CN113507519B - Edge computing bandwidth resource allocation method and system for smart home - Google Patents

Edge computing bandwidth resource allocation method and system for smart home Download PDF

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CN113507519B
CN113507519B CN202110771951.9A CN202110771951A CN113507519B CN 113507519 B CN113507519 B CN 113507519B CN 202110771951 A CN202110771951 A CN 202110771951A CN 113507519 B CN113507519 B CN 113507519B
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CN113507519A (en
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李世勇
刘欢
张芷源
孙微
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Yanshan University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/01Protocols
    • H04L67/10Protocols in which an application is distributed across nodes in the network
    • H04L67/1001Protocols in which an application is distributed across nodes in the network for accessing one among a plurality of replicated servers
    • H04L67/1004Server selection for load balancing
    • H04L67/101Server selection for load balancing based on network conditions
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L12/00Data switching networks
    • H04L12/28Data switching networks characterised by path configuration, e.g. LAN [Local Area Networks] or WAN [Wide Area Networks]
    • H04L12/2803Home automation networks
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/08Configuration management of networks or network elements
    • H04L41/0896Bandwidth or capacity management, i.e. automatically increasing or decreasing capacities
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00Network arrangements or protocols for supporting network services or applications
    • H04L67/01Protocols
    • H04L67/10Protocols in which an application is distributed across nodes in the network

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Abstract

The invention relates to an edge computing bandwidth resource allocation method facing smart home, which calculates user terminal resources and edge node resources according to edge computing allocation results; calculating the download link parameters of the user terminal by using a utility program in the user terminal according to the resources of the user terminal; calculating the uploading link parameters of the edge nodes according to the edge node capacity and the edge node resources; the absolute value of the difference value between the user terminal downloading link parameter and the edge node uploading link parameter is used as an optimization target, continuous optimization of the edge calculation distribution result is achieved, the optimal point of bandwidth resource distribution can be effectively converged, and therefore the satisfaction degree of the user terminal obtaining the bandwidth resource can be guaranteed.

Description

Edge computing bandwidth resource allocation method and system for smart home
Technical Field
The invention relates to the technical field of edge computing, in particular to an edge computing bandwidth resource allocation method and system for smart home.
Background
In recent years, research and applications on edge computing have shown a explosive growth trend in the context of everything interconnection. In a conventional smart home environment, cloud computing plays an important role in coordination and convenient service among smart home applications as a core point for providing platform services, however, when different smart home applications are connected and controlled through a network, there are many problems, such as data privacy, security, end-to-end delay, limited backbone link bandwidth, severe energy consumption, link congestion, and the like, especially data security. In general, smart home applications are single intelligent, such as smart security systems and surveillance cameras. Typically, they rely on cloud platforms for remote control, which can be lost to customers in the event of a network failure. However, the advent of edge computing technology will enable intelligent connectivity and stable operation between smart home applications. Edge computing refers to inserting an intermediate node layer between a user and a cloud computing center, wherein the intermediate node layer is closer to the user in a network and is positioned at the edge of the whole network. As an extended field of cloud computing technology development to a certain stage, edge computing focuses on solving the problem of resource sharing between devices at a lower layer of a network structure. Compared with cloud computing, the edge computing mode is a data computing mode that avoids transmission of processing tasks to the cloud and is decentralized, and is not so much a network structure that breaks up computing capacity into whole parts and fully utilizes resources near computing users to improve overall service performance under the condition that the amount of data to be processed is controlled within a certain range. For strong-interactivity software, the round-trip delay from the cloud to the user terminal should be controlled within 100 milliseconds, otherwise, the experience of a user for operating the cloud software is greatly reduced, so that edge computing has natural advantages from the perspective of delay, each edge computing node is placed close to the user, and excessive intermediate nodes in the past cloud computing mode are reduced, so that the edge computing has the characteristics of strong expandability, low delay, high mobility, bandwidth saving, low energy consumption, system safety, high performance and the like. When the edge computing system is deployed in the intelligent home environment, the intelligent home application serving as an edge node collects information through a wired/wireless sensor, the information comprises indoor temperature, brightness, air humidity, image information collected by an outdoor/indoor camera for comprehensive analysis and the like, and then sends a specific command to other intelligent home applications to complete intelligent linkage control of systems such as a lighting system, a temperature system and an alarm mechanism in the intelligent home environment, so that the problems of time delay, link congestion, safety and the like caused by excessive data transmission with a cloud computing center are solved.
The intelligent home oriented edge computing can further protect user data security, and avoids the time delay problem caused by the congestion of a backbone link under a cloud computing model, but meanwhile, the rapid increase of the data volume of an application side of the intelligent home also brings challenges to edge nodes with limited resources, on one hand, from the supply aspect, due to the development of mobile communication, the network data flow is increased rapidly in the last decade, and along with the appearance and the development of a fifth generation (5G) mobile network, the situation that the data processing demand is exponentially increased inevitably occurs at the application side of the intelligent home. On the other hand, from the aspect of demand, with the improvement of life quality of people and the continuous rising of demand for convenient and comfortable services, a large number of applications and devices with large resource demand and high bandwidth demand, including 4K/8K ultra-high-definition videos, virtual augmented reality devices (VR/AR) and the like, appear in the smart home environment.
Since edge computing mainly relies on the edge nodes with limited resources to provide resources and services for the user terminal, scheduling, allocation and management of network resources become particularly important, and currently, the resource allocation mechanism of edge computing includes two types, one is an index-based allocation policy, which proposes to select the most appropriate edge node for the user terminal, so as to reduce the computational complexity and communication overhead related to the policy. And the other is to increase the capability of the edge node cluster to provide resources for the user terminal. However, in both of the two ways, the improvement of the allocation efficiency is realized by constructing a smart resource allocation structure, and the utility problem of the user terminal is rarely considered.
Disclosure of Invention
The invention aims to provide an edge computing bandwidth resource allocation method and system for smart home, which are used for reasonably allocating limited resource quantity in an edge network of the smart home, realizing that a user terminal can obtain required resources when the resource demand on the edge side of the network is greatly increased, and ensuring the satisfaction degree of the user terminal obtaining bandwidth resources.
In order to achieve the purpose, the invention provides the following scheme:
the invention provides an edge computing bandwidth resource allocation method for smart home, which comprises the following steps:
calculating the user terminal resource and the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration; the user terminal resource is the resource quantity obtained by the user terminal, and the edge node resource is the resource quantity provided by the edge node;
according to the user terminal resource of the ith iteration, calculating the user terminal download link parameter of the ith iteration by using a utility program in the user terminal;
calculating the uploading link parameter of the edge node of the ith iteration according to the edge node capability and the edge node resource of the ith iteration; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation;
judging whether the absolute value of the difference value between the downloading link parameter of the user terminal of the ith iteration and the uploading link parameter of the edge node is smaller than an absolute value threshold value or not, and obtaining a judgment result;
if the judgment result shows no, optimizing the edge calculation distribution result of the ith iteration to obtain the edge calculation distribution result of the (i + 1) th iteration, increasing the value of i by 1, and returning to the step of calculating the user terminal resource and the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration;
and if the judgment result shows that the edge calculation distribution result of the ith iteration is the optimal distribution result, outputting the edge calculation distribution result of the ith iteration as the optimal distribution result.
Optionally, the outputting an edge calculation allocation result of the ith iteration as an optimal allocation result further includes:
calculating the user terminal resource of each user terminal according to the optimal distribution result to serve as the optimal user terminal resource of the user terminal;
and respectively comparing the optimal user terminal resource of each user terminal with the user terminal capacity, and updating the optimal user terminal resource of the user terminal into the user terminal capacity of the user terminal when the optimal user terminal resource of the user terminal is greater than the user terminal capacity.
