CN114500296B - Communication, storage and computing resource unified characterization method based on function expansion diagram - Google Patents

Communication, storage and computing resource unified characterization method based on function expansion diagram Download PDF

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CN114500296B
CN114500296B CN202210087697.5A CN202210087697A CN114500296B CN 114500296 B CN114500296 B CN 114500296B CN 202210087697 A CN202210087697 A CN 202210087697A CN 114500296 B CN114500296 B CN 114500296B
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刘伟
杨惠婷
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Xidian University
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Abstract

The invention discloses a unified characterization method of communication, storage and computing resources based on a function expansion diagram, which mainly solves the problem that the traditional time expansion diagram can not characterize the computing resources, and the realization scheme is as follows: initializing a characterization network parameter, dividing network nodes, and decomposing the network nodes according to the functions of the network nodes; dividing a planning period into T unequal time intervals; initializing a blank T-layer directed graph, and adding non-functional nodes, virtual sub-nodes and virtual computing nodes; adding a transmission link, a storage link and a virtual transmission link in the directed graph to form a function expansion graph; and setting communication capacity constraint, storage capacity constraint, calculation capacity constraint and flow conservation constraint, and converting the joint management problem of communication, storage and calculation resources into a data flow problem in a function expansion diagram. The invention can use the function expansion diagram to represent the time-varying property and the relativity of the resources in the network, and can be used for the unified analysis and management of communication, storage and computing resources in the time-varying network.

Description

基于功能扩展图的通信、存储和计算资源统一表征方法A Unified Representation Method for Communication, Storage and Computing Resources Based on Functional Expansion Graph

技术领域technical field

本发明属于信息技术领域，特别涉及一种基于功能扩展图的通信、存储和计算资源统一表征方法，可以用于公共交通、通信、供应链这些时变网络的通信、存储和计算资源分析与管理。The invention belongs to the field of information technology, and in particular relates to a unified characterization method for communication, storage and computing resources based on a function extension graph, which can be used for analysis and management of communication, storage and computing resources in time-varying networks such as public transportation, communication, and supply chains .

背景技术Background technique

为了建模网络拓扑对数据传输的影响，Fulkerson等人提出了时间扩展图，通过引入存储链路将离散的时间快照连接起来，从而实现网络节点的通信资源和存储资源的联合表征。时间扩展图被广泛应用于表征随时间变化的动态网络，比如，多商品问题，疏散计划问题，空间信息网络以及通信网络等。然而，网络节点除了拥有通信功能和存储功能外，还拥有其他的计算处理功能。比如，对于通信网络，其网络节点可能拥有图像处理功能，则流入该节点的原始图像可能被压缩处理成压缩图像从该节点流出；对于数据流问题，网络节点可能拥有处理功能，其将流入的原始材料处理后转化成产品，如将苹果处理成苹果汁，从该节点流出。然而，这种时间扩展图却无法表征在动态网络中节点的计算处理功能。In order to model the impact of network topology on data transmission, Fulkerson et al. proposed a time expansion graph, which connects discrete time snapshots by introducing storage links, so as to realize the joint representation of communication resources and storage resources of network nodes. Time-expanded graphs are widely used to represent dynamic networks that change over time, such as multi-commodity problems, evacuation planning problems, spatial information networks, and communication networks. However, in addition to communication and storage functions, network nodes also have other computing and processing functions. For example, for a communication network, its network nodes may have image processing functions, and the original images flowing into the node may be compressed and processed into compressed images to flow out of the node; for data flow problems, the network nodes may have processing functions, which will Raw materials are processed and converted into products, such as processing apples into apple juice, that flow out of this node. However, such time-expanded graphs cannot characterize the computational processing functions of nodes in dynamic networks.

例如，Huiting Yang的文章“Maximum flow routing strategy for spaceinformation network with service function constraints”中，提出采用时间扩展图表征时变的空间信息网络网络，其通过引入存储链路将离散的时间快照连接起来，从而实现网络节点的通信资源和存储资源的联合表征。但是，在空间信息网络中的节点，如卫星除了拥有通信功能和存储功能外，还拥有其他的计算处理功能，如图像压缩。而时间扩展图未能将空间信息网络节点相应的计算资源考虑在内，因而导致无法用于空间信息网络中的通信、存储和计算的联合规划。For example, in Huiting Yang's article "Maximum flow routing strategy for space information network with service function constraints", it is proposed to use a time expansion graph to represent a time-varying spatial information network network, which connects discrete time snapshots by introducing storage links, thereby Realize the joint representation of communication resources and storage resources of network nodes. However, in addition to communication and storage functions, nodes in the space information network, such as satellites, also have other computing and processing functions, such as image compression. However, the time-expanded graph fails to take into account the corresponding computing resources of the spatial information network nodes, so it cannot be used for the joint planning of communication, storage and computing in the spatial information network.

发明内容Contents of the invention

本发明的目的在于针对上述现有技术无法对通信、存储和计算资源联合表征的不足，提出一种基于功能扩展图的通信、存储和计算资源统一表征方法，以构成统一功能图模型，刻画不同资源间的承接转化关系，实现对时变网络中的通信、存储和计算资源的分析和管理。The purpose of the present invention is to solve the problem that the above-mentioned prior art cannot jointly represent communication, storage and computing resources, and propose a unified representation method for communication, storage and computing resources based on function extension graphs, so as to form a unified functional graph model and describe different The inheritance and transformation relationship between resources realizes the analysis and management of communication, storage and computing resources in time-varying networks.

为实现上述目的，本发明的技术方案包括如下：To achieve the above object, technical solutions of the present invention include as follows:

(1)初始化网络节点集合为

Figure BDA0003487692200000011
网络节点的个数为N；(1) Initialize the set of network nodes as
Figure BDA0003487692200000011
The number of network nodes is N;

(2)对网络节点进行划分，即将把网络中不能提供任务计算功能只起到通信和存储作用的节点分为非功能节点，将络中不仅能提供通信和存储功能还能提供计算功能的分为功能节点；根据此划分将网络节点集合

Figure BDA0003487692200000021
表示为：
Figure BDA0003487692200000022
其中
Figure BDA0003487692200000023
为非功能节点的集合，
Figure BDA0003487692200000024
为功能节点的集合，
Figure BDA0003487692200000025
表示第j个非功能节点，N1为非功能节点的个数，
Figure BDA0003487692200000026
表示第i个功能节点，N2为功能节点的个数，N＝N1+N2；(2) Divide the network nodes, that is, divide the nodes in the network that cannot provide task computing functions and only play the role of communication and storage into non-functional nodes, and divide the network nodes that can not only provide communication and storage functions but also provide computing functions. is a functional node; according to this division, the network nodes are aggregated
Figure BDA0003487692200000021
Expressed as:
Figure BDA0003487692200000022
in
Figure BDA0003487692200000023
is a collection of non-functional nodes,
Figure BDA0003487692200000024
is a collection of functional nodes,
Figure BDA0003487692200000025
Indicates the jth non-functional node, N 1 is the number of non-functional nodes,
Figure BDA0003487692200000026
Indicates the i-th function node, N 2 is the number of function nodes, N=N 1 +N 2 ;

(3)根据网络节点的功能对其进行分解：(3) Decompose the network nodes according to their functions:

若功能节点

Figure BDA0003487692200000027
能够提供Mi个计算功能，则将节点其分解为一个虚拟子节点vi和Mi个虚拟计算节点
Figure BDA0003487692200000028
以及两条虚拟传输链路
Figure BDA0003487692200000029
和
Figure BDA00034876922000000210
其中，Mi为功能节点
Figure BDA00034876922000000211
能够提供计算功能的总数，
Figure BDA00034876922000000212
表示的功能节点
Figure BDA00034876922000000213
分解的第m个虚拟计算节点，
Figure BDA00034876922000000214
表示的是从虚拟子节点vi到虚拟计算节点
Figure BDA00034876922000000215
的有向线段，
Figure BDA00034876922000000216
表示的是从虚拟计算节点
Figure BDA00034876922000000217
到虚拟子节点vi的有向线段，m∈[1,Mi]；If the function node
Figure BDA0003487692200000027
can provide M i computing functions, then decompose the node into a virtual child node v i and M i virtual computing nodes
Figure BDA0003487692200000028
and two virtual transmission links
Figure BDA0003487692200000029
and
Figure BDA00034876922000000210
Among them, M i is the function node
Figure BDA00034876922000000211
can provide the total number of computing functions,
Figure BDA00034876922000000212
Represents a function node
Figure BDA00034876922000000213
The mth virtual compute node of the decomposition,
Figure BDA00034876922000000214
Indicates from the virtual child node v i to the virtual computing node
Figure BDA00034876922000000215
The directed line segment of
Figure BDA00034876922000000216
Represents a slave virtual compute node
Figure BDA00034876922000000217
The directed line segment to the virtual child node v i , m∈[1,M i ];

(4)根据网络节点的连通性，将网络规划周期

Figure BDA00034876922000000218
划分为T个时间间隔
Figure BDA00034876922000000219
其中
Figure BDA00034876922000000220
且在时间间隔τq内网络拓扑保持不变，q∈[1,T]；(4) According to the connectivity of network nodes, the network planning cycle
Figure BDA00034876922000000218
Divided into T time intervals
Figure BDA00034876922000000219
in
Figure BDA00034876922000000220
And the network topology remains unchanged within the time interval τ q , q∈[1,T];

