured to: set up an edge computing network, the edge computing network including a cloud data center, a plurality of edge nodes with storage units, and a plurality of users;

[0080] The SDG problem modeling module is configured to: model the video service cache decision problem in the edge computing network as a stochastic differential game problem, i.e., the SDG problem, according to the remaining storage space status of each edge node and the status change of the task popularity based on the content popularity;

[0081] The optimal caching strategy obtaining module is configured to: use the mean field game method to solve the above SDG problem, obtain the Nash equilibrium of the video service caching decision problem in the edge computing network, and obtain the optimal caching strategy for each edge node.

[0082] The beneficial effects of the present invention are:

[0083] 1. The present invention provides a mean field game optimization method for video service caching strategy in an edge computing network based on content popularity. For the optimization problem of video service caching strategy in an edge computing network, the existing technologies mostly focus on meeting user needs, while the present invention takes into account the caching benefits of edge nodes. The goal of the caching decision problem is to maximize the edge node caching benefit value consisting of the waiting advantage delay benefit, the service advantage delay benefit and the storage space occupancy cost.

[0084] 2. The present invention establishes a reasonable connection between content popularity and the popularity of tasks at edge nodes, thereby taking into account the impact of content popularity on caching decisions, so that the video task caching decisions of edge nodes can meet dynamic and time-varying task requirements.

[0085] 3. The present invention adopts the MFG method to transform and solve the video service caching strategy optimization problem, which greatly reduces the computational complexity of the proposed optimization problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 This is a schematic diagram of the edge computing network structure;

[0087] Figure 2 Schematic diagram of the MFG problem solving process of the algorithm proposed in the present invention;

[0088] Figure 3 A comparison chart of the average cache revenue (aveMFG) of EN using the algorithm proposed in the present invention and the average cache revenue of EN using the other two existing algorithms when the content popularity continues to increase during the optimization period; DETAILED DESCRIPTION

[0089] The present invention will be further described below in conjunction with the embodiments and the accompanying drawings, but is not limited thereto.

[0090] Example 1

[0091] A mean field game optimization method for video service caching strategy in edge computing network based on content popularity is used to solve the video service caching decision problem of multiple edge nodes (EN) in edge computing network, so as to maximize the service revenue of each edge node EN and enable it to dynamically adjust the caching strategy in real time according to the change of content popularity; including:

[0092] (1) Setting a system model, including setting an edge computing network, where the edge computing network includes a cloud data center, a plurality of edge nodes (EN) with storage units, and a plurality of users;

[0093] (2) According to the remaining storage space status of each edge node and the change in the popularity of the task based on the content popularity, the video service cache decision problem in the edge computing network is modeled as a stochastic differential game (SDG) problem;

[0094] (3) When the number of edge nodes is particularly large, directly solving the above SDG problem will cause huge computational complexity and a large amount of information exchange between players. Therefore, in order to reduce the computational complexity of solving the problem, the Mean Field Game (MFG) method is used to solve the above SDG problem, so as to quickly obtain the Nash equilibrium of the video service caching decision problem in the edge computing network and obtain the optimal caching strategy for each edge node.

[0095] Example 2

[0096] The difference between the mean field game optimization method for video service caching strategy in an edge computing network based on content popularity described in Example 1 is that:

[0097] Set up the system model, including:

[0098] like Figure 1 As shown, the edge computing network includes a cloud data center, Q edge nodes (EN) with storage units, and K users; the edge node set is represented as The user set is represented as

[0099] Each edge node deploys an edge server with a storage unit and is connected to the cloud data center via a wireless link. The video task content requested by the user is downloaded via the wireless link. All task content files are stored in the content library of the cloud data center. The cloud data center allows the edge node to cache the video task content from the content library in advance. When the user generates a video task request, if the required content file is completely cached on the edge node, the edge node directly provides the user with video services. Otherwise, the edge node downloads the uncached task content from the cloud data center via a wireless link. The edge node caches the popular video task content in its storage unit in advance to reduce the delay in providing services to users. This method considers the caching decision problem of multiple edge nodes for a certain type of video service task (the size of the task content file is 200MB). For all edge nodes, the goal is to determine the storage ratio of the task content. The qth edge node EN q The cache decision for the task content in time slot t is c q (t) indicates that c q (t)∈[0,1], means EN qThe proportion of task content downloaded in advance from the cloud data center in time slot t; the qth edge node EN q The rate of downloading video task content from the cloud data center is R q$ .