Optionally, the calculating the user terminal resource of the ith iteration according to the edge calculation distribution result of the ith iteration specifically includes:
calculating distribution result according to the edge of the ith iteration by using a formula h m (i)=∑ g:g∈G(m) u gm (i) Calculating the user terminal resources of the task-intensive user terminal of the ith iteration;
calculating distribution result according to the edge of the ith iteration by using a formula h n (i)=∑ g:g∈G(n) u gn (i) Calculating the user of the delay sensitive user terminal of the ith iterationTerminal resources;
wherein h is m (i) And h n (i) Respectively are the user terminal resources of the ith iteration task intensive user terminal and the delay sensitive user terminal, and g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is an edge node set for providing resources for the task-intensive user terminal in the edge calculation distribution result of the ith iteration; g (n) is an edge node set for providing resources for the time delay sensitive user terminal in the edge calculation distribution result of the ith iteration; u. u gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the distribution result of the edge calculation of the ith iteration; u. of gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
Optionally, calculating the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration specifically includes:
calculating distribution result according to the edge of the ith iteration by using a formula
Figure BDA0003153959740000031
Calculating edge node resources provided by the edge nodes to the task-intensive user terminal during the ith iteration;
calculating distribution result according to the edge of the ith iteration by using a formula
Figure BDA0003153959740000032
Calculating edge node resources provided by the edge nodes to the delay sensitive user terminal in the ith iteration;
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003153959740000033
and
Figure BDA0003153959740000034
respectively representing edge node resources provided by the edge node to the task-intensive user terminal and the delay-sensitive user terminal during the ith iteration, wherein g is the edge node; m is task densityA centralized user terminal; n is a time delay sensitive user terminal; m (g) is a set of task-intensive user terminals that are provided resources by an edge node g; n (g) is a time delay sensitive user terminal set provided with resources by an edge node g; u. u gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the ith iteration; u. u gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
Optionally, the calculating, according to the user terminal resource of the ith iteration, the user terminal download link parameter of the ith iteration by using the utility program in the user terminal specifically includes:
using the formula alpha m (i)=X m ′(h m (i) Calculating the user terminal download link parameters of the ith iterative task-intensive user terminal;
using the formula alpha n (i)=X n ′(h n (i) Calculating the user terminal download link parameter of the time delay sensitive user terminal of the ith iteration;
wherein alpha is m (i) And alpha n (i) Downloading link parameters, h, for the user terminals of the ith iteration task-intensive user terminal and the delay-sensitive user terminal, respectively m (i) And h n (i) User terminal resources, X, for the ith iteration of the task-intensive user terminal and the delay-sensitive user terminal, respectively m ′(h m (i) A task-intensive user terminal m for i iterations is obtaining a user terminal resource h m (i) Derivative of utility function in the latter utility program, x n ′(h n (i) I iterations of delay-sensitive ue n obtaining ue resource h n (i) The derivative of the utility function in the latter utility program.
Optionally, calculating an edge node upload link parameter of the ith iteration according to the edge node capability and the edge node resource of the ith iteration, specifically including:
using formulas
Figure BDA0003153959740000035
Calculating the link parameters uploaded by the edge nodes of the ith iteration and related to the task-intensive user terminal;
using a formula
Figure BDA0003153959740000036
Calculating the link parameters uploaded by the edge nodes of the ith iteration and related to the delay sensitive user terminal;
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003153959740000037
and
Figure BDA0003153959740000038
uploading link parameters for the edge nodes of the ith iteration with respect to the task-intensive user terminal and the delay-sensitive user terminal respectively,
Figure BDA0003153959740000039
and
Figure BDA00031539597400000310
uploading link parameters for the edge nodes of the i-1 st iteration related to the task-intensive user terminal and the delay-sensitive user terminal respectively,
Figure BDA00031539597400000311
the edge node g is provided with the edge node capability of the resource to the task-intensive user terminals,
Figure BDA00031539597400000312
providing the edge node capability of resources for the edge node g to the time delay sensitive user terminal; gamma ray m An iteration step length of the link parameters uploaded by the edge node relative to the task-intensive user terminal; gamma ray n The iteration step length of the edge node about the time delay sensitive user terminal uploading link parameter is obtained;
Figure BDA0003153959740000041
and
Figure BDA0003153959740000042
respectively representing the edge node resources provided by the edge node to the task-intensive user terminal and the delay-sensitive user terminal during the ith iteration.
Optionally, the optimizing the edge calculation distribution result of the ith iteration to obtain the edge calculation distribution result of the (i + 1) th iteration specifically includes:
using formulas
Figure BDA0003153959740000043
Optimizing the resource quantity provided by the edge node of the ith iteration to the task-intensive user terminal to obtain the resource quantity provided by the edge node of the (i + 1) th iteration to the task-intensive user terminal;
using formulas
Figure BDA0003153959740000044
Optimizing the resource quantity provided by the edge node of the ith iteration to the task-intensive user terminal to obtain the resource quantity provided by the edge node of the (i + 1) th iteration to the delay-sensitive user terminal;
wherein u is gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the ith iteration; u. of gn (i) The resource quantity u provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration gm (i + 1) the resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the (i + 1) th iteration; u. of gn (i + 1) the resource quantity, kappa, provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the (i + 1) th iteration gm And kappa gn The iteration step length, alpha, of the edge node g with respect to the resource amount of the task-intensive user terminal m and the delay-sensitive user terminal n, respectively m (i) And alpha n (i) Respectively representing the download link parameters of the task-intensive user terminal m in the ith iteration and the download link parameters of the time-sensitive user terminal n in the ith iteration.
An edge computing bandwidth resource distribution system facing smart home, the distribution system comprising:
the user terminal resource and edge node resource calculation module is used for calculating the user terminal resource and edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration; the user terminal resource is the resource quantity obtained by the user terminal, and the edge node resource is the resource quantity provided by the edge node;
the user terminal download link parameter calculation module is used for calculating the user terminal download link parameter of the ith iteration by utilizing a utility program in the user terminal according to the user terminal resource of the ith iteration;
the edge node uploading link parameter calculating module is used for calculating the edge node uploading link parameter of the ith iteration according to the edge node capability and the edge node resource of the ith iteration; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation;
the judging module is used for judging whether the absolute value of the difference value between the link parameter downloaded by the user terminal of the ith iteration and the link parameter uploaded by the edge node is smaller than an absolute value threshold value or not to obtain a judging result;
an edge calculation distribution result optimization module, configured to optimize an edge calculation distribution result of the ith iteration if the determination result indicates no, obtain an edge calculation distribution result of the (i + 1) th iteration, increase the value of i by 1, and return to the step "calculate user terminal resources and edge node resources of the ith iteration according to the edge calculation distribution result of the ith iteration";
and the optimal distribution result output module is used for outputting the edge calculation distribution result of the ith iteration as the optimal distribution result if the judgment result shows that the edge calculation distribution result of the ith iteration is positive.
Optionally, the distribution system further comprises:
the optimal user terminal resource calculation module is used for calculating the user terminal resource of each user terminal according to the optimal allocation result and taking the user terminal resource as the optimal user terminal resource of the user terminal;
and the optimal user terminal resource updating module is used for respectively comparing the optimal user terminal resource of each user terminal with the user terminal capacity, and updating the optimal user terminal resource of the user terminal into the user terminal capacity of the user terminal when the optimal user terminal resource of the user terminal is greater than the user terminal capacity.