(5)构建功能扩展图：(5) Construct function expansion diagram:

(5a)初始化一张空白的T层有向图，其中第q层有向图的时间间隔为τq；(5a) Initialize a blank T-layer directed graph, wherein the time interval of the q-th layer directed graph is τ q ;

(5b)在有向图的每个时间间隔τq内分别添加网络中所有非功能节点、所有功能节点分解的虚拟子节点、所有功能节点分解的虚拟计算节点，构成功能节点图，并得到该功能节点图的三类节点集合：(5b) Add all non-functional nodes in the network, virtual child nodes decomposed by all functional nodes, and virtual computing nodes decomposed by all functional nodes in each time interval τ q of the directed graph to form a functional node graph, and obtain the Three types of node collections of functional node graphs:

Figure BDA00034876922000000221
Figure BDA00034876922000000221

Figure BDA00034876922000000222
Figure BDA00034876922000000222

Figure BDA00034876922000000223
Figure BDA00034876922000000223

其中，

Figure BDA00034876922000000224
为功能节点图的非功能节点集合，
Figure BDA00034876922000000225
为功能节点图的虚拟子节点集合，
Figure BDA00034876922000000226
为功能节点图的虚拟计算节点集合，
Figure BDA00034876922000000227
表示在时间间隔τq内网络非功能节点
Figure BDA00034876922000000228
的副本，
Figure BDA00034876922000000229
为虚拟子节点vi的副本，
Figure BDA00034876922000000230
表示在时间间隔τq内网络虚拟计算节点
Figure BDA00034876922000000231
的副本；in,
Figure BDA00034876922000000224
is the set of non-functional nodes of the functional node graph,
Figure BDA00034876922000000225
is the set of virtual child nodes of the functional node graph,
Figure BDA00034876922000000226
is a collection of virtual computing nodes in the functional node graph,
Figure BDA00034876922000000227
Indicates the non-functional nodes of the network within the time interval τ q
Figure BDA00034876922000000228
a copy of,
Figure BDA00034876922000000229
is a copy of the virtual child node v i ,
Figure BDA00034876922000000230
Indicates the network virtual computing node within the time interval τ q
Figure BDA00034876922000000231
a copy of;

(5c)在功能节点图中添加链路：(5c) Add links in the function node graph:

(5c1)根据节点的连通性添加传输链路：(5c1) Add transmission links according to the connectivity of nodes:

若在时间间隔τq内，网络中第j个非功能节点

Figure BDA0003487692200000031
能够给第k个非功能节点
Figure BDA0003487692200000032
传输数据，则在功能节点图中的第j个非功能节点
Figure BDA0003487692200000033
与第k个非功能节点
Figure BDA0003487692200000034
之间添加一条有向线段
Figure BDA0003487692200000035
If within the time interval τ q , the jth non-functional node in the network
Figure BDA0003487692200000031
able to give the kth non-functional node
Figure BDA0003487692200000032
To transmit data, the jth non-functional node in the functional node graph
Figure BDA0003487692200000033
with the kth non-functional node
Figure BDA0003487692200000034
Add a directed line segment between
Figure BDA0003487692200000035

若在时间间隔τq内，第j个非功能节点

Figure BDA0003487692200000036
能够给第i个功能节点
Figure BDA0003487692200000037
传输数据，则在功能节点图中的第j个非功能节点
Figure BDA0003487692200000038
与第i个虚拟子节点
Figure BDA0003487692200000039
之间添加一条有向线段
Figure BDA00034876922000000310
If within the time interval τ q , the jth non-functional node
Figure BDA0003487692200000036
can give the i-th function node
Figure BDA0003487692200000037
To transmit data, the jth non-functional node in the functional node graph
Figure BDA0003487692200000038
with the i-th virtual child node
Figure BDA0003487692200000039
Add a directed line segment between
Figure BDA00034876922000000310

若在时间间隔τq内，第i个功能节点

Figure BDA00034876922000000311
能够给第k个功能节点
Figure BDA00034876922000000312
传输数据，则在功能节点图中的第i个虚拟子节点
Figure BDA00034876922000000313
与第k个虚拟子节点
Figure BDA00034876922000000314
之间添加一条有向线段
Figure BDA00034876922000000315
If within the time interval τ q , the i-th functional node
Figure BDA00034876922000000311
Ability to give the kth functional node
Figure BDA00034876922000000312
To transmit data, the i-th virtual child node in the function node graph
Figure BDA00034876922000000313
with the kth virtual child node
Figure BDA00034876922000000314
Add a directed line segment between
Figure BDA00034876922000000315

若在时间间隔τq内，第i个功能节点

Figure BDA00034876922000000316
能够给第j个非功能节点
Figure BDA00034876922000000317
传输数据，则在功能节点图中第i个虚拟子节点
Figure BDA00034876922000000318
与第j个非功能节点
Figure BDA00034876922000000319
之间添加一条有向线段
Figure BDA00034876922000000320
If within the time interval τ q , the i-th functional node
Figure BDA00034876922000000316
able to give the jth non-functional node
Figure BDA00034876922000000317
To transmit data, the i-th virtual child node in the function node graph
Figure BDA00034876922000000318
with the jth non-functional node
Figure BDA00034876922000000319
Add a directed line segment between
Figure BDA00034876922000000320

(5c2)添加存储链路：(5c2) Add storage link:

在功能节点图每个非功能节点的相邻时间间隔之间添加一条从节点

Figure BDA00034876922000000321
到节点
Figure BDA00034876922000000322
的有向线段
Figure BDA00034876922000000323
Add a slave node between adjacent time intervals of each non-functional node in the functional node graph
Figure BDA00034876922000000321
to node
Figure BDA00034876922000000322
The directed segment of
Figure BDA00034876922000000323

在功能节点图每个虚拟子节点的相邻时间间隔之间添加一条从节点

Figure BDA00034876922000000324
到节点
Figure BDA00034876922000000325
的有向线段
Figure BDA00034876922000000326
Add a slave node between adjacent time intervals of each virtual child node in the function node graph
Figure BDA00034876922000000324
to node
Figure BDA00034876922000000325
The directed segment of
Figure BDA00034876922000000326

(5c3)添加虚拟传输链路：在功能节点图每个虚拟子节点

Figure BDA00034876922000000327
与其对应的虚拟子计算节点
Figure BDA00034876922000000328
之间添加两条有向线段
Figure BDA00034876922000000329
和
Figure BDA00034876922000000330
至此得到功能扩展图；(5c3) Add a virtual transmission link: each virtual child node in the function node graph
Figure BDA00034876922000000327
Its corresponding virtual child computing node
Figure BDA00034876922000000328
add two directed line segments between
Figure BDA00034876922000000329
and
Figure BDA00034876922000000330
So far, the function expansion diagram is obtained;

(6)设置通信容量约束、存储容量约束、计算容量约束和流量守恒约束：(6) Set communication capacity constraints, storage capacity constraints, computing capacity constraints and flow conservation constraints:

所述通信容量约束，是限定所有数据流在传输链路或虚拟传输链路上传输的数据量总和不能超过其传输链路或虚拟传输链路的通信容量；The communication capacity constraint is to limit the total amount of data transmitted by all data streams on the transmission link or the virtual transmission link to not exceed the communication capacity of the transmission link or the virtual transmission link;

所述存储容量约束，是限定所有数据流在存储链路上存储的数据量总和不能超过其存储链路的存储容量；The storage capacity constraint is to limit the sum of the amount of data stored on the storage link of all data streams to not exceed the storage capacity of its storage link;

所述计算容量约束，是限定数据流

Figure BDA00034876922000000331
流入虚拟计算节点
Figure BDA00034876922000000332
所消耗的计算容量不能超过虚拟计算节点
Figure BDA0003487692200000041
所提供的计算能力，其中
Figure BDA0003487692200000042
为即将接收计算功能
Figure BDA0003487692200000043
的数据流，
Figure BDA0003487692200000044
m∈[1,Mi]，
Figure BDA0003487692200000045
表示的是通过传输链路和存储链路流入功能扩展图中的虚拟子节点
Figure BDA0003487692200000046
的不同数据流的种类数；The computational capacity constraint is to limit the data flow
Figure BDA00034876922000000331
Flow into virtual compute nodes
Figure BDA00034876922000000332
The computing capacity consumed cannot exceed the virtual computing node
Figure BDA0003487692200000041
Computing power provided, where
Figure BDA0003487692200000042
Computational features for upcoming recipients
Figure BDA0003487692200000043
data flow,
Figure BDA0003487692200000044
m∈[1,M i ],
Figure BDA0003487692200000045
Indicates the virtual sub-nodes in the functional expansion diagram flowing through transmission links and storage links
Figure BDA0003487692200000046
The number of types of different data streams;

所述流量守恒约束，包括：限定每一种数据流流入非功能节点的数据量等于其流出非功能节点的数据量；限定每一种数据流流入虚拟子节点的数据量等于其流出虚拟子节点的数据量；限定即数据流

Figure BDA0003487692200000047
流入虚拟计算节点
Figure BDA0003487692200000048
的数据量乘于
Figure BDA0003487692200000049
等于数据流
Figure BDA00034876922000000410
流出虚拟计算节点
Figure BDA00034876922000000411
的数据量，其中，
Figure BDA00034876922000000412
为已接收计算功能
Figure BDA00034876922000000413
的数据流；The flow conservation constraint includes: limiting the amount of data that each data flow flows into a non-functional node to be equal to the amount of data that flows out of a non-functional node; limiting the amount of data that each data flow flows into a virtual child node to be equal to the amount of data that flows out of a virtual child node The amount of data; the limit is the data flow
Figure BDA0003487692200000047
Flow into virtual compute nodes
Figure BDA0003487692200000048
The amount of data multiplied by
Figure BDA0003487692200000049
equal to data flow
Figure BDA00034876922000000410
Outgoing Virtual Compute Node
Figure BDA00034876922000000411
The amount of data, where,
Figure BDA00034876922000000412
Calculate function for received
Figure BDA00034876922000000413
data flow;

(7)在上述设定的四个约束下，将通信、存储和计算资源联合管理问题转化为功能扩展图中的数据流问题，即用功能扩展图，统一表征随时间变化的动态网络通信、存储和计算资源。(7) Under the four constraints set above, the problem of joint management of communication, storage, and computing resources is transformed into a data flow problem in the function expansion graph, that is, the function expansion graph is used to uniformly represent the dynamic network communication that changes over time, storage and computing resources.