[0100] Establish a communication model between edge nodes and cloud centers; R q$ As shown in formula (I):

[0101]

[0102] In formula (I), B q Indicates the qth edge node EN q The allocated channel bandwidth, It represents the signal-to-noise ratio (9dB) in the current network environment. S and N refer to the signal power and noise power of the edge node EN in the current network environment when downloading the task content from the cloud data center. The signal power represents the strength of the useful signal, which refers to the task content information of interest. The noise power represents the strength of the noise in the signal, which is usually an interference or useless signal.

[0103] In step (2), the video service caching decision problem in the edge computing network is modeled as an SDG problem, including:

[0104] 2-1. Obtain a dynamic model of content cache and remaining storage space of edge nodes;

[0105] 2-2. Obtain a dynamic model of edge node popularity for tasks based on content popularity;

[0106] 2-3. Evaluate the cache benefit of the video service cache decision problem in the edge computing network;

[0107] 2-4. Establish the SDG problem of video service caching decision problem in edge computing network.

[0108] Obtaining a dynamic model of content cache and remaining storage space of edge nodes; including:

[0109] The remaining storage space of the edge node for the task content changes with the change of the cache strategy. The size of the task content is represented by H (200MB). The remaining storage space status changes dynamically over time during the whole process. q The remaining storage space for the task content in time slot t is r q Indicates that r q The dynamic differential equation of is expressed as:

[0110] dr q (t)=[D q -Hc q (t)]dt+η1dBq (t) (II)

[0111] Among them, D q Indicates EN q For the available storage space of the task (size is 250MB), H represents the size of the task content file, and η : is a positive coefficient, B q (t) is a standard Brownian motion, dr q (t) indicates EN q The remaining storage space change, D q -Hc q (t) indicates EN q Uncached content portion, η1dB q (t) indicates EN q The volatility of remaining storage space.

[0112] A dynamic model is developed to determine the popularity of edge nodes for tasks based on content popularity; including:

[0113] When a user generates a task request, different ENs have different popularity for the same task, and generally speaking, the popularity of a task changes dynamically over time. q The popularity of the task in time slot t is expressed as v q (t) indicates that v q The dynamic change process of (t) is described by the Ornstein-Uhlenbeck process, v q The stochastic differential equation for (t) is expressed as:

[0114] dv q (t) = θ[λ q (t)-v q (t)]dt+η2dF q (t) (III)

[0115] Among them, θ represents the mean reversion rate, θ>0, η2 represents the volatility of the Ornstein-Uhlenbeck process during dynamic changes, and F q (t) is the standard Brownian motion;

[0116] λ q (t) represents EN in the Ornstein-Uhlenbeck process q The mean of the task popularity change process is determined by the recognized basic mean λ of the task popularity and the popularity l(t) of the current time slot task, expressed as λ q (t) = (1-α q )λ+α ql(t), where l(t) is the popularity of the task in time slot t, expressed as the ratio of the number of tasks generated in the current region n(t) to the maximum number of tasks generated in the region N(t) α q Indicates EN q The popularity of a task affects the confidence value of the task's popularity. In simple terms, λ represents a common judgment value of the popularity of a task that is generally recognized by all edge nodes in the current network environment, and the popularity of the task l(t) affects EN q Personality judgment value on the popularity of the task.