Optionally, the user terminal resource and edge node resource calculating module specifically includes:
a first user terminal resource calculation submodule for calculating distribution result according to the ith iteration edge and using formula h m (i)=∑ g:g∈G(m) u gm (i) Calculating the user terminal resource of the task-intensive user terminal of the ith iteration;
the second user terminal resource calculation submodule calculates distribution results according to the edge of the ith iteration by using a formula h n (i)=∑ g:g∈G(n) u gn (i) Calculating the user terminal resource of the time delay sensitive user terminal of the ith iteration;
wherein h is m (i) And h n (i) The user terminal resources of the ith iteration task intensive user terminal and the delay sensitive user terminal are respectively, and g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is an edge node set for providing resources for the task-intensive user terminal in the edge calculation distribution result of the ith iteration; g (n) is an edge node set for providing resources for the time delay sensitive user terminal in the edge calculation distribution result of the ith iteration; u. of gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the distribution result of the edge calculation of the ith iteration; u. of gn (i) And calculating the resource quantity provided by the edge node g in the distribution result for the edge of the ith iteration to the delay sensitive user terminal n.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses an edge computing bandwidth resource allocation method for smart home, which comprises the following steps: calculating user terminal resources and edge node resources of the ith iteration according to the edge calculation distribution result of the ith iteration; the user terminal resource is the resource quantity obtained by the user terminal, and the edge node resource is the resource quantity provided by the edge node; according to the user terminal resource of the ith iteration, calculating the user terminal download link parameter of the ith iteration by using a utility program in the user terminal; calculating the uploading link parameter of the edge node of the ith iteration according to the edge node capability and the edge node resource of the ith iteration; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation; judging whether the absolute value of the difference value between the downloading link parameter of the user terminal of the ith iteration and the uploading link parameter of the edge node is smaller than an absolute value threshold value or not, and obtaining a judgment result; if the judgment result shows no, optimizing the edge calculation distribution result of the ith iteration to obtain the edge calculation distribution result of the (i + 1) th iteration, increasing the value of i by 1, and returning to the step of calculating the user terminal resource and the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration; and if the judgment result shows that the edge calculation distribution result of the ith iteration is used as the optimal distribution result, outputting the edge calculation distribution result of the ith iteration as the optimal distribution result. The invention takes the absolute value of the difference value between the downloading link parameter of the user terminal and the uploading link parameter of the edge node as the optimization target, realizes the continuous optimization of the edge calculation distribution result, and can effectively converge to the optimal point of bandwidth resource distribution, thereby ensuring the satisfaction degree of the user terminal obtaining the bandwidth resource.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of an edge computing bandwidth resource allocation method for smart home according to embodiment 1 of the present invention;
fig. 2 is a flowchart of an edge computing bandwidth resource allocation method for smart homes according to embodiment 2 of the present invention;
FIG. 3 is a diagram of a conventional edge computing architecture provided by the present invention;
fig. 4 is an edge calculation scene diagram facing smart home provided by the present invention;
fig. 5 is a network topology structure diagram of an edge node and a user terminal provided by the present invention;
fig. 6 is a diagram of a task-intensive user terminal downloading link parameter and an edge node uploading link parameter in embodiment 3 of the present invention;
FIG. 7 is a diagram of the utility and total utility of each task-intensive user terminal in embodiment 3 of the present invention;
fig. 8 is a diagram for acquiring an optimal resource allocation map by each task-intensive ue in embodiment 3 of the present invention;
fig. 9 is an optimal bandwidth resource allocation diagram obtained by each task-intensive ue under the download limitation condition in embodiment 3 of the present invention;
fig. 10 is an optimal bandwidth resource allocation diagram obtained by each task-intensive user terminal in different iteration step lengths in embodiment 3 of the present invention;
fig. 11 is a diagram of download link parameters and upload link parameters of edge nodes of each delay-sensitive user terminal in embodiment 3 of the present invention;
fig. 12 is a graph of the utility and the total utility of each delay-sensitive ue in embodiment 3 of the present invention;
fig. 13 is an optimal resource allocation map obtained by each delay-sensitive user equipment in embodiment 3 of the present invention;
fig. 14 is an optimal bandwidth resource allocation diagram obtained by each delay-sensitive user equipment under the download limiting condition in embodiment 3 of the present invention;
fig. 15 is an optimal bandwidth resource allocation diagram obtained by each delay-sensitive user terminal in different iteration step lengths in embodiment 3 of the present invention;
fig. 16 is a structural diagram of an edge computing bandwidth resource allocation system for smart home according to embodiment 5 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
The invention aims to provide an edge computing bandwidth resource allocation method and system for smart home, which are used for reasonably allocating limited resource quantity in an edge network of the smart home, realizing that a user terminal can obtain required resources when the resource demand on the edge side of the network is greatly increased, and ensuring the satisfaction degree of the user terminal obtaining bandwidth resources.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1
As shown in fig. 1, the present invention provides an edge computing bandwidth resource allocation method for smart home, which is applied to an edge computing architecture in the smart home environment shown in fig. 4; different from the conventional edge computing structure shown in fig. 3, the edge computing architecture in the smart home environment includes an edge node, a user terminal, and a utility program in the user terminal; the method for distributing the tasks of the user terminals comprises the following steps that a plurality of edge nodes and a plurality of user terminals exist under an edge computing framework, and different utility programs in each user terminal represent the task preference of the user terminal:
step A, calculating user terminal resources and edge node resources of the ith iteration according to the edge calculation distribution result of the ith iteration; the user terminal resource is the resource quantity obtained by the user terminal, and the edge node resource is the resource quantity provided by the edge node.
Calculating the user terminal resource of the ith iteration according to the edge calculation distribution result of the ith iteration, which specifically comprises the following steps: calculating distribution result according to the edge of the ith iteration by using a formula h m (i)=∑ g:g∈G(m) u gm (i) Computing the task-intensive of the ith iterationUser terminal resources of the user terminal; calculating distribution result according to the edge of the ith iteration by using a formula h n (i)=∑ g:g∈G(n) u gn (i) Calculating the user terminal resource of the time delay sensitive user terminal of the ith iteration; wherein h is m (i) And h n (i) The user terminal resources of the ith iteration task intensive user terminal and the delay sensitive user terminal are respectively, and g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is an edge node set for providing resources for the task-intensive user terminal in the edge calculation distribution result of the ith iteration; g (n) is an edge node set for providing resources for the time delay sensitive user terminal in the edge calculation distribution result of the ith iteration; u. of gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the distribution result of the edge calculation of the ith iteration; u. of gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
Calculating the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration, which specifically comprises the following steps: calculating distribution result according to the edge of the ith iteration by using a formula
Figure BDA0003153959740000071
Calculating edge node resources provided by the edge nodes to the task-intensive user terminal during the ith iteration; calculating distribution result according to the edge of the ith iteration by using a formula
Figure BDA0003153959740000072
Calculating edge node resources provided by the edge nodes to the delay sensitive user terminal in the ith iteration; wherein the content of the first and second substances,
Figure BDA0003153959740000073
and
Figure BDA0003153959740000074
respectively representing that the edge node is provided for the task-intensive user terminal and the time delay sensitive user during the ith iterationThe edge node resources of the terminal, g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; m (g) is a set of task-intensive user terminals provided with resources by an edge node g; n (g) is defined as the edge node g Providing a time delay sensitive user terminal set of resources; u. of gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the ith iteration; u. of gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
And step B, calculating the user terminal download link parameters of the ith iteration by using the utility program in the user terminal according to the user terminal resources of the ith iteration.
The method for calculating the user terminal download link parameter of the ith iteration by using the utility program in the user terminal according to the user terminal resource of the ith iteration specifically comprises the following steps: using the formula alpha m (i)=X m ′(h m (i) Calculating the user terminal download link parameters of the ith iterative task-intensive user terminal; using the formula alpha n (i)=X n ′(h n (i) Calculating the user terminal download link parameter of the time delay sensitive user terminal of the ith iteration; wherein alpha is m (i) And alpha n (i) Downloading link parameters, h, for the user terminals of the ith iteration task-intensive user terminal and the delay-sensitive user terminal, respectively m (i) And h n (i) User terminal resources, X, for the ith iteration of the task-intensive and delay-sensitive user terminals, respectively m ′(h m (i) A task-intensive user terminal m for i iterations is obtaining a user terminal resource h m (i) Derivative of utility function in the latter utility program, X n ′(h n (i) I iterations of the delay sensitive ue n is obtaining the ue resource h n (i) The derivative of the utility function in the latter utility program.
Step C, calculating the uploading link parameter of the edge node of the ith iteration according to the edge node capability and the edge node resource of the ith iteration; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation.
Calculating the uploading link parameter of the edge node of the ith iteration according to the edge node capability and the edge node resource of the ith iteration, and specifically comprising the following steps: using formulas
Figure BDA0003153959740000075
Calculating the link parameters uploaded by the edge nodes of the ith iteration and related to the task-intensive user terminal; using formulas
Figure BDA0003153959740000081
Figure BDA0003153959740000082
Calculating the link parameters uploaded by the edge nodes of the ith iteration and related to the delay sensitive user terminal; wherein the content of the first and second substances,
Figure BDA0003153959740000083
and
Figure BDA0003153959740000084
uploading link parameters for the edge nodes of the ith iteration with respect to the task-intensive user terminal and the delay-sensitive user terminal respectively,
Figure BDA0003153959740000085
and
Figure BDA0003153959740000086
uploading link parameters for the edge nodes of the i-1 st iteration related to the task-intensive user terminal and the delay-sensitive user terminal respectively,
Figure BDA0003153959740000087
the edge node g is provided with the edge node capability of the resource to the task-intensive user terminals,
Figure BDA0003153959740000088
providing the edge node capability of resources for the edge node g to the delay sensitive user terminal; gamma ray m An iteration step length of link parameters uploaded for the edge node with respect to the task-intensive user terminal; gamma ray n The iteration step length of the edge node about the time delay sensitive user terminal uploading link parameter is obtained;
Figure BDA0003153959740000089
and
Figure BDA00031539597400000813
respectively representing the edge node resources provided by the edge node to the task-intensive user terminal and the delay-sensitive user terminal during the ith iteration.
Step D, judging whether the absolute value of the difference value between the link parameter downloaded by the user terminal of the ith iteration and the link parameter uploaded by the edge node is smaller than an absolute value threshold value or not, and obtaining a judgment result;
step E, if the judgment result shows no, optimizing the edge calculation distribution result of the ith iteration to obtain the edge calculation distribution result of the (i + 1) th iteration, increasing the value of i by 1, and returning to the step of calculating the user terminal resource and the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration;
and F, if the judgment result shows yes, outputting an edge calculation distribution result of the ith iteration as an optimal distribution result.