本发明与现有技术相比，具有如下优点：Compared with the prior art, the present invention has the following advantages:

1)本发明由于通过功能扩展图框架来统一表征通信、存储和计算能力，解决了传统的时间扩展图中无法表征一个节点内的多种计算功能的问题。具体而言，基于传统时间扩展图，对每个具有计算功能的节点进行虚拟分解为三个虚拟组件：子虚拟节点，虚拟计算节点和虚拟传输链路，其中子虚拟节点保持原始节点的通信和存储能力，而虚拟计算节点提供原始节点的计算能力，虚拟传输链路连接子虚拟节点和虚拟计算节点。同时本发明的功能扩展图能够表征在一个节点内的多个并行或多个连续的计算功能。1) The present invention solves the problem that the traditional time-expanded graph cannot represent various computing functions in a node because the communication, storage and computing capabilities are represented uniformly through the function-expanded graph framework. Specifically, based on the traditional time-expanded graph, each node with computing function is virtually decomposed into three virtual components: sub-virtual nodes, virtual computing nodes and virtual transmission links, where the sub-virtual nodes maintain the communication and Storage capacity, while the virtual computing node provides the computing power of the original node, and the virtual transmission link connects the child virtual node and the virtual computing node. At the same time, the function expansion diagram of the present invention can represent multiple parallel or multiple continuous computing functions in one node.

2)本发明由于在构造功能扩展图中，通过引入虚拟传输链路的方法解决传统时间扩展图中无法表征节点的计算功能单元处理数据过程的问题。本发明用功能扩展图中的传输链路、存储链路和虚拟传输链路表征时变网络中的通信、存储和计算资源，为联合通信、存储和计算资源提供了统一的表示，且功能扩展图中的不同链路之间的位置关系表征了不同资源间的承接转化关系。2) The present invention solves the problem of processing data by computing functional units that cannot represent nodes in traditional time-expanded diagrams by introducing virtual transmission links in constructing function-expanded diagrams. The present invention uses the transmission link, storage link and virtual transmission link in the function expansion diagram to represent the communication, storage and computing resources in the time-varying network, and provides a unified representation for the joint communication, storage and computing resources, and the function expansion The positional relationship between different links in the figure represents the succession and transformation relationship between different resources.

3)本发明由于在功能扩展图中设定了对数据流的通信容量约束、存储容量约束、计算容量约束和流量守恒约束，克服了对于一个具有多个并行计算功能或多个连续功能的节点，因数据流的类型和输入的数据流量与输出的数据流量的比例可能发生改变所造成难于量化流量守恒约束的问题，可通过功能扩展图，统一表征随时间变化的动态网络通信、存储和计算资源。3) The present invention overcomes the problem for a node with multiple parallel computing functions or multiple continuous functions due to setting communication capacity constraints, storage capacity constraints, computing capacity constraints and flow conservation constraints on the data flow in the function expansion diagram. , due to the possible changes in the type of data flow and the ratio of input data flow to output data flow, it is difficult to quantify the problem of flow conservation constraints. The function expansion diagram can be used to uniformly represent the dynamic network communication, storage and computing that changes over time resource.

附图说明Description of drawings

图1是本发明使用的场景示意图；Fig. 1 is a schematic diagram of a scene used in the present invention;

图2是本发明的实现总流程图；Fig. 2 is the realization overall flowchart of the present invention;

图3是本发明中在规划周期内网络的节点与节点之间的连通关系示意图；Fig. 3 is a schematic diagram of the connection relationship between nodes of the network in the planning period in the present invention;

图4是本发明中功能节点分解得到的不同节点和虚拟传输链路示意图；Fig. 4 is a schematic diagram of different nodes and virtual transmission links obtained by decomposing functional nodes in the present invention;

图5是本发明中初始化的空白有向图；Fig. 5 is a blank directed graph initialized in the present invention;

图6是本发明中构建的功能节点图。Fig. 6 is a functional node diagram constructed in the present invention.

图7是本发明中构建的功能扩展图。Fig. 7 is a function expansion diagram constructed in the present invention.

具体实施方式Detailed ways

以下结合附图和实例对本发明进行详细说明，实例仅用于说明本发明，并不构成对本发明的任何限制。The present invention will be described in detail below in conjunction with the accompanying drawings and examples. The examples are only used to illustrate the present invention and do not constitute any limitation to the present invention.

参照图1，本实例的网络场景由6个网络节点

Figure BDA0003487692200000051
组成，其中网络节点
Figure BDA0003487692200000052
和
Figure BDA0003487692200000053
这三个节点不能提供任务计算功能只起到通信和存储作用，而
Figure BDA0003487692200000054
和
Figure BDA0003487692200000055
这三个网络节点不仅能提供通信和存储功能还分别能够提供M1,M2和M3个计算功能。网络的规划周期为
Figure BDA0003487692200000056
在规划周期内节点与节点之间的连通性如图3所示，图3中每一个横纵坐标对应一对节点的连通关系，其中横坐标表示时间，纵坐标表示连通性，状态1表示连通，状态0表示断开。Referring to Figure 1, the network scenario of this example consists of 6 network nodes
Figure BDA0003487692200000051
consists of network nodes
Figure BDA0003487692200000052
and
Figure BDA0003487692200000053
These three nodes cannot provide task computing functions and only play the role of communication and storage, while
Figure BDA0003487692200000054
and
Figure BDA0003487692200000055
These three network nodes can not only provide communication and storage functions but also provide M 1 , M 2 and M 3 computing functions respectively. The planning cycle of the network is
Figure BDA0003487692200000056
The connectivity between nodes in the planning cycle is shown in Figure 3. In Figure 3, each abscissa and ordinate corresponds to the connectivity relationship of a pair of nodes, where the abscissa represents time, the ordinate represents connectivity, and state 1 represents connectivity , state 0 means disconnected.

参照图2，本实例在上述场景条件下的具体实现步骤如下：Referring to Figure 2, the specific implementation steps of this example under the above scenario conditions are as follows:

步骤1，初始化网络参数并对网络节点进行划分。Step 1, initialize network parameters and divide network nodes.

初始化网络节点的个数为N,N＝6，初始化网络节点集合为

Figure BDA0003487692200000057
即该集合由
Figure BDA0003487692200000058
六个网络节点组成，其中网络节点
Figure BDA0003487692200000059
和
Figure BDA00034876922000000510
这三个节点不能提供任务计算功能只起到通信和存储作用，而
Figure BDA00034876922000000511
和
Figure BDA00034876922000000512
这三个网络节点不仅能提供通信和存储功能还分别能够提供M1,M2和M3个计算功能。The number of initialized network nodes is N, N=6, and the set of initialized network nodes is
Figure BDA0003487692200000057
That is, the collection consists of
Figure BDA0003487692200000058
Composed of six network nodes, the network nodes
Figure BDA0003487692200000059
and
Figure BDA00034876922000000510
These three nodes cannot provide task computing functions and only play the role of communication and storage, while
Figure BDA00034876922000000511
and
Figure BDA00034876922000000512
These three network nodes can not only provide communication and storage functions but also provide M 1 , M 2 and M 3 computing functions respectively.

将把网络中不能提供任务计算功能只起到通信和存储作用的节点分为非功能节点，将络中不仅能提供通信和存储功能还能提供计算功能的分为功能节点；The nodes in the network that cannot provide task computing functions and only play the role of communication and storage will be divided into non-functional nodes, and those that can not only provide communication and storage functions but also computing functions in the network will be divided into functional nodes;

根据此划分将网络节点集合

Figure BDA00034876922000000513
表示为：
Figure BDA00034876922000000514
其中
Figure BDA00034876922000000515
为非功能节点的集合，
Figure BDA0003487692200000061
为功能节点的集合，
Figure BDA0003487692200000062
表示第j个非功能节点，j∈[1,N1]，N1＝3为非功能节点的个数，
Figure BDA0003487692200000063
表示第i个功能节点，i∈[1,N2]，N2＝3为功能节点的个数，N＝N1+N2。According to this division, the network nodes are aggregated
Figure BDA00034876922000000513
Expressed as:
Figure BDA00034876922000000514
in
Figure BDA00034876922000000515
is a collection of non-functional nodes,
Figure BDA0003487692200000061
is a collection of functional nodes,
Figure BDA0003487692200000062
Indicates the jth non-functional node, j∈[1,N 1 ], N 1 =3 is the number of non-functional nodes,
Figure BDA0003487692200000063
Indicates the i-th functional node, i∈[1,N 2 ], N 2 =3 is the number of functional nodes, N=N 1 +N 2 .

