A mean field game optimization method and system in edge computing network based on content popularity

Abstract

The present invention relates to a mean field game optimization method and system in an edge computing network based on content popularity, comprising: (1) setting a system model; including setting 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; (2) modeling the video service caching decision problem in the edge computing network as a stochastic differential game problem, i.e., an SDG problem, based on the remaining storage space status of each edge node and the state change of the task popularity based on the content popularity; (3) using the mean field game method to solve the above SDG problem, obtaining the Nash equilibrium of the video service caching decision problem in the edge computing network, and obtaining the optimal caching strategy of each edge node. The present invention focuses on satisfying user needs and takes into account the caching benefits of edge nodes.

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, belonging 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, video services, such as high-definition video and live streaming, are rapidly increasing their share of internet traffic. This in turn places higher demands on service latency and user experience. Video service caching technology reduces network traffic burden and latency by caching required video content on multiple edge servers during off-peak hours, thereby delegating user service requests to each server. Due to the ever-changing user preferences and content popularity, the demand for video services is dynamic and time-varying. How to update the video caching ratio on edge servers to match the changing user demand for video services is a pressing issue. Furthermore, edge servers are deployed by different operators for revenue, leading to competition among their servers. Making decisions about edge caching to maximize edge server revenue while meeting user needs and improving overall network performance is a pressing issue.

[0003] The video service caching decision problem of multiple edge servers in edge computing networks can be modeled as a game optimization problem. However, 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 user requirements for caching service experience such as latency, while ignoring 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 ultra-dense networks. The proposed network model is divided into three layers: the user device layer, the MEC layer, and the cloud layer. The MEC layer consists of M small base stations (SBSs) and one macro base station. The small base stations communicate with each other through the macro base station and share their cache resources. To address the edge caching decision-making problem for each SBS, the patent uses a multi-agent reinforcement learning algorithm based on game theory to make the optimal caching decision for each SBS, maximizing the content cache hit rate for each SBS and minimizing the total content download latency for all user devices. However, the patent considers the collaborative edge caching optimization problem of edge servers (SBSs), and the caching decision objective is based solely on the user's perspective regarding the latency of user device downloads. It does not consider the service competition between edge servers (SBSs) and their respective benefits. Furthermore, the impact of content popularity on edge server caching benefits is not considered. As a result, when content popularity changes, edge servers cannot dynamically adjust their caching decisions in real time to maximize service benefits. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, 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 and high computational complexity when the number of players participating in the game is large.

[0006] Explanation of terms:

[0007] The Ornstein-Uhlenbeck process, or OU process for short, is a classic stochastic process often used to describe dynamic systems with a "regression to the mean" property. It is a linear, stationary stochastic process. Specifically, the OU process is a continuous-time, continuous-state-space Markov process. Its most important characteristic is that it can regress to the mean, that is, the process has an equilibrium point. Over time, the process value 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 "regression to the mean" phenomenon. It has stationarity and regression properties, and is suitable for various systems that need to simulate random fluctuations but tend to a stable state. It is widely used in fields such as physics, finance, engineering, and sociology.

[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] Here, 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, indicating how quickly the process regresses to the long-term mean; σ is the volatility of the process, controlling the intensity of random perturbations; and W(t) is a standard Brownian motion, representing the random disturbances in the process. Therefore, the OU process regresses toward the mean μ over time, with the regression speed controlled by the parameter θ. If θ is large, the process regresses to the mean more quickly; if θ is small, the process regresses more slowly. Furthermore, the OU process is stationary, meaning that 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 edge computing networks based on content popularity, comprising:

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

[0014] (2) Based on the remaining storage space status of each edge node and the status change of the task popularity based on the content popularity, the video service caching 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] According to the preferred embodiment of 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. It downloads the video task content requested by the user 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 video service to the user. 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 in the process of the edge node EN downloading the task content from the cloud data center in the current network environment, respectively.