The optimizing the edge calculation distribution result of the ith iteration to obtain the edge calculation distribution result of the (i + 1) th iteration specifically includes: using formulas
Figure BDA00031539597400000811
Optimizing the resource quantity provided by the edge node of the ith iteration to the task-intensive user terminal to obtain the resource quantity provided by the edge node of the (i + 1) th iteration to the task-intensive user terminal; using formulas
Figure BDA00031539597400000812
Optimizing the resource quantity provided by the edge node of the ith iteration to the task-intensive user terminal, and obtaining the time delay sensitivity provided by the edge node of the (i + 1) th iterationAmount of resources of the type user terminal; wherein u is gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the ith iteration; u. of gn (i) The resource quantity u provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration gm (i + 1) the resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the (i + 1) th iteration; u. of gn (i + 1) the resource quantity, kappa, provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the (i + 1) th iteration gm And kappa gn The iteration step lengths, alpha, of the edge node g with respect to the resource amounts of the task-intensive user terminal m and the delay-sensitive user terminal n, respectively m (i) And alpha n (i) Respectively representing the download link parameters of the task-intensive user terminal m in the ith iteration and the download link parameters of the time-sensitive user terminal n in the ith iteration.
Step 106, outputting the edge calculation distribution result of the ith iteration as an optimal distribution result, and then: calculating the user terminal resource of each user terminal according to the optimal allocation result, and taking the user terminal resource as the optimal user terminal resource of the user terminal; and respectively comparing the optimal user terminal resource of each user terminal with the user terminal capacity, and updating the optimal user terminal resource of the user terminal to the user terminal capacity of the user terminal when the optimal user terminal resource of the user terminal is greater than the user terminal capacity.
Example 2
As shown in fig. 2, an edge computing bandwidth resource allocation method for smart home is applied to an edge computing architecture in the smart home environment shown in fig. 4; different from the conventional edge computing structure shown in fig. 3, the edge computing architecture in the smart home environment includes an edge node, a user terminal, and a utility program in the user terminal; a plurality of edge nodes and a plurality of user terminals exist under an edge computing framework, and different utility programs in each user terminal represent the task preference of the user terminal; the edge computing resource allocation method comprises the following steps:
101, acquiring uploading link parameters and downloading link parameters at the current moment and resources distributed to a user terminal by an edge node in the intelligent home environment at the current moment; uploading link parameters at the current moment are index variables of each unit of resource provided in the edge node uploading link; the current downloading link parameter is an index variable of each unit resource obtained in a downloading link of the user terminal; the resources distributed to the user terminals by the edge nodes in the intelligent home environment at the current moment are resources provided for the user terminals by the edge nodes in the edge calculation.
102, calculating user terminal resources according to the edge calculation resource distribution at the current moment; the user terminal resources are the resource amount obtained by the user terminals with different utility programs at the current moment.
103, judging whether the absolute value of the difference value between the uploading link parameter and the downloading link parameter at the current moment is smaller than a fixed value or not to obtain an iteration judgment result; if the absolute value of the difference value expressed by the iteration judgment result is smaller than the fixed value, the iteration is stopped, step 110 is executed, the allocation result obtained at the current moment is determined as the optimal resource allocation, and the resource allocation is carried out on the user terminal according to the optimal resource allocation result; if the absolute value of the difference value expressed by the iteration judgment result is larger than the fixed value, the iteration is continued, and step 104 is executed to calculate the edge calculation resource allocation at the next moment.
And 104, calculating the download link parameters of the user terminal at the next moment by utilizing the utility program in the user terminal according to the user terminal resources.
105, distributing and calculating edge node resources according to edge calculation resources at the next moment; the edge node resources are the resource amount provided by each edge node at the next moment;
106, calculating the uploading link parameters of the edge nodes at the next moment according to the edge node resources and the edge node capacity; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation;
step 107, judging whether the absolute value of the difference value between the uploading link parameter and the downloading link parameter at the next moment is smaller than a fixed value or not, and obtaining an iteration judgment result; if the absolute value of the difference value expressed by the iteration judgment result is smaller than the fixed value, the iteration is stopped, step 108 is executed, the allocation result obtained at the next moment is determined to be the optimal resource allocation, and the resource allocation is carried out on the user terminal according to the optimal resource allocation result; and if the absolute value of the difference value expressed by the iteration judgment result is larger than the fixed value, the iteration is continued, and the edge calculation resource distribution result at the next moment is calculated. And returning to the step 109 of calculating the user terminal resources according to the resource allocation until the absolute value of the difference value between the uploading link parameters and the downloading link parameters is less than the fixed value, and performing resource allocation on the user terminal according to the current edge node resource allocation result if the iteration is stopped.
And 108, calculating the user terminal resources according to the resource distribution result at the next moment.
Step 109, updating the link resource allocation and calculating the user terminal resource at the next moment, returning to step 204 to calculate again until the absolute value of the difference value between the uploading link parameter and the downloading link parameter is less than the fixed value.
Step 110, judging whether the current optimal resource allocation exceeds the capability of each user terminal to obtain a receiving judgment result; if the optimal resource allocation expressed by the received judgment result is smaller than the capability of the user terminal, executing step 111, and finally allocating the resource of the user terminal as the optimal resource allocation; if the optimal resource allocation expressed by the received judgment result is greater than the user terminal capability, executing step 112, and finally allocating the resource of the user terminal as the resource quantity of the user terminal capability; the user terminal capability is the maximum resource receiving capability of the user terminal in the edge calculation.
Step 111: and performing resource allocation according to the optimal resource allocation result obtained by calculation at the moment.
Step 112: and performing resource allocation according to the maximum receiving capacity of each user terminal.
Wherein, the calculation formula of the user terminal resource is according to the formula h m (i+1)=∑ g:g∈G(m) u gm (i + 1) computing user terminal resources for the task-intensive user terminal; according to the formula h n (i+1)=∑ g:g∈G(n) u gn (i + 1), calculating time delay sensitivityUser terminal resources of the sensory user terminal.
Wherein g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is an edge node set for providing resources for the task-intensive user terminal; g (n) is an edge node set for providing resources for the time delay sensitive user terminal; u. of gm (i + 1) is the amount of resources provided to user terminal m at time i +1 by edge node g; u. of gn (i + 1) is the amount of resources provided by the edge node g to the user terminal n at time i + 1.
In step 104, the parameters of the download link of the user terminal at the next moment are calculated, specifically including the step of calculating the parameters according to the formula α m (i+1)=X m ′(h m (i + 1)) calculating the parameter of the user terminal m at the time of i +1 in the downloading link, alpha n (i+1)=X n ′(h n (i + 1)) calculating the parameters of the user terminal n at the time of i +1 in the downloading link;
wherein, X m (h m (i + 1)) the task-intensive user terminal m is acquiring the user terminal resource h at the moment i +1 m (i + 1) utility function in post-utility program, X m ′(h m (i + 1)) is X m (h m (i + 1)).
The formula for computing the edge node resources in step 105 is based on the formula
Figure BDA0003153959740000101
Calculating edge node resources provided by the edge node g to all task-intensive user terminals; according to
Figure BDA0003153959740000102
Figure BDA0003153959740000103
Calculating edge node resources provided by the edge node g to all the delay sensitive user terminals;
wherein g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; m (g) is a set of task-intensive user terminals provided with resources by an edge node g; n (g) is a time delay sensitive user terminal set with resources provided by edge nodes gCombining; u. u gm (i + 1) is the amount of resources provided to user terminal m by edge node g at time i + 1; u. u gn (i + 1) is the amount of resources provided by the edge node g to the user terminal n at time i + 1.
The formula for calculating the upload link parameters of the edge node g at the next time point with respect to the task-intensive user terminal in step 106 is
Figure BDA0003153959740000104
The formula for calculating the parameters of the edge node g about the uplink of the time delay sensitive user terminal at the next moment is
Figure BDA0003153959740000105
Wherein the content of the first and second substances,
Figure BDA0003153959740000106
edge node g is provided with the edge node capability of the resource to the task-intensive user terminals,
Figure BDA0003153959740000107
providing edge node capability of resources for an edge node g to a time-sensitive user terminal, wherein the edge node capability provides capability for the maximum resources of the edge node in edge calculation; gamma ray m An iteration step length of the link parameters uploaded by the edge node relative to the task-intensive user terminal; gamma ray n Uploading an iteration step length of a link parameter for the edge node relative to the time sensitive user terminal;
Figure BDA0003153959740000108
means, when c > 0, a = b; c =0, a = max {0, b }.