[0117] Evaluate the cache benefit of video service cache decision problem in edge computing network; including:

[0118] a. Obtaining the waiting advantage delay benefit: When a task request arrives at an edge node, it needs to wait for a period of time before getting a response from the edge node. Only then can the edge node serve the task request. The task waiting delay depends on the popularity of each edge node for the task v(t). The higher the popularity of the edge node for the task, the shorter the waiting delay of the task at the edge node. The popularity of each edge node for the task is different and changes with time and content popularity. Therefore, we define EN q Compared with other edge nodes, the benefit of waiting for the advantage delay for the task is the waiting advantage delay benefit The formula is:

[0119]

[0120] Among them, v q (t) is EN q The popularity of the task in time slot t, v q′ (t) is the difference between EN q The popularity of other edge nodes to the task, ε t is the waiting delay corresponding to the popularity of a unit task (taken as 2s), assuming that the waiting delay is linearly related to the popularity of the edge node for the task;

[0121] b. Seeking service advantage delay benefits: EN q Service Advantages Delay The task service delay after adopting the cache strategy cq(t) and the expected average task service delay P after other edge nodes in the region adopt their own cache strategies are derived from mean The difference of (t) is expressed as P mean (t) can be expressed as: Among them, H represents the size of the task content file, R qIndicates EN q The rate at which content is downloaded from the cloud via the wireless link; c mean (t) represents the average size of cached content files of other edge nodes in the region, which can be expressed as c q′ (t) is the difference between EN q The cache strategy adopted by other edge nodes other than P q (t) is EN q The download delay caused by downloading the uncached part of the task content file from the cloud through the wireless link is expressed as

[0122] c. Calculate the storage space usage cost: EN q Determine the cache strategy c q (t), some task content files are cached from the cloud data center in advance, which will occupy EN q The storage space occupied by q (t) is expressed as φ q (t) = D q -r q (t);

[0123] d. Obtain instantaneous cache benefit evaluation: When the video task request arrives at EN q When, EN q Can save more waiting delay and service delay for task completion, then EN q The shorter the delay in completing the task, the more rewards it will receive. In addition, EN q You will also be penalized for the cached task content files taking up storage space. q The instantaneous profit function J at time slot t q (t) is expressed as:

[0124]

[0125] Among them, ω represents the penalty coefficient of storage space occupancy (taken as 0.2).

[0126] Establish the SDG problem of video service caching decision problem in edge computing network; including:

[0127] Definition q At time slot t, the state of the video task cache is s q (t)=(r q (t), v q (t)); The SDG problem defines a four-tuple representation: in, represents the set of players (ENs here), Indicates EN q The state space of Indicates EN q A collection of cache strategies, Indicates EN q The profit function in a limited time horizon T Finally, the video task caching problem within a limited time range is modeled as a SDG problem as follows:

[0128]

[0129] dr q (t)=[D q -Hc q (t)]dt+η1dB q (t) (VI)

[0130] dv q (t) = θ[λ q (t)-v q (t)]dt+η2dF q (t)

[0131] Among them, c q (t) is the cache strategy within a limited time range (0 to T), c q′ (t) is the difference between EN q The cache strategy of other edge nodes other than s q′ Indicates except EN q The state of other edge nodes except If there is an optimal solution to the SDG problem subproblem within the time range [t, T], the optimal solution of the SDG problem within the range [0, T] is obtained. Based on this, the profit objective function O is defined within the time period [t, T] q (t) is:

[0132]

[0133] The solution to the above SDG problem is obtained by solving the following Q coupled Hamilton-Jacobi-Bellman (HJB) equations using the inverse solution method:

[0134]

[0135] The drift function term D in the above equation q -Hc q (t),θ[λ q (t)-v q (t)] and the profit function J qare all smooth, so the above HJB equation has a unique Nash equilibrium solution. But in fact, in order to solve the Nash equilibrium of Q HJB equations, it is necessary to obtain the cache strategies and state information of the other Q-1 ENs, which is bound to cause huge computational complexity and a large amount of information exchange between players. When the number of ENs is particularly large, the direct solution method is not practical. Therefore, considering the above difficulties, the Mean Field Game (MFG) method is used to solve this original SDG problem in order to quickly obtain the Nash equilibrium of the original optimization problem. According to existing theories, when the number of players participating in the game is large enough, the solution obtained by the MFG method is almost equivalent to the solution of the SDG problem, and the complexity of the MFG method is much lower than directly solving the SDG problem involving the original Q players.