[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. Obtaining a dynamic model of content cache and remaining storage space at edge nodes;

[0024] 2-2. Calculate the dynamic model of edge node popularity for tasks based on content popularity;

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

[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 an edge node 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 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 a 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 the remaining storage space.

[0031] Further preferably, obtaining a dynamic model of the popularity of edge nodes for tasks based on content popularity includes:

[0032] EN q The popularity of the task in time slot t is expressed as v q (t) represents, 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, 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, which is 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 generated tasks n(t) in the current region to the maximum number of generated tasks N(t) in the region in time slot t α q Indicates EN q The popularity of a task affects the confidence value of its judgment on the popularity of the task. λ represents a common judgment value of the popularity of the task that is generally recognized by all edge nodes in the current network environment. The popularity of the task l(t) affects EN q Personality judgment value of task popularity.

[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 delay benefit of waiting advantage: Define EN q Compared with other edge nodes, the benefit of waiting advantage delay for tasks is waiting advantage delay benefit It can be expressed as:

[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 the task among other edge nodes, 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 Advantage Latency It comes from the cache strategy c q (t), and the expected average task service delay P after other edge nodes in the region adopt their own caching strategies mean The difference in (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 via the wireless link is expressed as

[0041] c. Calculate the storage space 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 is q (t) is expressed as:

[0043]

[0044] Where ω represents the penalty coefficient for storage space occupancy.

[0045] Further preferably, an SDG problem for video service caching decision problem in edge computing network is established; including:

[0046] Definition EN 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 The cache strategy set, Indicates EN q The profit function in a finite 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 status 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 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; including:

[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 in (r(t)) 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] Where δ is an indicator function. When the edge node is in the state (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 average value c of the cached content file size of other edge nodes in the service advantage delay benefit mean (t), is approximately converted to:

[0062]

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

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

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

[0066]

[0067] By establishing the average field, the optimal caching 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 equations are decoupled as follows:

[0071]

[0072] 32. MFG problem solution: For edge nodes, if the optimal cache policy 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 achieved;

[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 from two consecutive calculations is within a certain threshold range. The average field distribution is considered to have converged. At this time, the average field distribution at convergence is m*(t, r(t), v(t)). When the average field distribution converges, the optimal caching 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 includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it 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.

[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 caching decision problem in the edge computing network as a stochastic differential game problem, or SDG problem, based on the remaining storage space status of each edge node and the change in the popularity of the task based on the content popularity;

[0081] The optimal caching strategy determination module is configured to: use the mean field game method to solve the above-mentioned 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 edge computing networks based on content popularity. For the optimization problem of video service caching strategy in edge computing networks, 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, which includes the waiting advantage delay benefit, service advantage delay benefit and storage space occupancy cost.

[0084] 2. The present invention establishes a reasonable connection between content popularity and the popularity of edge nodes for tasks, 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 The figure shows a comparison of the average caching benefit (aveMFG) of EN using the proposed algorithm and the average caching benefit of EN using two other existing algorithms during the optimization period when the content popularity continues to increase. DETAILED DESCRIPTION

[0089] The present invention will be further described below with reference to 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 networks based on content popularity is proposed. The method is used to solve the video service caching decision problem of multiple edge nodes (EN) in the edge computing network, maximize the service revenue of each edge node, and enable it to dynamically adjust the caching strategy in real time according to the changes in content popularity. The method includes:

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

[0093] (2) Based on the remaining storage space status of each edge node and the status change of the task popularity based on the content popularity, the video service caching 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 SDG problem will result in huge computational complexity and a large amount of information exchange between players. Therefore, to reduce the computational complexity of solving the problem, the Mean Field Game (MFG) method is used to solve the SDG problem, in order 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 a user generates a video task request, if the required content file is completely cached on the edge node, the edge node directly provides the video service to the user. 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 to reduce the delay in providing services to the user. This method considers the caching decision problem of multiple edge nodes for a certain type of video service task (the task content file size 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, This represents the signal-to-noise ratio (SNR) in the current network environment (9dB). S and N refer to the signal power and noise power, respectively, when the edge node (EN) downloads the task content from the cloud data center. Signal power indicates the strength of the useful signal, which refers to the task content information of interest. Noise power indicates the strength of the noise present in the signal, which is typically interference or unwanted signals.