步骤2，根据网络节点的功能对其进行分解。Step 2, decompose the network nodes according to their functions.

若功能节点

Figure BDA00034876922000000640
能够提供Mi个计算功能，则将节点其分解为一个虚拟子节点vi和Mi个虚拟计算节点
Figure BDA0003487692200000064
以及两条虚拟传输链路
Figure BDA0003487692200000065
和
Figure BDA0003487692200000066
如图4所示，其中，Mi为功能节点
Figure BDA0003487692200000067
能够提供计算功能的总数，
Figure BDA0003487692200000068
表示的功能节点
Figure BDA0003487692200000069
分解的第m个虚拟计算节点，
Figure BDA00034876922000000610
表示的是从虚拟子节点vi到虚拟计算节点
Figure BDA00034876922000000611
的有向线段，
Figure BDA00034876922000000612
表示的是从虚拟计算节点
Figure BDA00034876922000000613
到虚拟子节点vi的有向线段，m∈[1,Mi]，虚拟子节点vi实现通信和存储功能，虚拟计算节点
Figure BDA00034876922000000614
实现计算功能
Figure BDA00034876922000000615
且数据流
Figure BDA00034876922000000616
流入虚拟计算节点
Figure BDA00034876922000000617
将被处理并被转化为新类型的数据流
Figure BDA00034876922000000618
从该虚拟计算节点
Figure BDA00034876922000000619
流出，其中，
Figure BDA00034876922000000620
为即将接收计算功能
Figure BDA00034876922000000621
的数据流，
Figure BDA00034876922000000622
为已接收计算功能
Figure BDA00034876922000000623
的数据流。If the function node
Figure BDA00034876922000000640
can provide M i computing functions, then decompose the node into a virtual child node v i and M i virtual computing nodes
Figure BDA0003487692200000064
and two virtual transmission links
Figure BDA0003487692200000065
and
Figure BDA0003487692200000066
As shown in Figure 4, where Mi is a function node
Figure BDA0003487692200000067
can provide the total number of computing functions,
Figure BDA0003487692200000068
Represents a function node
Figure BDA0003487692200000069
The mth virtual compute node of the decomposition,
Figure BDA00034876922000000610
Indicates from the virtual child node v i to the virtual computing node
Figure BDA00034876922000000611
The directed line segment of
Figure BDA00034876922000000612
Represents a slave virtual compute node
Figure BDA00034876922000000613
Directed line segment to virtual child node v i , m∈[1,M i ], virtual child node v i implements communication and storage functions, virtual computing node
Figure BDA00034876922000000614
Realize the calculation function
Figure BDA00034876922000000615
and data flow
Figure BDA00034876922000000616
Flow into virtual compute nodes
Figure BDA00034876922000000617
will be processed and transformed into a new type of data stream
Figure BDA00034876922000000618
From this virtual compute node
Figure BDA00034876922000000619
flow out of which,
Figure BDA00034876922000000620
Computational features for upcoming recipients
Figure BDA00034876922000000621
data flow,
Figure BDA00034876922000000622
Calculate function for received
Figure BDA00034876922000000623
data flow.

步骤3，根据网络节点的连通性，将网络规划周期划分为T个连续不均等的时间间隔。Step 3, according to the connectivity of the network nodes, divide the network planning cycle into T consecutive and unequal time intervals.

如图3所示，其包括三个时间间隔，即第一时间间隔τ1，第二时间间隔τ2，第三个时间间隔τ3，其中：As shown in Figure 3, it includes three time intervals, namely the first time interval τ 1 , the second time interval τ 2 , and the third time interval τ 3 , where:

第一时间间隔τ1内，第1个非功能节点

Figure BDA00034876922000000624
可以给第1个功能节点
Figure BDA00034876922000000625
传输数据，第1个功能节点
Figure BDA00034876922000000626
可以给第2个功能节点
Figure BDA00034876922000000627
传输数据，第2个非功能节点
Figure BDA00034876922000000628
可以给第3个非功能节点
Figure BDA00034876922000000629
传输数据；In the first time interval τ 1 , the first non-functional node
Figure BDA00034876922000000624
Can be given to the first function node
Figure BDA00034876922000000625
Transfer data, the first function node
Figure BDA00034876922000000626
Can be given to the second function node
Figure BDA00034876922000000627
Transmit data, 2nd non-functional node
Figure BDA00034876922000000628
Can give the 3rd non-functional node
Figure BDA00034876922000000629
transfer data;

第二个时间间隔τ2内，第1个非功能节点

Figure BDA00034876922000000630
可以给第1个功能节点
Figure BDA00034876922000000631
传输数据，第2个功能节点
Figure BDA00034876922000000632
可以给第3个功能节点
Figure BDA00034876922000000633
传输数据，第3个功能节点
Figure BDA00034876922000000634
可以给第2个非功能节点
Figure BDA00034876922000000635
传输数据；In the second time interval τ 2 , the first non-functional node
Figure BDA00034876922000000630
Can be given to the first function node
Figure BDA00034876922000000631
Transfer data, the second function node
Figure BDA00034876922000000632
Can give the third function node
Figure BDA00034876922000000633
Transfer data, the 3rd functional node
Figure BDA00034876922000000634
Can be given to the second non-functional node
Figure BDA00034876922000000635
transfer data;

第三个时间间隔τ3内，第1个功能节点

Figure BDA00034876922000000641
可以给第2个功能节点
Figure BDA00034876922000000636
传输数据，第2个功能节点
Figure BDA00034876922000000637
可以给第3个功能节点
Figure BDA00034876922000000638
传输数据，第3个功能节点
Figure BDA00034876922000000642
可以给第2个非功能节点
Figure BDA00034876922000000639
传输数据，第2个非功能节点
Figure BDA0003487692200000071
可以给第3个非功能节点
Figure BDA0003487692200000072
传输数据。In the third time interval τ 3 , the first function node
Figure BDA00034876922000000641
Can be given to the second function node
Figure BDA00034876922000000636
Transfer data, the second function node
Figure BDA00034876922000000637
Can give the third function node
Figure BDA00034876922000000638
Transfer data, the 3rd functional node
Figure BDA00034876922000000642
Can be given to the second non-functional node
Figure BDA00034876922000000639
Transmit data, 2nd non-functional node
Figure BDA0003487692200000071
Can give the 3rd non-functional node
Figure BDA0003487692200000072
transfer data.

根据上述6个网络节点的连通性，将网络规划周期

Figure BDA0003487692200000073
划分为3个时间间隔{τ1,τ2,τ3}，其中T＝3，τq＝[tq-1,tq)且在时间间隔τq内网络拓扑保持不变，q∈[1,T]。According to the connectivity of the above six network nodes, the network planning cycle
Figure BDA0003487692200000073
Divided into 3 time intervals {τ 1 ,τ 2 ,τ 3 }, where T=3, τ q =[t q-1 ,t q ) and the network topology remains unchanged in the time interval τ q , q∈[ 1,T].

步骤4，构建功能扩展图。Step 4, build the function expansion diagram.

4.1)初始化一张空白的T＝3层有向图，其中第q层有向图的时间间隔为τq，1≤q≤3，如图5所示；4.1) Initialize a blank T=3 layer directed graph, wherein the time interval of the qth layer directed graph is τ q , 1≤q≤3, as shown in Figure 5;

4.2)在有向图的每个时间间隔τq内分别添加网络中所有非功能节点、所有功能节点分解的虚拟子节点、所有功能节点分解的虚拟计算节点，构成功能节点图，如图6所示，其中：4.2) Add all non-functional nodes in the network, virtual child nodes decomposed by all functional nodes, and virtual computing nodes decomposed by all functional nodes in each time interval τ q of the directed graph to form a functional node graph, as shown in Figure 6 shown, where:

功能节点图的非功能节点集合为

Figure BDA0003487692200000074
即该集合由
Figure BDA0003487692200000075
九个非功能节点组成，如图6五边形节点所示，其中，
Figure BDA0003487692200000076
表示第j个网络非功能节点
Figure BDA0003487692200000077
在第q个时间间隔τq内的副本，1≤j≤N1，1≤q≤T，N1＝3，T＝3；The set of non-functional nodes in the functional node graph is
Figure BDA0003487692200000074
That is, the collection consists of
Figure BDA0003487692200000075
It consists of nine non-functional nodes, as shown in Figure 6 pentagonal nodes, where,
Figure BDA0003487692200000076
Indicates the jth network non-functional node
Figure BDA0003487692200000077
The replica within the qth time interval τ q , 1≤j≤N 1 , 1≤q≤T, N 1 =3, T=3;

功能节点图的虚拟子节点集合为

Figure BDA0003487692200000078
即该集合由
Figure BDA0003487692200000079
九个虚拟子节点组成，如图6圆节点所示，其中，
Figure BDA00034876922000000710
表示第i个网络虚拟子节点vi在第q个时间间隔τq内的副本，1≤i≤N2，1≤q≤T，N2＝3，T＝3；The set of virtual child nodes of the functional node graph is
Figure BDA0003487692200000078
That is, the collection consists of
Figure BDA0003487692200000079
It consists of nine virtual sub-nodes, as shown in the circle nodes in Figure 6, where,
Figure BDA00034876922000000710
Indicates the copy of the i-th network virtual child node v i in the q-th time interval τ q , 1≤i≤N 2 , 1≤q≤T, N 2 =3, T=3;