In step 109, link resource allocation is updated, and the calculation formula of edge calculation resource allocation at the next moment is:
Figure BDA0003153959740000109
Figure BDA00031539597400001010
wherein, κ gm And kappa gn Are iteration step sizes, respectively, and κ gm ,κ gn >0;
Figure BDA00031539597400001011
Means, when c > 0, a = b; c =0, a = max {0, b }.
Example 3
The invention selects two forms of utility functions for improving the satisfaction degree of the user terminal, forms an edge computing resource allocation optimization model facing the smart home, converts the resource allocation problem into the problem of maximizing the utility of the user terminal, and designs a distributed resource allocation method which can effectively converge to the optimal point of the bandwidth allocation problem, namely the user terminal obtains the optimal bandwidth resource allocation.
The edge computing architecture under the intelligent home environment comprises edge nodes, a user terminal and a utility program in the user terminal; as shown in fig. 4, there are a plurality of edge nodes and a plurality of user terminals under the edge computing framework, and a different utility program in each user terminal represents the task preference of the user terminal; wherein G belongs to G as an edge node; m belongs to M and is used as a task-intensive user terminal; n belongs to N and is a time delay sensitive user terminal; if only one node provides resources, the node belongs to the edge node G; as long as one node needs resources due to large processing calculation amount, the node belongs to M; as long as one node needs resources for processing tasks with high delay requirements, the node belongs to an edge node set which provides resources for task-intensive user terminals, wherein G (m) is N; g (n) is an edge node set for providing resources for the time delay sensitive user terminal; m (g) is a set of task-intensive user terminals that are provided resources by an edge node g; n (g) is a time delay sensitive user terminal set provided with resources by an edge node g; note that G ∈ G (M) is if and only if M ∈ M (G), G ∈ G (N) is if and only if N ∈ N (G).
If the edge node g provides the bandwidth resource u for the task-intensive user terminal m gm The edge node g provides bandwidth resource u for the time delay sensitive user terminal n gn ,h m =∑ g:g∈G(m) u gm Represents all bandwidth resources, h, received by the task-intensive user terminal m n =∑ g:g∈G(n) u gn Representing all bandwidth resources received by the delay sensitive user terminal n,
Figure BDA0003153959740000111
respectively download bandwidth limit for user terminal m and download link bandwidth limit for user terminal n, i.e.
Figure BDA0003153959740000112
Meanwhile, one edge node can provide resources for a plurality of user terminals,
Figure BDA0003153959740000113
and
Figure BDA0003153959740000114
respectively providing bandwidth resources for the edge node g to the user terminals m and n;
Figure BDA0003153959740000115
and
Figure BDA0003153959740000116
respectively representing the maximum bandwidth resource amount provided by the edge node g for the user terminals m and n, then
Figure BDA0003153959740000117
Utility function of user terminal: in the process of processing tasks, the satisfaction degrees of the user terminals m and n are closely related to the obtained bandwidth resources, the more the obtained bandwidth resources are, the higher the satisfaction degrees are, the satisfaction degrees of the user terminals when obtaining services can be expressed by using utility functions, namely, as the received bandwidth resources are increased, the utility of the user terminals is gradually increased, but a law of diminishing marginal utility is also presented, and the user terminals processing different task types can display different utility curves according to the task characteristics, so that the following utility functions are selected:
X m (h m )=ω m log(h m +1)
Figure BDA0003153959740000118
wherein, ω is m Obtaining bandwidth resource willingness, h, for task-intensive user terminals m m Indicates that user terminal m receives all bandwidth resources, X m (h m ) For the utility obtained by the user terminal m after receiving the resource, I n Is the time limit when the time sensitive user terminal n processes the task, fn is the task amount when the user terminal n processes the corresponding type of task, B n To meet the minimum requirement of the user terminal n for allocating bandwidth during resource allocation, sgn (h) n -B n ) Meaning if h n >B n Then sgn (h) n -B n ) =1, if h n ≤B n Then sgn (h) n -B n )=-1;
Bandwidth resource allocation model: aiming at a task-intensive user terminal m and a time-sensitive user terminal n, the models need to respectively obtain the respective optimal utility of the two, and the sum of the two is used as the target function of the models.
Max∑ m:m∈M X m (h m )+∑ n:n∈N X n (h n )
Figure BDA0003153959740000119
Figure BDA00031539597400001110
Figure BDA0003153959740000121
Figure BDA0003153959740000122
Figure BDA0003153959740000123
Figure BDA0003153959740000124
Figure BDA0003153959740000125
Based on convex optimization theory, a convex objective function and a linear constrained resource allocation model are a convex optimization problem, and a utility function Xm (h) is obtained by matching m ),X n (h n ) Determines that the objective function of the model is convex, so that the objective of the resource allocation model represented in the model is with respect to h m ,h n Is strictly convex, but with respect to u gm ,u gn Not strictly convex. This leads to non-uniqueness of the optimal solution of the original problem, because each user terminal can obtain resources from multiple edge nodes or each edge node can provide resources for multiple user terminals. In the process of solving the optimal resource allocation, generally speaking, the uploading bandwidth resource of the edge node is a scarce resource, so the constraint in the corresponding model is positive constraint, the downloading link bandwidth of the user terminal is not a scarce resource, and the constraint in the corresponding model is non-positive constraint, so the constraint of the uploading link bandwidth of the edge node is only considered when the Lagrangian function is stated.
Establishing a lagrangian function of the above optimization problem:
Figure BDA0003153959740000126
wherein the content of the first and second substances,
Figure BDA0003153959740000127
upload link parameters, alpha, for edge node g with respect to user terminals m and n, respectively m ≥0,α n And more than or equal to 0 download link parameters of the user terminals m and n respectively.
The lagrangian method is utilized to process the resource optimization allocation problem, and optimal uploading link parameters and downloading link parameters of each user terminal m and n can also be obtained.
Figure BDA0003153959740000128
Figure BDA0003153959740000129
Therefore, when resources are distributed to the task-intensive user terminal, the uploading link parameters of the edge node g are equal to the downloading link parameters of the task-intensive user terminal m; when the time sensitive user terminal is allocated with resources, the uploading link parameter of the edge node g is equal to the downloading link parameter of the time sensitive user terminal n, namely
Figure BDA00031539597400001210
As shown in fig. 6 and 11.
The Lagrange method is utilized to process the resource optimization allocation problem, and the optimal bandwidth resource allocation value of each user terminal m and n can be obtained
Figure BDA00031539597400001211
As shown in fig. 8 and 13
Wherein, the ratio of tau,
Figure BDA00031539597400001212
in order to number a plurality of areas which are divided by the whole network, all the areas are not connected, wherein each area corresponds to a part of nodes. M is a group of τ For the set of user terminals m in the τ -th zone, G τ As a set of edge nodes g in the τ -th region,
Figure BDA00031539597400001213
is at the first
Figure BDA00031539597400001214
A set of user terminals n in an individual area,
Figure BDA00031539597400001215
is at the first
Figure BDA00031539597400001216
Set of user terminals g in an individual area.
It can be seen that the resource amount obtained by each user terminal m and n is not only related to solving the optimal resource allocation according to the lagrangian method, but also related to the maximum resource receiving capability of itself, i.e. the optimal resource allocation
Figure BDA00031539597400001217
Figure BDA0003153959740000131
As shown in fig. 9 and 14. By adjusting the size of the iteration step, the influence of the iteration step on the convergence speed of resource allocation can be observed, as shown in fig. 10 and 15.
The invention provides an edge computing bandwidth resource allocation method facing an intelligent home, wherein an edge computing architecture under an intelligent home environment comprises an edge node g, user terminals m and n and a utility program in the user terminals; a plurality of edge nodes and a plurality of user terminals exist under an edge computing framework, and different utility programs in each user terminal represent task preference of the user terminal.
The specific bandwidth resource allocation method is as follows:
step 1, in an edge computing network facing to intelligent home, at a moment i, an edge node g initializes bandwidth resource allocation u for each user terminal m gm (i) The download link parameter of the user terminal m is alpha m (i) The upload link parameters of the edge node g to m are
Figure BDA0003153959740000132
The edge node g distributes the resource bandwidth resource u for each user terminal n gn (i) The download link parameter of the user terminal n is alpha n (i) The upload link parameter of the edge node g to n is
Figure BDA0003153959740000133
Step 2, the user terminal m and the user terminal n respectively calculate to obtain the user terminal resource h at the moment i m (t) and h n (t)。
Step 3, according to the download link parameter alpha of the user terminal at the moment i m (i),α n (i) And the edge node uploads the link parameters to the user terminal
Figure BDA0003153959740000134
Judging whether the resource allocation at the moment i reaches the iteration termination condition, if so, determining the resource allocation at the moment i as the optimal resource allocation, if not, continuing to calculate, and adjusting the bandwidth resource u allocated at the moment i +1 gm (i+1),u gn (i+1);
Figure BDA0003153959740000135
Figure BDA0003153959740000136
Downloading link parameter alpha of user terminal m and n at moment 4, i +1 m (i+1),α n (i+1);
α m (i+1)=X m ′(h m (i + 1)), i.e.