[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. Obtaining a dynamic model of content cache and remaining storage space at edge nodes;

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

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

[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 at 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 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, 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 the remaining storage space.

[0112] A dynamic model is used to determine the popularity of tasks at edge nodes based on content popularity. This includes:

[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) represents, 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, 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, which is 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 generated tasks n(t) in the current region to the maximum number of generated tasks N(t) in the region in time slot t α q Indicates EN q The popularity of a task affects its confidence value in judging the popularity of the task. In simple terms, λ represents a common judgment value of the popularity of the 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 of task popularity.

[0117] Evaluate the cache benefits of video service cache decision-making in edge computing networks; including:

[0118] a. Obtaining the delay benefit of waiting advantage: When a task request arrives at an edge node, it needs to wait for a period of time before receiving 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 advantage delay for tasks is waiting advantage delay benefit It can be expressed as:

[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 the task among other edge nodes, ε t is the waiting delay corresponding to the unit task popularity (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 Advantage Latency The task service delay after adopting the caching strategy cq(t) and the expected average task service delay P after other edge nodes in the region adopt their own caching strategies are derived from it. mean The difference in (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 via the wireless link is expressed as

[0122] c. Calculate the storage space usage cost: EN q Determine the cache strategy c q After (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 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 taking up storage space due to cached task content files. q The instantaneous profit function J at time slot t is q (t) is expressed as:

[0124]

[0125] Where ω represents the penalty coefficient for storage space occupancy (taken as 0.2).

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

[0127] Definition EN 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 The cache strategy set, Indicates EN q The profit function in a finite 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 caching 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 sub-problem within the time range [t, T], the optimal solution of the SDG problem in the range [0, T] is obtained. Based on this, the profit objective function O is defined in the time period [t, T] q (t) is:

[0132]

[0133] The solution to the 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 payoff function J qare all smooth, so the above HJB equation has a unique Nash equilibrium solution. However, 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 inevitably leads to huge computational complexity and a large amount of information exchange between players. When the number of ENs is extremely large, direct solution methods are impractical. Therefore, considering these difficulties, the mean field game (MFG) method is used to solve the original SDG problem, in order to quickly obtain the Nash equilibrium of the original optimization problem. According to existing theory, 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 far lower than directly solving the original SDG problem involving Q players.

[0136] In step (3), the mean field game method is used to solve the optimal caching 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, and the mean field distribution 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, and by defining an empirical distribution M(t, r(t), v(t)) under a single task type, we give the probability distribution m(t) of the state of the edge node; the empirical distribution M(t, r(t), v(t)) is the probability distribution of the state of the edge node at (r(t)) 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] Where 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)), which is the probability density function of EN in the state (r(t), v(t)). To this end, 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:

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

[0144]

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

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

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

[0148]

[0149] By establishing the average field, the optimal caching 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) (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 files, so as to use The waiting advantage delay benefit and service advantage delay benefit components of the benefit function are replaced separately. Furthermore, the objective function O(t) depends only on the caching strategy and state of each individual, as well as the mean field distribution of the entire EN, without considering interactions between individuals. The original SDG problem is now completely transformed into an MFG problem. When making caching decisions, a single EN no longer needs to consider the caching strategies and states of other ENs; instead, it only needs to make decisions based on its own state and the mean field distribution of the entire EN. Therefore, 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 * (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 are within a certain threshold range. The average field distribution is considered to have converged. 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 obtained optimal caching 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, solving the HJB equation can obtain the objective function benefit value O(t) and the corresponding caching strategy c(t) under the current mean field distribution. The solution of the HJB equation will affect the solution of the FPK equation. Finally, the optimal caching 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 solution is optimized every 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, it iteratively calculates the average field distribution m(t), the profit objective function O(t), and the instantaneous profit function J(t) 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 in the figure, 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 the edge node EN updates its caching decision every 1 second during the optimization period of 1-10 seconds. The vertical axis refers to the average caching strategy benefit. Because this is a comparison of the benefits of a group of edge nodes using the MFG caching decision scheme proposed in this product and the two control schemes MFGNOP and RANDOM, the average benefits of this group of edge nodes at each moment using different caching decision schemes are calculated to represent the performance of the scheme.