功能节点图的虚拟计算节点集合为

Figure BDA00034876922000000711
该集合由三个时间间隔内的虚拟计算节点组成，如图6长方型节点所示，即，The set of virtual computing nodes in the function node graph is
Figure BDA00034876922000000711
The set consists of virtual computing nodes in three time intervals, as shown in Figure 6 with rectangular nodes, namely,

在第一个时间间隔τ1内有

Figure BDA00034876922000000712
Figure BDA00034876922000000713
共M1+M2+M3个虚拟计算节点；In the first time interval τ 1 there are
Figure BDA00034876922000000712
Figure BDA00034876922000000713
A total of M 1 +M 2 +M 3 virtual computing nodes;

在第二个时间间隔τ2内有

Figure BDA00034876922000000714
Figure BDA00034876922000000715
共M1+M2+M3个虚拟计算节点；In the second time interval τ 2 there are
Figure BDA00034876922000000714
Figure BDA00034876922000000715
A total of M 1 +M 2 +M 3 virtual computing nodes;

在第三个时间间隔τ3内有

Figure BDA00034876922000000716
Figure BDA0003487692200000081
共M1+M2+M3个虚拟计算节点；其中，
Figure BDA0003487692200000082
表示第i个网络虚拟计算节点
Figure BDA0003487692200000083
在第q个时间间隔τq内的副本，1≤i≤N2，1≤m≤Mi，1≤q≤T，N2＝3，T＝3；In the third time interval τ 3 there are
Figure BDA00034876922000000716
Figure BDA0003487692200000081
A total of M 1 +M 2 +M 3 virtual computing nodes; among them,
Figure BDA0003487692200000082
Indicates the i-th network virtual computing node
Figure BDA0003487692200000083
The replica within the qth time interval τ q , 1≤i≤N 2 , 1≤m≤M i , 1≤q≤T, N 2 =3, T=3;

4.3)在功能节点图中添加链路，如图7所示：4.3) Add links in the function node graph, as shown in Figure 7:

4.3.1)根据节点的连通性添加传输链路，如图7的实线所示：4.3.1) Add transmission links according to the connectivity of nodes, as shown in the solid line in Figure 7:

若在时间间隔τq内，网络中第j个非功能节点

Figure BDA0003487692200000084
能够给第k个非功能节点
Figure BDA0003487692200000085
传输数据，则在功能节点图中的第j个非功能节点
Figure BDA0003487692200000086
与第k个非功能节点
Figure BDA0003487692200000087
之间添加一条有向线段
Figure BDA0003487692200000088
If within the time interval τ q , the jth non-functional node in the network
Figure BDA0003487692200000084
able to give the kth non-functional node
Figure BDA0003487692200000085
To transmit data, the jth non-functional node in the functional node graph
Figure BDA0003487692200000086
with the kth non-functional node
Figure BDA0003487692200000087
Add a directed line segment between
Figure BDA0003487692200000088

若在时间间隔τq内，第j个非功能节点

Figure BDA0003487692200000089
能够给第i个功能节点
Figure BDA00034876922000000810
传输数据，则在功能节点图中的第j个非功能节点
Figure BDA00034876922000000811
与第i个虚拟子节点
Figure BDA00034876922000000833
之间添加一条有向线段
Figure BDA00034876922000000812
If within the time interval τ q , the jth non-functional node
Figure BDA0003487692200000089
can give the i-th function node
Figure BDA00034876922000000810
To transmit data, the jth non-functional node in the functional node graph
Figure BDA00034876922000000811
with the i-th virtual child node
Figure BDA00034876922000000833
Add a directed line segment between
Figure BDA00034876922000000812

若在时间间隔τq内，第i个功能节点

Figure BDA00034876922000000813
能够给第k个功能节点
Figure BDA00034876922000000814
传输数据，则在功能节点图中的第i个虚拟子节点
Figure BDA00034876922000000815
与第k个虚拟子节点
Figure BDA00034876922000000816
之间添加一条有向线段
Figure BDA00034876922000000817
If within the time interval τ q , the i-th functional node
Figure BDA00034876922000000813
Ability to give the kth functional node
Figure BDA00034876922000000814
To transmit data, the i-th virtual child node in the function node graph
Figure BDA00034876922000000815
with the kth virtual child node
Figure BDA00034876922000000816
Add a directed line segment between
Figure BDA00034876922000000817

若在时间间隔τq内，第i个功能节点

Figure BDA00034876922000000818
能够给第j个非功能节点
Figure BDA00034876922000000819
传输数据，则在功能节点图中第i个虚拟子节点
Figure BDA00034876922000000820
与第j个非功能节点
Figure BDA00034876922000000821
之间添加一条有向线段
Figure BDA00034876922000000822
If within the time interval τ q , the i-th functional node
Figure BDA00034876922000000818
able to give the jth non-functional node
Figure BDA00034876922000000819
To transmit data, the i-th virtual child node in the function node graph
Figure BDA00034876922000000820
with the jth non-functional node
Figure BDA00034876922000000821
Add a directed line segment between
Figure BDA00034876922000000822

4.3.2)添加存储链路如，图7的虚线所示：4.3.2) Add a storage link as shown in the dotted line in Figure 7:

在功能节点图每个非功能节点的相邻时间间隔之间添加一条从第q个时间间隔的节点

Figure BDA00034876922000000823
到第q+1个时间间隔的节点
Figure BDA00034876922000000824
的有向线段
Figure BDA00034876922000000825
Add a node from the qth time interval between adjacent time intervals of each non-functional node in the functional node graph
Figure BDA00034876922000000823
to the node of the q+1th time interval
Figure BDA00034876922000000824
The directed segment of
Figure BDA00034876922000000825

在功能节点图每个虚拟子节点的相邻时间间隔之间添加一条从第q个时间间隔的节点

Figure BDA00034876922000000826
到第q个时间间隔的节点
Figure BDA00034876922000000827
的有向线段
Figure BDA00034876922000000828
Add a node from the qth time interval between adjacent time intervals of each virtual child node in the function node graph
Figure BDA00034876922000000826
to the node of the qth time interval
Figure BDA00034876922000000827
The directed segment of
Figure BDA00034876922000000828

4.3.3)添加虚拟传输链路：在功能节点图每个虚拟子节点

Figure BDA00034876922000000829
与其对应的虚拟子计算节点
Figure BDA00034876922000000830
之间添加两条有向线段
Figure BDA00034876922000000831
和
Figure BDA00034876922000000832
如图7的点虚线所示，至此得到如图7所示的功能扩展图。4.3.3) Add a virtual transmission link: each virtual child node in the function node graph
Figure BDA00034876922000000829
Its corresponding virtual child computing node
Figure BDA00034876922000000830
add two directed line segments between
Figure BDA00034876922000000831
and
Figure BDA00034876922000000832
As shown by the dotted line in FIG. 7 , the function expansion diagram shown in FIG. 7 is obtained so far.

步骤5，设置通信容量约束、存储容量约束、计算容量约束和流量守恒约束。Step 5, setting communication capacity constraints, storage capacity constraints, computing capacity constraints and flow conservation constraints.

5.1)设置通信容量约束，即限定所有数据流在传输链路或虚拟传输链路上传输的数据量总和不能超过其传输链路或虚拟传输链路的通信容量：5.1) Set communication capacity constraints, that is, limit the sum of the data volume transmitted by all data streams on the transmission link or virtual transmission link to not exceed the communication capacity of its transmission link or virtual transmission link:

5.1.1)对于传输链路，其通信容量约束所限定的所有数据流在传输链路上传输的数据量总和不能超过其传输链路的通信容量，公式表示如下：5.1.1) For a transmission link, the total amount of data transmitted by all data streams limited by its communication capacity constraints on the transmission link cannot exceed the communication capacity of its transmission link. The formula is expressed as follows:

Figure BDA0003487692200000091
Figure BDA0003487692200000091

Figure BDA0003487692200000092
Figure BDA0003487692200000092

Figure BDA0003487692200000093
Figure BDA0003487692200000093

Figure BDA0003487692200000094
Figure BDA0003487692200000094

其中，

Figure BDA0003487692200000095
表示从第j个非功能节点
Figure BDA0003487692200000096
到第k个非功能节点
Figure BDA0003487692200000097
的传输链路
Figure BDA0003487692200000098
上的数据流的种类数，
Figure BDA0003487692200000099
表示从第j个非功能节点
Figure BDA00034876922000000910
到第i个虚拟子节点
Figure BDA00034876922000000911
的传输链路
Figure BDA00034876922000000912
上的数据流的种类数，
Figure BDA00034876922000000913
表示从第i个虚拟子节点
Figure BDA00034876922000000914
到第k个虚拟子节点
Figure BDA00034876922000000915
的传输链路
Figure BDA00034876922000000916
上的数据流的种类数，
Figure BDA00034876922000000917
表示从第i个虚拟子节点
Figure BDA00034876922000000918
到第j个非功能节点
Figure BDA00034876922000000919
的传输链路
Figure BDA00034876922000000920
上的数据流的种类数，
Figure BDA00034876922000000921
Figure BDA00034876922000000922
和
Figure BDA00034876922000000923
分别表示数据流ξn在传输链路
Figure BDA00034876922000000924
Figure BDA00034876922000000925
和
Figure BDA00034876922000000926
上传输的数据量，
Figure BDA00034876922000000927
和
Figure BDA00034876922000000928
分别为传输链路
Figure BDA00034876922000000929
和
Figure BDA00034876922000000930
的通信容量，
Figure BDA00034876922000000931
为功能扩展图中传输链路的集合；in,
Figure BDA0003487692200000095
Indicates that starting from the jth non-functional node
Figure BDA0003487692200000096
to the kth non-functional node
Figure BDA0003487692200000097
transmission link
Figure BDA0003487692200000098
The number of types of data streams on
Figure BDA0003487692200000099
Indicates that starting from the jth non-functional node
Figure BDA00034876922000000910
to the i-th virtual child node
Figure BDA00034876922000000911
transmission link
Figure BDA00034876922000000912
The number of types of data streams on
Figure BDA00034876922000000913
Indicates that from the i-th virtual child node
Figure BDA00034876922000000914
to the kth virtual child node
Figure BDA00034876922000000915
transmission link
Figure BDA00034876922000000916
The number of types of data streams on
Figure BDA00034876922000000917
Indicates that from the i-th virtual child node
Figure BDA00034876922000000918
to the jth non-functional node
Figure BDA00034876922000000919
transmission link
Figure BDA00034876922000000920
The number of types of data streams on
Figure BDA00034876922000000921
Figure BDA00034876922000000922
and
Figure BDA00034876922000000923
Respectively represent the data flow ξ n in the transmission link
Figure BDA00034876922000000924
Figure BDA00034876922000000925
and
Figure BDA00034876922000000926
The amount of data transferred on,
Figure BDA00034876922000000927
and
Figure BDA00034876922000000928
transmission link
Figure BDA00034876922000000929
and
Figure BDA00034876922000000930
communication capacity,
Figure BDA00034876922000000931
is a collection of transmission links in the function expansion diagram;

5.1.2)对于虚拟传输链路，其通信容量约束中所限定的数据流在虚拟传输链路上传输的数据量总和不能超过其虚拟传输链路的通信容量，公式表示如下：5.1.2) For a virtual transmission link, the sum of the data volumes transmitted by the data flow defined in the communication capacity constraint on the virtual transmission link cannot exceed the communication capacity of the virtual transmission link. The formula is expressed as follows:

Figure BDA00034876922000000932
Figure BDA00034876922000000932

Figure BDA00034876922000000933
Figure BDA00034876922000000933

其中,

Figure BDA00034876922000000934
为数据流ξn在虚拟传输链路
Figure BDA00034876922000000935
上传输的数据量；in,
Figure BDA00034876922000000934
For the data flow ξ n in the virtual transmission link
Figure BDA00034876922000000935
the amount of data transferred;

Figure BDA00034876922000000936
为已接收计算功能转化而成的新类型的数据流ξn'在虚拟传输链路
Figure BDA0003487692200000101
上传输的数据量；
Figure BDA00034876922000000936
The new type of data stream ξ n ' transformed by the received computing function in the virtual transmission link
Figure BDA0003487692200000101
the amount of data transferred;

Figure BDA0003487692200000102
为数据流ξn在虚拟传输链路
Figure BDA0003487692200000103
的传输容量，其表示能够传输的最大数据量；
Figure BDA0003487692200000102
For the data flow ξ n in the virtual transmission link
Figure BDA0003487692200000103
The transmission capacity, which represents the maximum amount of data that can be transmitted;

Figure BDA0003487692200000104
为已接收计算功能转化而成的新类型的数据流ξn'在虚拟传输链路
Figure BDA0003487692200000105
的传输容量；
Figure BDA0003487692200000104
The new type of data stream ξ n ' transformed by the received computing function in the virtual transmission link
Figure BDA0003487692200000105
transmission capacity;

Figure BDA0003487692200000106
为功能扩展图中从虚拟子节点到虚拟计算节点的虚拟传输链路的集合；
Figure BDA0003487692200000106
is a collection of virtual transmission links from virtual child nodes to virtual computing nodes in the function expansion diagram;

Figure BDA0003487692200000107
为功能扩展图中从虚拟子计算节点到虚拟子节点的虚拟传输链路的集合。
Figure BDA0003487692200000107
is a collection of virtual transmission links from virtual sub-computing nodes to virtual sub-nodes in the function expansion diagram.

5.2)设置存储容量约束，即限定所有数据流在存储链路上存储的数据量总和不能超过其存储链路的存储容量，其公式表示如下：5.2) Set storage capacity constraints, that is, limit the sum of the data volumes stored in all data streams on storage links to not exceed the storage capacity of their storage links. The formula is expressed as follows:

Figure BDA0003487692200000108
Figure BDA0003487692200000108

Figure BDA0003487692200000109
Figure BDA0003487692200000109

其中，

Figure BDA00034876922000001010
和
Figure BDA00034876922000001011
分别表示数据流ξn在存储链路
Figure BDA00034876922000001012
和
Figure BDA00034876922000001013
上存储的数据量，
Figure BDA00034876922000001014
和
Figure BDA00034876922000001015
分别表示存储链路
Figure BDA00034876922000001016
和
Figure BDA00034876922000001017
的存储容量，
Figure BDA00034876922000001018
表示通过传输链路和存储链路流入功能扩展图中的第j个非功能节点
Figure BDA00034876922000001019
的不同数据流的种类数，
Figure BDA00034876922000001020
表示通过传输链路、存储链路和虚拟传输链路流入功能扩展图中的第i个虚拟子节点
Figure BDA00034876922000001021
的不同数据流的种类数，
Figure BDA00034876922000001022
为功能扩展图中存储链路的集合。in,
Figure BDA00034876922000001010
and
Figure BDA00034876922000001011
Respectively represent the data flow ξ n in the storage link
Figure BDA00034876922000001012
and
Figure BDA00034876922000001013
the amount of data stored on the
Figure BDA00034876922000001014
and
Figure BDA00034876922000001015
storage link
Figure BDA00034876922000001016
and
Figure BDA00034876922000001017
storage capacity,
Figure BDA00034876922000001018
Indicates the j-th non-functional node in the function expansion graph flowing through the transmission link and the storage link
Figure BDA00034876922000001019
The number of different types of data streams,
Figure BDA00034876922000001020
Indicates the i-th virtual child node in the function expansion diagram flowing through transmission links, storage links and virtual transmission links
Figure BDA00034876922000001021
The number of different types of data streams,
Figure BDA00034876922000001022
A collection of stored links in the function extension graph.

5.3)设置计算容量约束，即限定的即将接收计算功能

Figure BDA00034876922000001023
的数据流
Figure BDA00034876922000001024
流入虚拟计算节点
Figure BDA00034876922000001025
所消耗的计算容量不能超过虚拟计算节点
Figure BDA00034876922000001026
所提供的计算能力，其公式表示如下：5.3) Set the computing capacity constraint, that is, the limited receiving computing function
Figure BDA00034876922000001023
data flow
Figure BDA00034876922000001024
Flow into virtual compute nodes
Figure BDA00034876922000001025
The computing capacity consumed cannot exceed the virtual computing node
Figure BDA00034876922000001026
Provided computing power, its formula is expressed as follows:

Figure BDA0003487692200000111
Figure BDA0003487692200000111

其中，

Figure BDA0003487692200000112
为即将接收计算功能
Figure BDA0003487692200000113
的数据流，
Figure BDA0003487692200000114
为已接收计算功能
Figure BDA0003487692200000115
的数据流，
Figure BDA0003487692200000116
为数据流
Figure BDA0003487692200000117
在虚拟传输链路
Figure BDA0003487692200000118
上传输的数据量，
Figure BDA0003487692200000119
为计算因子，表示的是处理每单元的数据流
Figure BDA00034876922000001110
并转化为数据流
Figure BDA00034876922000001111
所需要消耗的计算能力，
Figure BDA00034876922000001112
表示的是虚拟计算节点
Figure BDA00034876922000001113
具有的计算能力。in,
Figure BDA0003487692200000112
Computational features for upcoming recipients
Figure BDA0003487692200000113
data flow,
Figure BDA0003487692200000114
Calculate function for received
Figure BDA0003487692200000115
data flow,
Figure BDA0003487692200000116
for data flow
Figure BDA0003487692200000117
in the virtual transmission link
Figure BDA0003487692200000118
The amount of data transferred on,
Figure BDA0003487692200000119
For the calculation factor, it means to process the data flow per unit
Figure BDA00034876922000001110
and convert it into a data stream
Figure BDA00034876922000001111
the computing power required to consume,
Figure BDA00034876922000001112
Represents a virtual compute node
Figure BDA00034876922000001113
have computing power.