Figure BDA0003153959740000137
α n (i+1)=X n ′(h n (i + 1)), i.e.
Figure BDA0003153959740000138
Wherein ω is m Obtaining bandwidth resource willingness, h, for task-intensive user terminals m m Indicates that the user terminal m receives all bandwidth resources, X m (h m ) For the utility of the user terminal m after receiving the resource, I n Time constraints when processing its tasks for a time sensitive user terminal n, F n Is the amount of tasks, B, when the user terminal n processes its corresponding type of tasks n To meet the minimum requirement of the user terminal n for allocating bandwidth during resource allocation, sgn (h) n -B n ) Meaning if h n >B n Then sgn (h) n -B n ) =1, if h n ≤B n Then sgn (h) n -B n )=-1。
Step 5, calculating edge node resources distributed to the user terminal by the edge node at the moment i +1 and calculating the uploading link parameters of the edge node at the next moment;
Figure BDA0003153959740000139
Figure BDA00031539597400001310
Figure BDA00031539597400001311
Figure BDA00031539597400001312
wherein g is an edge node, m and n are user terminals; m (g) refers to the provision of a set of user terminals M by an edge node g, N (g) refers to the provision of a set of user terminals N by an edge node g, u gm (i) And u gn (i) Bandwidth resources obtained by the user terminals m and n at time i, respectively;
Figure BDA0003153959740000141
and
Figure BDA0003153959740000142
respectively providing bandwidth resources for all user terminals m and n by the edge node g at the moment i + 1;
Figure BDA0003153959740000143
and
Figure BDA0003153959740000144
respectively representing the limitation of providing bandwidth resources for all user terminals m and n for the edge node g; gamma ray m And gamma n Is an iteration step size, and γ m >0,γ n >0。
And 6, judging whether the resource allocation at the moment i +1 reaches an iteration termination condition, if so, determining the resource allocation at the moment i +1 as the optimal resource allocation, and if not, continuing to return to the step 4 for iteration until the iteration termination condition is reached to obtain the optimal resource allocation.
Step 7, after obtaining the optimal resource allocation, judging whether the optimal resource received by each user terminal is smaller than the receiving capacity of the user terminal, if the optimal resource allocation received by the user terminal is smaller than the receiving capacity of the user terminal, the final resource allocation of the user terminal is the optimal resource allocation of the user terminal; if the optimal resource allocation received by the user terminal is greater than the receiving capacity of the user terminal, the final resource allocation of the user terminal is the receiving capacity of the end user terminal.
And 8, if a new edge node or a user terminal is added or the original edge node or the original user terminal is withdrawn in the intelligent home-oriented edge computing network, the iterative process from the step 1 to the step 7 is carried out again until the final bandwidth resource allocation is achieved.
And (3) convergence analysis:
convergence is an important index for measuring the performance of the algorithm. The invention considers that 3 edge nodes exist in the edge computing network facing the smart homeAnd 6 user terminals, the topology of which is shown in fig. 5, the bandwidth resource of the upload link of the edge node is limited to
Figure BDA0003153959740000145
The download link bandwidth resource of the user terminal is limited to
Figure BDA0003153959740000146
In the simulation process, it is assumed that 6 ues are a task-intensive ue m and a time-sensitive ue n, respectively, and the optimal resource allocation is obtained according to the assumed results, and the simulation results are shown in fig. 6, 7, 8, 9 and 10 and fig. 11, 12, 13, 14 and 15, respectively. When the number of user terminals is m, the optimal resource allocation is as shown in fig. 8, and when the number of iterations is 200, the algorithm has already converged to the optimal point, taking m =1 as an example, and the result of the optimal bandwidth resource allocation is
Figure BDA0003153959740000147
When the number of iterations is 300, the algorithm converges to the optimal point, taking n =1 as an example, and the optimal bandwidth resource allocation result is
Figure BDA0003153959740000148
Therefore, it can be shown from the above data that the algorithm can effectively converge to the equilibrium point within a limited number of iterations, and the equilibrium point is the optimal point of the resource allocation model. The convergence speed of the algorithm mainly depends on the iteration step size of the algorithm, as shown in fig. 10 and fig. 15, when the iteration step size is large, the algorithm iteration speed is high, but the iteration step size cannot be too large, otherwise the algorithm fluctuates around the equilibrium point.
Example 4
The invention also provides an edge computing bandwidth resource allocation system for smart home, which comprises:
the user terminal resource and edge node resource calculation module is used for calculating the user terminal resource and edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration; the user terminal resource is the resource quantity obtained by the user terminal, and the edge node resource is the resource quantity provided by the edge node;
the user terminal resource and edge node resource calculation module specifically includes: a first user terminal resource calculation submodule for calculating distribution result according to the ith iteration edge by using formula h m (i)=∑ g:g∈G ( m )u gm (i) Calculating the user terminal resource of the task-intensive user terminal of the ith iteration; the second user terminal resource calculation submodule calculates distribution results according to the edge of the ith iteration by using a formula h n (i)=∑ g:g∈G(n) u gn (i) Calculating the user terminal resource of the time delay sensitive user terminal of the ith iteration; wherein h is m (i) And h n (i) The user terminal resources of the ith iteration task intensive user terminal and the delay sensitive user terminal are respectively, and g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is an edge node set for providing resources for the task-intensive user terminal in the edge calculation distribution result of the ith iteration; g (n) is an edge node set for providing resources for the time delay sensitive user terminal in the edge calculation distribution result of the ith iteration; u. u gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the ith iteration; u. u gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
And the user terminal download link parameter calculation module is used for calculating the user terminal download link parameters of the ith iteration by using the utility program in the user terminal according to the user terminal resources of the ith iteration.
The edge node uploading link parameter calculating module is used for calculating the edge node uploading link parameter of the ith iteration according to the edge node capacity and the edge node resource of the ith iteration; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation.
And the judging module is used for judging whether the absolute value of the difference value between the link parameter downloaded by the user terminal of the ith iteration and the link parameter uploaded by the edge node is smaller than the absolute value threshold value or not, and obtaining a judging result.
And if the judgment result shows no, optimizing the edge calculation distribution result of the ith iteration to obtain an edge calculation distribution result of the (i + 1) th iteration, increasing the value of i by 1, and returning to the step of calculating the user terminal resources and the edge node resources of the ith iteration according to the edge calculation distribution result of the ith iteration.
And the optimal distribution result output module is used for outputting the edge calculation distribution result of the ith iteration as the optimal distribution result if the judgment result shows that the edge calculation distribution result is positive.
The dispensing system further comprises:
the optimal user terminal resource calculation module is used for calculating the user terminal resource of each user terminal according to the optimal distribution result and taking the user terminal resource as the optimal user terminal resource of the user terminal;
and the optimal user terminal resource updating module is used for respectively comparing the optimal user terminal resource of each user terminal with the user terminal capacity, and updating the optimal user terminal resource of the user terminal into the user terminal capacity of the user terminal when the optimal user terminal resource of the user terminal is greater than the user terminal capacity.
Example 5
As shown in fig. 16, this embodiment provides an edge computing bandwidth resource allocation system for an intelligent home, which is applied to an edge computing architecture in the intelligent home environment of fig. 4, where the edge computing architecture in the intelligent home environment includes an edge node, a user terminal, and a utility program in the user terminal; a plurality of edge nodes and a plurality of user terminals exist under an edge computing framework, and different utility programs in each user terminal represent the task preference of the user terminal; the edge computing resource allocation system includes:
an obtaining module 201, configured to obtain the current upload link parameter and the current download link parameter, and resources allocated to the user terminal by the edge node in the smart home environment; the uploading link parameter at the current moment is an index variable of each unit resource provided in the uploading link of the edge node; the current downloading link parameter is an index variable of each unit resource obtained in a downloading link of the user terminal; the resources distributed to the user terminals by the edge nodes in the intelligent home environment at the current moment are resources provided for the plurality of user terminals by the plurality of edge nodes in edge calculation;
a current-time user terminal resource calculation module 202, configured to calculate user terminal resources according to current-time edge calculation resource allocation; the user terminal resources are the resource quantity obtained by the user terminals with different utility programs at the current moment;
the time i iteration judgment module 203 is configured to judge whether an absolute value of a difference between the upload link parameter and the download link parameter at the current time is smaller than a fixed value, so as to obtain an iteration judgment result; if the absolute value of the difference value expressed by the iteration judgment result is smaller than the fixed value, the iteration is stopped, the distribution result obtained at the current moment is determined as the optimal resource distribution, and the resource distribution is carried out on the user terminal according to the optimal resource distribution result; and if the absolute value of the difference value expressed by the iteration judgment result is larger than the fixed value, the iteration is continued, and the edge calculation resource allocation at the next moment is calculated.