[0161] Figure 3The graph depicts how the average caching strategy benefit of this group of edge nodes ENs changes over time under different caching schemes as the popularity of the task 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 popularity of the task, 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 the mean value of task popularity. We can see that during the entire optimization period, the average caching strategy benefit of the proposed algorithm scheme continues to increase with the increase of task popularity, and the average caching 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 the popularity of the content 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, it implements the steps of the mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity as described in embodiment 1 or 2.

[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 the mean field game optimization method for a video service caching strategy in an edge computing network based on content popularity described in embodiment 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 caching decision problem in the edge computing network as a stochastic differential game problem, or SDG problem, based on the remaining storage space status of each edge node and the change in the popularity of the task based on the content popularity;

[0170] The optimal caching strategy determination module is configured to: use the mean field game method to solve the above-mentioned 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 by: 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) Based on 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 caching decision problem in the edge computing network is modeled as a stochastic differential game problem, namely the SDG problem; (3) Using the mean field game method to solve the above SDG problem, we 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; In step (2), the video service caching decision problem in the edge computing network is modeled as an SDG problem, including: 2-1. Obtaining a dynamic model of content cache and remaining storage space at edge nodes; 2-2. Calculate the dynamic model of edge node popularity for tasks based on content popularity; 2-3. Evaluate the cache benefit of video service cache decision-making in edge computing networks; 2-4. Establish the SDG problem of video service caching decision problem in edge computing network; Obtaining a dynamic model of content cache and remaining storage space at edge nodes; including: 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 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 a 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; A dynamic model is used to determine the popularity of tasks at edge nodes based on content popularity. This includes: EN q The popularity of the task in time slot t is expressed as v q (t) represents, 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: 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 Ornstein-Uhlenbeck process during dynamic changes, 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 generated tasks n(t) in the current region to the maximum number of generated tasks N(t) in the region in time slot t α q Indicates EN q The popularity of a task affects the confidence value of its judgment on the popularity of the task. λ represents a common judgment value of the popularity of the task that is generally recognized by all edge nodes in the current network environment. The popularity of the task l(t) affects EN q Personality judgment value of the task's popularity; Evaluate the cache benefits of video service cache decision-making in edge computing networks; including: a. Obtaining the waiting advantage delay benefit: Define EN q Compared with other edge nodes, the benefit of waiting advantage delay for tasks is waiting advantage delay benefit It can be expressed as: 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 the task among other edge nodes, ε - 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 Advantage Latency It comes from the cache strategy c q (t), and the expected average task service delay P after other edge nodes in the region adopt their own caching strategies mean The difference in (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 EN q The download delay caused by downloading the uncached part of the task content file from the cloud via the wireless link is expressed as c. Calculate the storage space 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 is q (t) is expressed as: Among them, ω represents the penalty coefficient of storage space occupancy; Establish the SDG problem of video service caching decision-making in edge computing networks; including: Definition EN 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 The cache strategy set, Indicates EN q The profit function in a finite 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 status 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 SDG problem is obtained by solving the following Q coupled Hamilton-Jacobi-Bellman equations using the inverse solution method:

2. The mean field game optimization method for video service caching strategy in edge computing network based on content popularity according to claim 1 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. It downloads the video task content requested by the user 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 video service to the user. 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 .

3. The mean field game optimization method for video service caching strategy in edge computing network based on content popularity according to claim 2 is characterized in that: 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 in the process of the edge node EN downloading the task content from the cloud data center in the current network environment, respectively.