[0136] In step (3), the mean field game method is used to solve the optimal cache strategy for the SDG problem; including:

[0137] 3-1. The SDG problem is transformed into the MFG problem: Due to the interchangeability of states between players, each individual in the environment is indistinguishable. In this case, the task caching strategy of each EN is determined only by its own state and the mean field distribution, which is obtained by simplifying the previous HJB equation. In this case, replacing the sequence number of the player does not change their caching strategy. Under this interchangeability, the general EN can be described by removing the subscript q. The information interaction between ordinary players and other players is reflected in the mean field (MF) state distribution. Therefore, we pay more attention to the general EN at time slot t. By defining an empirical distribution M(t, r(t), v(t)) under a single task type, the probability distribution m(t) of the state of the edge node is given; the empirical distribution M(t, r(t), v(t)) is the probability distribution of the state of the edge node at time slot t. q (t), v q The statistical distribution density of edge nodes under the (t) state is expressed as follows:

[0138]

[0139] Among them, δ is an indicator function. When the edge node is in the state (r(t), v(t)), δ = 1, otherwise, δ = 0; as the number of edge nodes Q increases, the empirical distribution M(t, r(t), v(t)) will converge to m(t, r(t), v(t)), that is, the probability density function of EN in the state (r(t), v(t)); for this reason, the Fokker-Planck-Kolmogorov (FPK) equation is used to describe the evolution of the mean field distribution m(t) under the dynamic changes of the remaining storage space state and the popularity state of the task, which is expressed as follows:

[0140]

[0141] In order to solve the above model more easily, we define As the average popularity of other edge nodes for the task, given the average field distribution m(t, r(t), v(t)), The distribution is approximately expressed as follows:

[0142]

[0143] The mean value c of the cached content file size of other edge nodes in the service advantage delay benefit mean (t), is approximately converted into:

[0144]

[0145] When the number of edge nodes Q participating in the game approaches infinity, in current related research, most of the time the number of edge nodes participating in the game is set to be greater than 10. Of course, the larger the number of edge nodes participating in the game, the more accurate the result calculated by the mean field game method will be, and the closer it will be to the theoretical value. Then:

[0146] c mean (t)=H∫∫m(t, r(t), v(t))c q (t)drdv (XIII)

[0147] Assume m * (t, r(t), v(t)) represents the solution of the FPK equation (XIII). Under the commutativity of the mean field distribution, we get the waiting advantage delay benefit: and service advantages delay benefits The approximate formula is as follows:

[0148]

[0149] By establishing the average field, the optimal cache strategy is obtained according to the local state information of each edge node and the average field distribution;

[0150] Therefore, for each player, the SDG problem is transformed into the following MFG problem:

[0151]

[0152] The objective function (XVI) is exactly the same as (VI), except that (XI), (XII), and (XIII) use the mean field method to approximate the average popularity of other ENs for the task and the mean size of the cached content file, thereby using Replace the waiting advantage delay benefit and service advantage delay benefit in the benefit function respectively. In addition, the objective function O(t) depends only on the cache strategy, state and average field distribution of the entire EN of a single individual, without considering the interaction between individuals. At this point, the original SDG problem is completely transformed into the MFG problem. When making a cache decision, a single EN no longer needs to consider the cache strategy and state of other ENs, but only needs to make decisions based on its own state and the average field distribution of the entire EN. Then, in this MFG problem, the HJB equation is decoupled as follows:

[0153]