5.4)设置流量守恒约束：5.4) Set flow conservation constraints:

此约束包括对非功能节点、虚拟子节点和虚拟计算节点这三个方面，具体实现如下：This constraint includes three aspects of non-functional nodes, virtual child nodes and virtual computing nodes. The specific implementation is as follows:

5.4.1)对于非功能节点，限定数据流ξn流入非功能节点的数据量等于其流出非功能节点的数据量，公式表示如下：5.4.1) For non-functional nodes, the amount of data flow ξ n flowing into non-functional nodes is equal to the amount of data flowing out of non-functional nodes, the formula is expressed as follows:

Figure BDA00034876922000001114
Figure BDA00034876922000001114

其中，

Figure BDA00034876922000001115
和
Figure BDA00034876922000001116
分别表示数据流ξn在传输链路
Figure BDA00034876922000001117
和
Figure BDA00034876922000001118
上传输的数据量，
Figure BDA00034876922000001119
和
Figure BDA00034876922000001120
分别表示数据流ξn在存储链路
Figure BDA00034876922000001121
和
Figure BDA00034876922000001122
上存储的数据量，
Figure BDA00034876922000001123
为通过传输链路和存储链路流入非功能节点
Figure BDA00034876922000001124
的不同数据流的集合，
Figure BDA00034876922000001125
为功能扩展图中传输链路的集合。in,
Figure BDA00034876922000001115
and
Figure BDA00034876922000001116
Respectively represent the data flow ξ n in the transmission link
Figure BDA00034876922000001117
and
Figure BDA00034876922000001118
The amount of data transferred on,
Figure BDA00034876922000001119
and
Figure BDA00034876922000001120
Respectively represent the data flow ξ n in the storage link
Figure BDA00034876922000001121
and
Figure BDA00034876922000001122
the amount of data stored on the
Figure BDA00034876922000001123
For inflow to non-functional nodes via transmission links and storage links
Figure BDA00034876922000001124
A collection of different data streams,
Figure BDA00034876922000001125
It is a collection of transmission links in the function expansion diagram.

5.4.2)对于虚拟子节点，限定数据流ξn流入虚拟子节点的数据量等于其流出虚拟子节点的数据量，公式表示如下：5.4.2) For a virtual child node, the amount of data flowing into the virtual child node of the limited data flow ξ n is equal to the amount of data flowing out of the virtual child node, and the formula is expressed as follows:

Figure BDA00034876922000001126
Figure BDA00034876922000001126

其中，

Figure BDA0003487692200000121
和
Figure BDA0003487692200000122
分别表示数据流ξn在传输链路
Figure BDA0003487692200000123
和
Figure BDA0003487692200000124
上传输的数据量，
Figure BDA0003487692200000125
和
Figure BDA0003487692200000126
分别表示数据流ξn在虚拟传输链路
Figure BDA0003487692200000127
和
Figure BDA0003487692200000128
上传输的数据量，
Figure BDA0003487692200000129
和
Figure BDA00034876922000001210
分别表示数据流ξn在存储链路
Figure BDA00034876922000001211
和
Figure BDA00034876922000001212
上存储的数据量，
Figure BDA00034876922000001213
为通过传输链路、存储链路和虚拟传输链路流入第i个虚拟子节点
Figure BDA00034876922000001214
的不同数据流的集合，
Figure BDA00034876922000001215
为功能扩展图中传输链路的集合；in,
Figure BDA0003487692200000121
and
Figure BDA0003487692200000122
Respectively represent the data flow ξ n in the transmission link
Figure BDA0003487692200000123
and
Figure BDA0003487692200000124
The amount of data transferred on,
Figure BDA0003487692200000125
and
Figure BDA0003487692200000126
Respectively represent the data flow ξ n in the virtual transmission link
Figure BDA0003487692200000127
and
Figure BDA0003487692200000128
The amount of data transferred on,
Figure BDA0003487692200000129
and
Figure BDA00034876922000001210
Respectively represent the data flow ξ n in the storage link
Figure BDA00034876922000001211
and
Figure BDA00034876922000001212
the amount of data stored on the
Figure BDA00034876922000001213
To flow into the i-th virtual child node through the transmission link, storage link and virtual transmission link
Figure BDA00034876922000001214
A collection of different data streams,
Figure BDA00034876922000001215
is a collection of transmission links in the function expansion diagram;

Figure BDA00034876922000001216
为功能扩展图中从虚拟子节点到虚拟计算节点的虚拟传输链路的集合；
Figure BDA00034876922000001216
is a collection of virtual transmission links from virtual child nodes to virtual computing nodes in the function expansion diagram;

Figure BDA00034876922000001217
为功能扩展图中从虚拟子计算节点到虚拟子节点的虚拟传输链路的集合。
Figure BDA00034876922000001217
is a collection of virtual transmission links from virtual sub-computing nodes to virtual sub-nodes in the function expansion diagram.

5.4.3)对于虚拟计算节点，限定数据流

Figure BDA00034876922000001218
流入虚拟计算节点
Figure BDA00034876922000001219
的数据量乘于
Figure BDA00034876922000001220
等于另一种类型的数据流
Figure BDA00034876922000001221
流出虚拟计算节点
Figure BDA00034876922000001222
的数据量，公式表示如下：5.4.3) For virtual computing nodes, limit data flow
Figure BDA00034876922000001218
Flow into virtual compute nodes
Figure BDA00034876922000001219
The amount of data multiplied by
Figure BDA00034876922000001220
equal to another type of data stream
Figure BDA00034876922000001221
Outgoing Virtual Compute Node
Figure BDA00034876922000001222
The amount of data, the formula is as follows:

Figure BDA00034876922000001223
Figure BDA00034876922000001223

其中，

Figure BDA00034876922000001224
为即将接收计算功能
Figure BDA00034876922000001225
的数据流，
Figure BDA00034876922000001226
为已接收计算功能
Figure BDA00034876922000001227
的数据流；in,
Figure BDA00034876922000001224
Computational features for upcoming recipients
Figure BDA00034876922000001225
data flow,
Figure BDA00034876922000001226
Calculate function for received
Figure BDA00034876922000001227
data flow;

Figure BDA00034876922000001228
为即将接收计算功能
Figure BDA00034876922000001229
的数据流
Figure BDA00034876922000001230
在虚拟传输链路
Figure BDA00034876922000001231
上传输的数据量；
Figure BDA00034876922000001228
Computational features for upcoming recipients
Figure BDA00034876922000001229
data flow
Figure BDA00034876922000001230
in the virtual transmission link
Figure BDA00034876922000001231
the amount of data transferred;

Figure BDA00034876922000001232
为已接收计算功能
Figure BDA00034876922000001233
的数据流
Figure BDA00034876922000001234
在虚拟传输链路
Figure BDA00034876922000001235
上传输的数据量；
Figure BDA00034876922000001232
Calculate function for received
Figure BDA00034876922000001233
data flow
Figure BDA00034876922000001234
in the virtual transmission link
Figure BDA00034876922000001235
the amount of data transferred;

Figure BDA00034876922000001236
表示的是即将接收计算功能
Figure BDA00034876922000001237
的数据流
Figure BDA00034876922000001238
与已接收计算功能
Figure BDA00034876922000001239
的数据流
Figure BDA00034876922000001240
之间的比例因子。
Figure BDA00034876922000001236
Indicates that the computing function is about to be received
Figure BDA00034876922000001237
data flow
Figure BDA00034876922000001238
with the received compute function
Figure BDA00034876922000001239
data flow
Figure BDA00034876922000001240
scale factor between.

步骤6，用功能扩展图统一表征通信、存储和计算资源。Step 6, use the function expansion diagram to represent communication, storage and computing resources in a unified manner.

由于功能扩展图中的传输链路、存储链路和虚拟传输链路分别表征了时变网络中的通信、存储和计算资源，且功能扩展图中的不同链路之间的位置关系表征了不同资源间的承接转化关系，同时由于在步骤5设定的四个约束下，可使功能扩展图中的数据流满足网络中的通信资源约束、存储资源约束、计算约束以及各种数据流之间的转化关系，因而能将通信、存储和计算资源联合管理问题转化为功能扩展图中的数据流问题，即用功能扩展图，统一表征随时间变化的动态网络通信、存储和计算资源。用该功能扩展图可以对时变网络的通信、存储和计算资源进行统一分析与管理。Since the transmission link, storage link and virtual transmission link in the function expansion diagram respectively represent the communication, storage and computing resources in the time-varying network, and the positional relationship between different links in the function expansion diagram represents different The inheritance and conversion relationship between resources, and because of the four constraints set in step 5, the data flow in the function expansion diagram can meet the communication resource constraints, storage resource constraints, computing constraints and various data flow constraints in the network. Therefore, the problem of joint management of communication, storage and computing resources can be transformed into a data flow problem in the function expansion diagram, that is, the function expansion diagram can be used to uniformly represent the dynamic network communication, storage and computing resources that change over time. Using this function expansion diagram, the communication, storage and computing resources of the time-varying network can be analyzed and managed in a unified manner.

以上描述仅是本发明的一个具体实例，显然对于本领域的专业人员来说，在了解了本发明内容和原理后，都可能在不背离本发明原理、结构的情况下，进行形式和细节上的各种修正和改变，但是这些基于本发明思想的修正和改变仍在本发明的权利要求保护范围之内。The above description is only a specific example of the present invention. Obviously, for those skilled in the art, after understanding the content and principle of the present invention, it is possible to carry out the form and details without departing from the principle and structure of the present invention. Various amendments and changes, but these amendments and changes based on the idea of the present invention are still within the protection scope of the claims of the present invention.