4. 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 to 3, characterized in that: In step (3), the mean field game method is used to solve the optimal caching 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 in (r(t)) at time slot t. q (t),v q The statistical distribution density of edge nodes under the (t) state is expressed as follows: Where δ is an indicator function. When the edge node is in the state (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 average value c of the cached content file size of other edge nodes in the service advantage delay benefit mean (t), is approximately converted to: When the number Q of edge nodes participating in the game approaches infinity, then: c mean (t)=H∫∫m(t,r(t),v(t))c q (t)drdv(XIII) Let m * (t, r(t), v(t)) represents the solution of the FPK equation (XIII). Under the commutativity of the mean field distribution, the waiting advantage delay benefit is obtained and service advantages, latency benefits The approximate formula is as follows: By establishing the average field, the optimal caching 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: O(t)=max c(-) u(c(t),s(t),m(t,r(t),v(t)))(XVI) In this MFG problem, the HJB equations are decoupled as follows: 3-2、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; 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 are within a certain threshold range. The average field distribution is considered to have converged. At this time, the average field distribution at convergence is m * (t,r(t),v(t)), when the mean field distribution converges, the optimal caching strategy c * (t) is calculated by the following formula: Using the mean field distribution m at convergence * (t,r(t),v(t)) and the obtained optimal caching strategy c * (t), solve equation (XVII) and calculate the optimal cache strategy benefit O of the edge node in the current time slot * (t).

5. 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 the mean field game optimization method for video service caching strategy in an edge computing network based on content popularity as described in any one of claims 1-4 are implemented.

6. 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 1-4.

7. A mean field game optimization system for video service caching strategy in edge computing network based on content popularity, characterized by: 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 caching decision problem in the edge computing network as a stochastic differential game problem, or SDG problem, based on the remaining storage space status of each edge node and the change in the popularity of the task based on the content popularity; The optimal caching strategy determination module is configured to: use the mean field game method to solve the above-mentioned 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; The video service caching decision problem in edge computing networks is modeled as an SDG problem, including: 2-1. Obtaining a dynamic model of content cache and remaining storage space at edge nodes; 2-2. Calculate the dynamic model of edge node popularity for tasks based on content popularity; 2-3. Evaluate the cache benefit of video service cache decision-making in edge computing networks; 2-4. Establish the SDG problem of video service caching decision problem in edge computing network; Obtaining a dynamic model of content cache and remaining storage space at edge nodes; including: 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 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 a 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; A dynamic model is used to determine the popularity of tasks at edge nodes based on content popularity. This includes: EN q The popularity of the task in time slot t is expressed as v q (t) represents, 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: 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 Ornstein-Uhlenbeck process during dynamic changes, 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 generated tasks n(t) in the current region to the maximum number of generated tasks N(t) in the region in time slot t α q Indicates EN q The popularity of a task affects the confidence value of its judgment on the popularity of the task. λ represents a common judgment value of the popularity of the task that is generally recognized by all edge nodes in the current network environment. The popularity of the task l(t) affects EN q Personality judgment value of the task's popularity; Evaluate the cache benefits of video service cache decision-making in edge computing networks; including: a. Obtaining the waiting advantage delay benefit: Define EN q Compared with other edge nodes, the benefit of waiting advantage delay for tasks is waiting advantage delay benefit It can be expressed as: 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 the task among other edge nodes, ε - 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 Advantage Latency It comes from the cache strategy c q (t), and the expected average task service delay P after other edge nodes in the region adopt their own caching strategies mean The difference in (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 EN q The download delay caused by downloading the uncached part of the task content file from the cloud via the wireless link is expressed as c. Calculate the storage space 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 is q (t) is expressed as: Among them, ω represents the penalty coefficient of storage space occupancy; Establish the SDG problem of video service caching decision-making in edge computing networks; including: Definition EN 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 The cache strategy set, Indicates EN q The profit function in a finite 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 status 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 SDG problem is obtained by solving the following Q coupled Hamilton-Jacobi-Bellman equations using the inverse solution method:

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