[0154] 3-2. Solution to the MFG problem: The cache benefit O(t) of each time slot is calculated by reverse induction of the HJB equation, and its corresponding mean field distribution m(t, r(t), v(t)) is obtained by directly solving the FPK equation. The mean field distribution m(t, r(t), v(t)) obtained at this time will affect the solution of the HJB equation. It can be seen that the HJB equation (XVII) and the FPK equation (Ⅹ) are coupled with each other due to the continuous changes in the optimal cache strategy, individual state and mean field distribution, and ultimately affect the cache benefit O(t). Our goal is to solve these two coupled equations and achieve the mean field equilibrium (MFE) of this MFG problem. Specifically, for edge nodes, if the optimal cache strategy c is required * (t) satisfies J(c * (t),m * (t,r(t),v(t))≥J(c(t),m * (t,r(t),v(t)), then the MFE state of the MFG cache decision problem is reached;

[0155] The HJB equation and the FPK equation are solved iteratively until the difference between the average field distributions m(t, r(t), v(t)) obtained twice is within a certain threshold range. The average field distribution is considered to converge. At this time, the average field distribution at convergence is m * (t,r(t),v(t)), this MFG problem achieves the mean field equilibrium (MFE) state. When the mean field distribution converges, the optimal cache strategy c * (t) is calculated by the following formula:

[0156]

[0157] Using the mean field distribution m at convergence * (t,r(t),v(t)) and the optimal cache strategy c *(t), solve equation (XVII) and calculate the optimal cache strategy benefit O of the edge node in the current time slot * (t).

[0158] It can be seen that the forward FPK equation describes the overall evolution process of the mean field, while the HJB equation describes the change process of each EN participating in the game. By solving the FPK equation, the mean field distribution m(t) of the current time slot can be obtained. Then, by solving the HJB equation, the objective function benefit value O(t) and the corresponding cache strategy c(t) under the current mean field distribution can be obtained. The solution of the HJB equation will affect the solution of the FPK equation. Finally, the optimal cache strategy within a limited time range can be obtained through multiple rounds of iterative calculations of the HJB-FPK equation. The entire calculation process is as follows: Figure 2 shown.

[0159] In the optimization time range from 0 to T, the cache scheme is optimized every unit time slot. During the optimization process of each time slot, the edge node first obtains the task popularity l(t) of the current time slot; then, the average field distribution m(t), the benefit objective function O(t) and the instantaneous benefit function J(t) are iteratively calculated according to the above process; finally, a series of optimal cache strategies c for the edge node in each time slot are obtained. * (t) and its cache benefits.

[0160] During the optimization period, when the popularity of video content continues to increase, the average cache revenue of all edge nodes is as follows: Figure 3 As shown, a comparison chart is shown of the average cache benefit (aveMFG) of EN using the algorithm proposed in the present invention and the average cache benefit of EN using the other two existing algorithms. Figure 3 In the figure, the horizontal axis is the time scale, indicating that in the optimization period of 1-10s, the edge node EN updates the cache decision every 1s; the vertical axis refers to the average cache strategy benefit. Because the benefits of a group of edge nodes under the MFG cache decision scheme proposed in this product and the two control schemes of MFGNOP and RANDOM are compared, the average value of the benefits of this group of edge nodes at each moment under different cache decision schemes is calculated to represent the performance of the scheme.

[0161] Figure 3It depicts the change of the average cache strategy benefit of this group of edge nodes ENs over time under different cache schemes when the task popularity continues to increase. Among them, aveMFG is the average benefit of the proposed algorithm scheme based on content popularity, aveMFGNOP is the average benefit of the conventional MFG algorithm scheme that does not consider the task popularity, and aveRANDOM is the average benefit under the random cache decision algorithm scheme. During the experiment, the three schemes adopted the same initial mean field distribution and task popularity mean. We can see that during the entire optimization time period, the average cache strategy benefit of the proposed algorithm scheme continues to increase with the increase of task popularity, and the average cache decision benefit of the proposed algorithm scheme is higher than that of the other two comparison schemes. It can be seen that the method proposed in the present invention is superior to the MFG method that does not consider content popularity and the benchmark algorithm with random fixed content popularity, which proves the effectiveness of the algorithm of the present invention.