A next time download link parameter calculating module 204, configured to calculate a next time download link parameter of the user terminal by using a utility program in the user terminal according to the user terminal resource;
an edge node resource calculating module 205, configured to calculate an edge node resource according to a resource allocation result of an edge node to a user terminal at the next time; the edge node resources are the resource amount provided by each edge node at the next moment;
a next-time upload link parameter calculation module 1506, configured to calculate next-time upload link parameters of the edge nodes according to the edge node resources and the edge node capabilities; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation;
the time i +1 iteration judgment module 207 is configured to judge whether an absolute value of a difference between the upload link parameter and the download link parameter at the next time is smaller than a fixed value, so as to obtain an iteration judgment result; if the absolute value of the difference value expressed by the iteration judgment result is smaller than the fixed value, the iteration is stopped, the allocation result obtained at the next moment is determined to be the optimal resource allocation, and the resource allocation is carried out on the user terminal according to the optimal resource allocation result; and if the absolute value of the difference value expressed by the iteration judgment result is larger than the fixed value, the iteration is continued, and the edge calculation resource distribution result at the next moment is calculated. And returning to the step of calculating the resources of the user terminal according to the resource allocation until the absolute value of the difference value between the uploading link parameter and the downloading link parameter is smaller than a fixed value, stopping iteration, and performing resource allocation on the user terminal according to the current edge node resource allocation result.
And an updating module 208, configured to calculate the user terminal resource according to the resource allocation result at the next time.
A receiving and judging module 209, configured to judge whether the current ue resource exceeds the capability of each ue, and obtain a receiving and judging result; if the user terminal resource expressed by the received judgment result is smaller than the user terminal capability, the final resource of the user terminal is allocated as the user terminal resource; if the user terminal resource expressed by the received judgment result is larger than the user terminal capability, the final resource allocation of the user terminal is the resource amount of the user terminal capability; the user terminal capability is the maximum resource receiving capability of the user terminal in the edge calculation;
wherein the user terminal resource calculation formula for the calculation task intensive user terminal in the user terminal resource calculation module 202 at the current moment is h m (i+1)=∑ g:g∈G(m) u gm (i + 1); the calculation formula for calculating the user terminal resources of the delay sensitive user terminal is h n (i+1)=∑ g:g∈G(n) u g n(i+1)。
Wherein g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is an edge node set for providing resources for the task-intensive user terminal; g (n) is an edge node set for providing resources for the time delay sensitive user terminal; u. of g:n (i + 1) is provided to the user terminal for the edge node g at time i +1m resource amount; u. of gn (i + 1) is the amount of resources provided by the edge node g to the user terminal n at time i + 1.
The formula for calculating the downlink parameter of the user terminal m at the moment i +1 in the next time downlink parameter calculation module 204 is α m (i+1)=X m ′(h m (i + 1)), calculating the parameter alpha of the user terminal n at the time of i +1 in the downloading link n (i+1)=X n ′(h n (i + 1)), wherein X m (h m (i + 1)) the task-intensive user terminal m is obtaining the user terminal resource h at the moment i +1 m (i + 1) utility function in post-utility program, X m ′(h m (i + 1)) is X m (h m (i + 1)).
The formula for calculating the edge node resource provided by the edge node g to all the task-intensive user terminals in the edge node resource calculation module 205 is
Figure BDA0003153959740000171
The formula for calculating the edge node resources provided by the edge node g to all the time delay sensitive user terminals is
Figure BDA0003153959740000172
Wherein g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; m (g) is a set of task-intensive user terminals that are provided resources by an edge node g; n (g) is a time delay sensitive user terminal set provided with resources by an edge node g; u. u gm (i + 1) is the amount of resources provided to user terminal m at time i +1 by edge node g; u. of gn (i + 1) is the amount of resources provided by the edge node g to the user terminal n at time i + 1.
The formula for calculating the upload link parameters of the next time edge node g with respect to the task-intensive ue in the next time upload link parameter calculation module 206 is
Figure BDA0003153959740000173
The formula for calculating the parameters of the edge node g about the uplink of the time delay sensitive user terminal at the next moment is
Figure BDA0003153959740000174
Wherein the content of the first and second substances,
Figure BDA0003153959740000175
edge node g is provided with the edge node capability of the resource to the task-intensive user terminals,
Figure BDA0003153959740000176
providing the edge node capability of resources for an edge node g to a time sensitive user terminal, wherein the edge node capability provides the capability for the maximum resources of the edge node in edge calculation; gamma ray m The iteration step length of the link parameters uploaded by the edge node for the task-intensive user terminal; gamma ray n The iterative step length of the link parameters downloaded by the edge node for the time sensitive user terminal;
Figure BDA0003153959740000177
means, when c > 0, a = b; c =0, a = max {0, b }.
Update Module 1508, calculating user terminal resources
Figure BDA0003153959740000178
Figure BDA0003153959740000179
Wherein, κ gm And kappa gn Are iteration step sizes, respectively, and κ gm ,κ gn >0;
Figure BDA00031539597400001710
Means, when c > 0, a = b; c =0, a = max {0, b }.
The invention analyzes the edge computing bandwidth resource allocation process facing to the intelligent home, firstly resolves the resource allocation problem in the edge computing network into a utility optimization problem, secondly sets a corresponding utility objective function and a resource allocation model according to different processing task characteristics of user terminals, and through the analysis of the models, the invention provides the edge computing bandwidth resource allocation method facing to the intelligent home, which can effectively converge to the optimal point of bandwidth resource allocation, thereby ensuring the satisfaction degree of the user terminals obtaining bandwidth resources.
In the present specification, the embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principle and the embodiment of the present invention are explained by applying specific examples, and the above description of the embodiments is only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (8)

1. An edge computing bandwidth resource allocation method for smart home is characterized by comprising the following steps:
calculating the user terminal resource and the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration; the user terminal resource is the resource quantity obtained by the user terminal, and the edge node resource is the resource quantity provided by the edge node;
according to the user terminal resource of the ith iteration, calculating the user terminal download link parameter of the ith iteration by using a utility program in the user terminal;
calculating the uploading link parameter of the edge node of the ith iteration according to the edge node capability and the edge node resource of the ith iteration; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation;
judging whether the absolute value of the difference value between the downloading link parameter of the user terminal of the ith iteration and the uploading link parameter of the edge node is smaller than an absolute value threshold value or not, and obtaining a judgment result;
if the judgment result shows no, optimizing the edge calculation distribution result of the ith iteration, obtaining the edge calculation distribution result of the (i + 1) th iteration, increasing the value of i by 1, and returning to the step of calculating the user terminal resource and the edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration;
if the judgment result shows that the edge calculation distribution result of the ith iteration is the optimal distribution result, outputting the edge calculation distribution result of the ith iteration as the optimal distribution result;
the outputting the edge calculation distribution result of the ith iteration as an optimal distribution result further comprises:
calculating the user terminal resource of each user terminal according to the optimal distribution result to serve as the optimal user terminal resource of the user terminal;
and respectively comparing the optimal user terminal resource of each user terminal with the user terminal capacity, and updating the optimal user terminal resource of the user terminal into the user terminal capacity of the user terminal when the optimal user terminal resource of the user terminal is greater than the user terminal capacity.