[0162] Example 3

[0163] A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of a mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity as described in Example 1 or 2 are implemented.

[0164] Example 4

[0165] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of a mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity as described in Example 1 or 2 are implemented.

[0166] Example 5

[0167] A mean field game optimization system for video service caching strategy in an edge computing network based on content popularity, comprising:

[0168] The system model setting module is configured to: set up an edge computing network, the edge computing network including a cloud data center, a plurality of edge nodes with storage units, and a plurality of users;

[0169] The SDG problem modeling module is configured to: model the video service cache decision problem in the edge computing network as a stochastic differential game problem, i.e., the SDG problem, according to the remaining storage space status of each edge node and the status change of the task popularity based on the content popularity;

[0170] The optimal caching strategy obtaining module is configured to: use the mean field game method to solve the above SDG problem, obtain the Nash equilibrium of the video service caching decision problem in the edge computing network, and obtain the optimal caching strategy for each edge node.

Claims

1. A mean field game optimization method for video service caching strategy in edge computing network based on content popularity, characterized in that: include: (1) Set up the system model; The method includes setting up an edge computing network, the edge computing network including a cloud data center, a plurality of edge nodes having storage units, and a plurality of users; (2) According to the remaining storage space status of each edge node and the change in the popularity of the task based on the content popularity, the video service cache decision problem in the edge computing network is modeled as a stochastic differential game problem, namely the SDG problem; (3) The mean field game method is used to solve the above SDG problem, obtain the Nash equilibrium of the video service caching decision problem in the edge computing network, and obtain the optimal caching strategy for each edge node.

2. According to claim 1, a mean field game optimization method for video service caching strategy in an edge computing network based on content popularity is characterized in that: Set up the system model, including: The edge computing network includes a cloud data center, Q edge nodes with storage units, and K users; the edge node set is represented as The user set is represented as Each edge node deploys an edge server with a storage unit and is connected to the cloud data center via a wireless link. The video task content requested by the user is downloaded through the wireless link. All task content files are stored in the content library of the cloud data center. The cloud data center allows the edge node to cache the video task content from the content library in advance. When the user generates a video task request, if the required content file is completely cached on the edge node, the edge node directly provides the user with video service. Otherwise, the edge node downloads the uncached task content from the cloud data center via the wireless link. The edge node caches the popular video task content in its storage unit in advance. For all edge nodes, the goal is to determine the storage ratio of the task content. The qth edge node EN q The cache decision for the task content in time slot t is c q (t) indicates that c q (t)∈[0,1], means EN q The proportion of task content downloaded in advance from the cloud data center in time slot t; the qth edge node EN q The rate of downloading video task content from the cloud data center is R qc ; More preferably, R qc As shown in formula (I): In formula (I), B q Indicates the qth edge node EN q The allocated channel bandwidth, It represents the signal-to-noise ratio in the current network environment. S and N refer to the signal power and noise power of the edge node EN in the process of downloading the task content from the cloud data center in the current network environment.

3. According to claim 1, a mean field game optimization method for video service caching strategy in an edge computing network based on content popularity is characterized in that: In step (2), the video service caching decision problem in the edge computing network is modeled as an SDG problem, including: 2-1. Obtain a dynamic model of content cache and remaining storage space of edge nodes; 2-2. Obtain a dynamic model of edge nodes’ popularity for tasks based on content popularity; 2-3. Evaluate the cache benefit of the video service cache decision problem in the edge computing network; 2-4. Establish the SDG problem of video service caching decision problem in edge computing network.

4. According to claim 3, a mean field game optimization method for video service caching strategy in an edge computing network based on content popularity is characterized in that: Obtain a dynamic model of content cache and remaining storage space at edge nodes; include: EN q The remaining storage space for the task content in time slot t is r q Indicates that r q The dynamic differential equation of is expressed as: dr q (t)=[D q -Hc q (t)]dt+η1dB q (t)(II) Among them, D q Indicates EN q For the available storage space of the task, H represents the size of the task content file, η1 is a positive coefficient, and B q (t) is a standard Brownian motion, dr q (t) indicates EN q The remaining storage space change, D q -Hc q (t) indicates EN q Uncached content portion, η1dB q (t) indicates EN q The volatility of remaining storage space; Further preferably, a dynamic model of the popularity of edge nodes for tasks based on content popularity is obtained; including: EN q The popularity of the task in time slot t is expressed as v q (t) indicates that v q The dynamic change process of (t) is described by the Ornstein-Uhlenbeck process, v a The stochastic differential equation for (t) is expressed as: dv q (t)=θ[λ q (t)-v q (t)]dt+η2dF q (t) (III) Among them, θ represents the mean reversion rate, θ>0, η2 represents the volatility of the Omstein-Uhlenbeck process during dynamic changes, and F q (t) is the standard Brownian motion; λ q (t) represents EN in the Ornstein-Uhlenbeck process q The mean of the task popularity change process is determined by the recognized basic mean λ of the task popularity and the popularity l(t) of the current time slot task, expressed as λ q (t) = (1-α q )λ+α q l(t), where l(t) is the popularity of the task in time slot t, expressed as the ratio of the number of tasks generated in the current region n(t) to the maximum number of tasks generated in the region N(t) α q Indicates EN q The popularity of a task affects the confidence value of the task’s popularity. λ represents a common judgment value of the popularity of a task that is generally recognized by all edge nodes in the current network environment. The popularity of a task l(t) affects EN q Personality judgment value on the popularity of the task.

5. According to claim 3, a mean field game optimization method for video service caching strategy in an edge computing network based on content popularity is characterized in that: Evaluate the cache benefit of video service cache decision problem in edge computing network; including: a. Obtaining the waiting advantage delay benefit: Define EN q Compared with other edge nodes, the benefit of waiting for the advantage delay for the task is the waiting advantage delay benefit The formula is: Among them, v q (t) is EN q The popularity of the task in time slot t, v q , (t) is the difference between EN q The popularity of other edge nodes to the task, ε t is the waiting delay corresponding to the unit task popularity, assuming that the waiting delay is linearly related to the popularity of the edge node to the task; b. Seeking service advantage delay benefits: EN q Service Advantages Delay It comes from the cache strategy c q The task service delay after (t) is compared with the expected average task service delay P after other edge nodes in the region adopt their own caching strategies mean The difference of (t) is expressed as P mean (t) can be expressed as: Among them, H represents the size of the task content file, R q Indicates EN q The rate at which content is downloaded from the cloud via the wireless link; c mean (t) represents the average size of cached content files of other edge nodes in the region, which can be expressed as c q′ (t) is the difference between EN q The cache strategy adopted by other edge nodes other than P q (t) is the target N q The download delay caused by downloading the uncached part of the task content file from the cloud through the wireless link is expressed as c. Calculate the storage space occupation cost: the occupied storage space φ q (t) is expressed as φ q (t) = D q -r q (t); d. Obtain instantaneous cache benefit evaluation: EN q The instantaneous profit function J at time slot t q (t) is expressed as: Among them, ω represents the penalty coefficient of storage space occupancy.