2. The intelligent home-oriented edge computing bandwidth resource allocation method according to claim 1, wherein the step of computing user terminal resources of an ith iteration according to an edge computing allocation result of the ith iteration specifically comprises:
calculating distribution result according to the edge of the ith iteration by using a formula h m (i)=∑ g:g∈G(m) u gm (i) Calculating the user terminal resources of the task-intensive user terminal of the ith iteration;
calculating distribution result according to the edge of the ith iteration by using a formula h n (i)=∑ g:g∈G(n) u gn (i) Calculating the user terminal resource of the time delay sensitive user terminal of the ith iteration;
wherein h is m (i) And h n (i) The user terminal resources of the ith iteration task intensive user terminal and the delay sensitive user terminal are respectively, and g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is the task density in the edge calculation distribution result of the ith iterationThe type user terminal provides an edge node set of resources; g (n) is an edge node set for providing resources for the time delay sensitive user terminal in the edge calculation distribution result of the ith iteration; u. of gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the ith iteration; u. of gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
3. The intelligent home-oriented edge computing bandwidth resource allocation method according to claim 1, wherein the computing of the edge node resources of the ith iteration according to the edge computing allocation result of the ith iteration specifically comprises:
calculating distribution result according to the edge of the ith iteration by using a formula
Figure FDA0003750103640000021
Calculating edge node resources provided by the edge nodes to the task-intensive user terminal during the ith iteration;
calculating distribution result according to the edge of the ith iteration by using a formula
Figure FDA0003750103640000022
Calculating edge node resources provided by the edge nodes to the delay sensitive user terminal in the ith iteration;
wherein the content of the first and second substances,
Figure FDA0003750103640000023
and
Figure FDA0003750103640000024
respectively representing edge node resources provided by the edge node to the task-intensive user terminal and the delay-sensitive user terminal during the ith iteration, wherein g is the edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; m (g) is a set of task-intensive user terminals provided with resources by an edge node g; n (g) is funded by edge node gA source delay sensitive user terminal set; u. of gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the distribution result of the edge calculation of the ith iteration; u. of gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
4. The intelligent home-oriented edge computing bandwidth resource allocation method according to claim 1, wherein the calculating of the ith iteration user terminal download link parameters by using utility programs in the user terminals according to the ith iteration user terminal resources specifically comprises:
using the formula alpha m (i)=X m '(h m (i) Calculating the user terminal download link parameters of the ith iterative task-intensive user terminal;
using the formula alpha n (i)=X n '(h n (i) Calculating the user terminal download link parameters of the ith iterative time delay sensitive user terminal;
wherein alpha is m (i) And alpha n (i) Downloading link parameters, h, for the user terminals of the ith iteration task-intensive user terminal and the delay-sensitive user terminal, respectively m (i) And h n (i) User terminal resources, X, for the ith iteration of the task-intensive and delay-sensitive user terminals, respectively m '(h m (i) A task-intensive user terminal m for i iterations is obtaining a user terminal resource h m (i) Derivative of utility function in the latter utility program, X n '(h n (i) I iterations of delay-sensitive ue n obtaining ue resource h n (i) The derivative of the utility function in the latter utility program.
5. The intelligent home-oriented edge computing bandwidth resource allocation method according to claim 1, wherein the step of computing the edge node upload link parameters of the ith iteration according to the edge node capability and the edge node resources of the ith iteration specifically comprises the steps of:
using formulas
Figure FDA0003750103640000031
Calculating the link parameters uploaded by the edge nodes of the ith iteration and related to the task-intensive user terminal;
using formulas
Figure FDA0003750103640000032
Calculating the link parameters uploaded by the edge nodes of the ith iteration and related to the delay sensitive user terminal;
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003750103640000033
and
Figure FDA0003750103640000034
uploading link parameters for the edge nodes of the ith iteration with respect to the task-intensive user terminal and the delay-sensitive user terminal respectively,
Figure FDA0003750103640000035
and
Figure FDA0003750103640000036
uploading link parameters for the edge nodes of the i-1 st iteration related to the task-intensive user terminal and the delay-sensitive user terminal respectively,
Figure FDA0003750103640000037
edge node g is provided with the edge node capability of the resource to the task-intensive user terminals,
Figure FDA0003750103640000038
providing the edge node capability of resources for the edge node g to the time delay sensitive user terminal; gamma ray m An iteration step length of the link parameters uploaded by the edge node relative to the task-intensive user terminal; gamma ray n Uploading link parameters for edge nodes with respect to delay-sensitive user terminalsA number of iteration steps;
Figure FDA0003750103640000039
and
Figure FDA00037501036400000310
respectively representing the edge node resources provided by the edge node to the task-intensive user terminal and the delay-sensitive user terminal during the ith iteration.
6. The intelligent home-oriented edge computing bandwidth resource allocation method according to claim 1, wherein the optimizing the edge computing allocation result of the ith iteration to obtain the edge computing allocation result of the (i + 1) th iteration specifically comprises:
using formulas
Figure FDA0003750103640000041
Optimizing the resource quantity provided by the edge node of the ith iteration to the task-intensive user terminal to obtain the resource quantity provided by the edge node of the (i + 1) th iteration to the task-intensive user terminal;
using formulas
Figure FDA0003750103640000042
Optimizing the resource quantity provided by the edge node of the ith iteration to the task-intensive user terminal to obtain the resource quantity provided by the edge node of the (i + 1) th iteration to the delay-sensitive user terminal;
wherein u is gm (i) The resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result of the ith iteration; u. u gn (i) The resource quantity u provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration gm (i + 1) calculating the resource amount provided by the edge node g to the task-intensive user terminal m in the distribution result for the (i + 1) th iteration edge; u. of gn (i + 1) providing resource quantity of time delay sensitive user terminal n for edge node g in the edge calculation distribution result of the (i + 1) th iteration,k gm And kappa gn The iteration step length, alpha, of the edge node g with respect to the resource amount of the task-intensive user terminal m and the delay-sensitive user terminal n, respectively m (i) And alpha n (i) Respectively representing the download link parameters of the task-intensive user terminal m in the ith iteration and the download link parameters of the time-sensitive user terminal n in the ith iteration.
7. An edge computing bandwidth resource distribution system for smart home, the distribution system comprising:
the user terminal resource and edge node resource calculation module is used for calculating the user terminal resource and edge node resource of the ith iteration according to the edge calculation distribution result of the ith iteration; the user terminal resource is the resource quantity obtained by the user terminal, and the edge node resource is the resource quantity provided by the edge node;
the user terminal download link parameter calculation module is used for calculating the user terminal download link parameter of the ith iteration by utilizing a utility program in the user terminal according to the user terminal resource of the ith iteration;
the edge node uploading link parameter calculating module is used for calculating the edge node uploading link parameter of the ith iteration according to the edge node capability and the edge node resource of the ith iteration; the edge node capability provides the capability for the maximum resource of the edge node in the edge calculation;
the judging module is used for judging whether the absolute value of the difference value between the downloading link parameter of the user terminal of the ith iteration and the uploading link parameter of the edge node is smaller than an absolute value threshold value or not to obtain a judging result;
an edge calculation distribution result optimization module, configured to optimize an edge calculation distribution result of the ith iteration if the determination result indicates no, obtain an edge calculation distribution result of the (i + 1) th iteration, increase the value of i by 1, and return to the step "calculate user terminal resources and edge node resources of the ith iteration according to the edge calculation distribution result of the ith iteration";
the optimal distribution result output module is used for outputting the edge calculation distribution result of the ith iteration as the optimal distribution result if the judgment result indicates yes;
the dispensing system further comprises:
the optimal user terminal resource calculation module is used for calculating the user terminal resource of each user terminal according to the optimal distribution result and taking the user terminal resource as the optimal user terminal resource of the user terminal;
and the optimal user terminal resource updating module is used for respectively comparing the optimal user terminal resource of each user terminal with the user terminal capacity, and updating the optimal user terminal resource of the user terminal into the user terminal capacity of the user terminal when the optimal user terminal resource of the user terminal is greater than the user terminal capacity.
8. The intelligent home-oriented edge computing bandwidth resource allocation system according to claim 7, wherein the user terminal resource and edge node resource computing module specifically comprises:
a first user terminal resource calculation submodule for calculating distribution result according to the ith iteration edge and using formula h m (i)=∑ g:g∈G(m) u gm (i) Calculating the user terminal resource of the task-intensive user terminal of the ith iteration;
a second user terminal resource calculation submodule for calculating distribution result according to the ith iteration edge by using formula h n (i)=∑ g:g∈G(n) u gn (i) Calculating the user terminal resource of the time delay sensitive user terminal of the ith iteration;
wherein h is m (i) And h n (i) The user terminal resources of the ith iteration task intensive user terminal and the delay sensitive user terminal are respectively, and g is an edge node; m is a task-intensive user terminal; n is a time delay sensitive user terminal; g (m) is an edge node set for providing resources for the task-intensive user terminal in the edge calculation distribution result of the ith iteration; g (n) is an edge node set for providing resources for the time delay sensitive user terminal in the edge calculation distribution result of the ith iteration; u. of gm (i) For the i-th iterationThe resource amount provided by the edge node g to the task-intensive user terminal m in the edge calculation distribution result; u. of gn (i) And providing the resource quantity provided by the edge node g to the time delay sensitive user terminal n in the edge calculation distribution result of the ith iteration.
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