6. The mean field game optimization method for video service caching strategy in edge computing network based on content popularity according to claim 3 is characterized in that: Establish the SDG problem of video service caching decision problem in edge computing network; including: Definition q At time slot t, the state of the video task cache is s q (t)=(r q (t), v q (t)); The SDG problem defines a four-tuple representation: in, represents the set of players, Indicates EN q The state space of Indicates EN q A collection of cache strategies, Indicates EN q The profit function in a limited time horizon T Finally, the video task caching problem within a limited time range is modeled as a SDG problem as follows: dr q (t)=[D q -Hc q (t)]dt+η1dB q (t) (VI) dv q (t)=θ[λ q (t)-V q (t)]dt+η2dF q (t) Among them, c q (t) is the caching strategy within a limited time range, c q′ (t) is the difference between EN q The cache strategy of other edge nodes other than s q′ Indicates except EN q The state of other edge nodes other than t; define the profit objective function O in the time period [t, T] q (t) is: The solution to the above SDG problem is obtained by solving the following Q coupled Hamilton-Jacobi-Bellman equations using the inverse solution method:

7. A mean field game optimization method for video service caching strategy in an edge computing network based on content popularity according to any one of claims 1-6, characterized in that: In step (3), the mean field game method is used to solve the optimal cache strategy for the SDG problem; including: 3-1. The SDG problem is transformed into the MFG problem: By defining an empirical distribution M(t, r(t), v(t)) under a single task type, the probability distribution m(t) of the edge node state is given; the empirical distribution M(t, r(t), v(t)) is the probability distribution of the edge node state at time slot t. q (t), v q The statistical distribution density of edge nodes under the (t) state is expressed as follows: Among them, δ is an indicator function. When the edge node is in the state of (r(t), v(t)), δ = 1, otherwise, δ = 0. The Fokker-Planck-Kolmogorov equation is used to describe the evolution of the mean field distribution m(t) under the dynamic changes of the remaining storage space state and the popularity of the task, which is expressed as follows: definition As the average popularity of other edge nodes for the task, given the average field distribution m(t, r(t), v(t)), The distribution is approximately expressed as follows: The mean value c of the cached content file size of other edge nodes in the service advantage delay benefit mean (t), is approximately converted into: When the number of edge nodes participating in the game Q approaches infinity, then: c mean (t)=H∫∫m(t,r(t),v(t))c q (t)drdv (XIII) Assume m * (t, r(t), v(t)) represents the solution of the FPK equation (XIII). Under the commutativity of the mean field distribution, we get the waiting advantage delay benefit: and service advantages delay benefits The approximate formula is as follows: By establishing the average field, the optimal cache strategy is obtained according to the local state information of each edge node and the average field distribution; Therefore, for each player, the SDG problem is transformed into the following MFG problem: In this MFG problem, the HJB equation is decoupled as follows: 3-2. MFG problem solution: For edge nodes, if the optimal cache strategy c is * (t) satisfies J(c * (t), m * (t, r(t), v(t))≥J(c(t), m * (t, r(t), v(t)), then the MFE state of the MFG cache decision problem is reached; The HJB equation and the FPK equation are solved iteratively until the difference between the average field distributions m(t, r(t), v(t)) obtained twice is within a certain threshold range. The average field distribution is considered to converge. At this time, the average field distribution at convergence is m * (t, r(t), v(t)), when the average field distribution converges, the optimal cache strategy c * (t) is calculated by the following formula: Using the mean field distribution m at convergence * (t, r(t), v(t)) and the optimal cache strategy c * (t), solve equation (XVII) and calculate the optimal cache strategy benefit O of the edge node in the current time slot * (t).

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of a mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity are implemented as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of a mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity are implemented as described in any one of claims 1-7.

10. A mean field game optimization system for video service caching strategy in an edge computing network based on content popularity, characterized in that: include: The system model setting module is configured to: set up an edge computing network, the edge computing network including a cloud data center, a plurality of edge nodes with storage units, and a plurality of users; The SDG problem modeling module is configured to: model the video service cache decision problem in the edge computing network as a stochastic differential game problem, i.e., the SDG problem, according to the remaining storage space status of each edge node and the status change of the task popularity based on the content popularity; The optimal caching strategy obtaining module is configured to: use the mean field game method to solve the above SDG problem, obtain the Nash equilibrium of the video service caching decision problem in the edge computing network, and obtain the optimal caching strategy for each edge node.

Images