Claims (8)

1. A unified characterization method for communication, storage and computing resources based on a function expansion diagram is characterized by comprising the following steps:
(1) Initializing a set of network nodes to
Figure FDA0003997834590000011
The number of the network nodes is N;
(2) Dividing network nodes, namely dividing nodes which can not provide task computing function and only play communication and storage roles in a network into non-functional nodes, and dividing nodes which can not only provide communication and storage functions but also can provide computing function in the network into functional nodes; aggregating network nodes according to the partitioning
Figure FDA0003997834590000012
Expressed as:
Figure FDA0003997834590000013
wherein
Figure FDA0003997834590000014
Is a collection of non-functional nodes that,
Figure FDA0003997834590000015
in the form of a collection of functional nodes,
Figure FDA0003997834590000016
denotes the jth non-functional node, N 1 The number of non-functional nodes is,
Figure FDA0003997834590000017
denotes the ith functional node, N 2 For the number of functional nodes, N = N 1 +N 2 ；
(3) Decomposing the network nodes according to the functions of the network nodes:
if function node
Figure FDA0003997834590000018
Can provide M i A computing function, then decomposing the node into a virtual child node v i And M i A virtual computing node
Figure FDA0003997834590000019
And two virtual transmission links
Figure FDA00039978345900000110
And
Figure FDA00039978345900000111
wherein M is i As a functional node
Figure FDA00039978345900000112
The total number of calculation functions can be provided,
Figure FDA00039978345900000113
functional node of a representation
Figure FDA00039978345900000114
The mth virtual compute node of the decomposition,
Figure FDA00039978345900000115
representing a slave virtual child node v i To virtual computing node
Figure FDA00039978345900000116
The directional line segment of (a) is,
Figure FDA00039978345900000117
representing slave virtual computing nodes
Figure FDA00039978345900000118
To virtual child node v i Is directed line segment of (1), m is E [1,M i ]；
(4) Planning the network period according to the connectivity of the network node
Figure FDA00039978345900000119
Divided into T time intervals
Figure FDA00039978345900000120
Wherein tau is q ＝[t q-1 ,t q ) And at a time interval tau q The internal network topology remains unchanged, q ∈ [1,T ∈ [ ]]；
(5) Constructing a function expansion diagram:
(5a) Initializing a blank T-layer directed graph, wherein the time interval of the q-th layer directed graph is tau q ；
(5b) At each time interval τ of the directed graph q Adding all non-functional nodes, virtual sub-nodes decomposed by all functional nodes and virtual computing nodes decomposed by all functional nodes in the network respectively to form a functional node graph and obtain three types of node sets of the functional node graph:
Figure FDA00039978345900000121
Figure FDA00039978345900000122
Figure FDA0003997834590000021
wherein,
Figure FDA0003997834590000022
is a set of non-functional nodes of a functional node map,
Figure FDA0003997834590000023
is a set of virtual child nodes of the functional node map,
Figure FDA0003997834590000024
virtual meter for a functional node graphA set of the compute nodes is then selected,
Figure FDA0003997834590000025
is expressed in time interval tau q Non-functional node of internal network
Figure FDA0003997834590000026
A copy of (a) is made of,
Figure FDA0003997834590000027
for a virtual sub-node v i A copy of (a) is made of,
Figure FDA0003997834590000028
is expressed in time interval tau q Intra-network virtual compute node
Figure FDA0003997834590000029
A copy of (1);
(5c) Adding links in the functional node graph:
(5c1) Adding a transmission link according to the connectivity of the node:
if at time interval τ q The jth non-functional node in the internal and external network
Figure FDA00039978345900000210
Can give the kth non-functional node
Figure FDA00039978345900000211
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure FDA00039978345900000212
And the kth non-functional node
Figure FDA00039978345900000213
Adding a directed line segment between
Figure FDA00039978345900000214
If at time interval τ q Inner, j th non-functional node
Figure FDA00039978345900000215
Can give the ith functional node
Figure FDA00039978345900000216
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure FDA00039978345900000217
And the ith virtual child node
Figure FDA00039978345900000218
Adding a directed line segment between
Figure FDA00039978345900000219
If at time interval τ q Inner, i-th function node
Figure FDA00039978345900000220
Can give the kth function node
Figure FDA00039978345900000221
When data is transmitted, the ith virtual child node in the functional node diagram
Figure FDA00039978345900000222
And the kth virtual child node
Figure FDA00039978345900000223
Adding a directed line segment between
Figure FDA00039978345900000224
If at time interval τ q Inner, i-th function node
Figure FDA00039978345900000225
Can give the jth non-functional node
Figure FDA00039978345900000226
When data is transmitted, the ith virtual child node in the functional node diagram
Figure FDA00039978345900000227
And the jth non-functional node
Figure FDA00039978345900000228
Adding a directed line segment between
Figure FDA00039978345900000229
(5c2) Adding a storage link:
adding a slave node between adjacent time intervals of each non-functional node of the functional node map
Figure FDA00039978345900000230
To the node
Figure FDA00039978345900000231
Directed line segment of
Figure FDA00039978345900000232
Adding a slave node between adjacent time intervals of each virtual child node of the functional node graph
Figure FDA00039978345900000233
To node
Figure FDA00039978345900000234
Directed line segment of
Figure FDA00039978345900000235
(5c3) Adding a virtual transmission link: at each virtual child node of the functional node map
Figure FDA00039978345900000236
Virtual sub-computing node corresponding thereto
Figure FDA00039978345900000237
Adding two directed line segments in between
Figure FDA00039978345900000238
And
Figure FDA00039978345900000239
obtaining a function expansion diagram;
(6) Setting communication capacity constraint, storage capacity constraint, calculation capacity constraint and flow conservation constraint:
the communication capacity constraint is to limit the sum of the data quantity transmitted by all the data streams on the transmission link or the virtual transmission link not to exceed the communication capacity of the transmission link or the virtual transmission link;
the storage capacity constraint is to limit the sum of the data amount stored on the storage link of all the data streams to be not more than the storage capacity of the storage link;
the computing capacity constraint is to restrict the data flow
Figure FDA0003997834590000031
Streaming virtual compute nodes
Figure FDA0003997834590000032
The consumed computing capacity cannot exceed the virtual computing node
Figure FDA0003997834590000033
Provided computing power, wherein
Figure FDA0003997834590000034
To calculate the function for the upcoming reception
Figure FDA0003997834590000035
The data stream of (a) is transmitted,
Figure FDA0003997834590000036
Figure FDA0003997834590000037
Figure FDA0003997834590000038
showing the flow of the transport links and storage links into virtual child nodes in a function expansion graph
Figure FDA00039978345900000335
The number of types of different data streams;
the flow conservation constraint includes: defining the amount of data flowing into the non-functional node of each data stream to be equal to the amount of data flowing out of the non-functional node; defining the amount of data flowing into the virtual child node for each data stream to be equal to the amount of data flowing out of the virtual child node; qualifying instant data streams
Figure FDA0003997834590000039
Streaming virtual compute nodes
Figure FDA00039978345900000310
Is multiplied by the amount of data of
Figure FDA00039978345900000311
Equaling data streams
Figure FDA00039978345900000312
Egress virtual compute node
Figure FDA00039978345900000313
The amount of data of (a), wherein,
Figure FDA00039978345900000314
computing functions for received
Figure FDA00039978345900000315
The data stream of (2);
said defined data stream
Figure FDA00039978345900000316
Streaming virtual compute nodes
Figure FDA00039978345900000317
Is multiplied by the amount of data of
Figure FDA00039978345900000318
Equal to another type of data stream
Figure FDA00039978345900000319
Egress virtual compute node
Figure FDA00039978345900000320
The formula is as follows:
Figure FDA00039978345900000321
wherein,
Figure FDA00039978345900000322
to calculate the function for the upcoming reception
Figure FDA00039978345900000323
Of a data stream
Figure FDA00039978345900000324
In virtual transmission links
Figure FDA00039978345900000325
The amount of data transmitted;
Figure FDA00039978345900000326
computing functions for received
Figure FDA00039978345900000327
Of a data stream
Figure FDA00039978345900000328
In virtual transmission links
Figure FDA00039978345900000329
The amount of data transmitted;
Figure FDA00039978345900000330
indicating that a computing function is about to be received
Figure FDA00039978345900000331
Of a data stream
Figure FDA00039978345900000332
And received computing function
Figure FDA00039978345900000333
Of a data stream
Figure FDA00039978345900000334
A scaling factor in between;
(7) Under the four set constraints, the problem of joint management of communication, storage and computing resources is converted into a data flow problem in a function expansion diagram, namely the function expansion diagram is used for uniformly representing dynamic network communication, storage and computing resources changing along with time.
2. The method of claim 1, wherein the virtual child nodes and virtual compute nodes in (3), each implement different functions, namely:
virtual child node v i Communication and storage functions are realized;
virtual computing node
Figure FDA0003997834590000041
Implementing a computing function
Figure FDA0003997834590000042
And data flow
Figure FDA0003997834590000043
Streaming virtual compute nodes
Figure FDA0003997834590000044
Will be processed and converted into a new type of data stream
Figure FDA0003997834590000045
From the virtual computing node
Figure FDA0003997834590000046
And the water flows out, wherein,
Figure FDA0003997834590000047
to calculate the function for the upcoming reception
Figure FDA0003997834590000048
The data stream of (a) is transmitted,
Figure FDA0003997834590000049
for a received computing function
Figure FDA00039978345900000410
The data stream of (2).
3. The method of claim 1, wherein the sum of the data amounts transmitted on the transmission link for all the data streams defined by the communication capacity constraint in (6) cannot exceed the communication capacity of the transmission link, and the formula is as follows:
Figure FDA00039978345900000411
Figure FDA00039978345900000412
Figure FDA00039978345900000413
Figure FDA00039978345900000414
wherein,
Figure FDA00039978345900000415
representing slave non-functional nodes
Figure FDA00039978345900000416
To non-functional nodes
Figure FDA00039978345900000417
Is transmitted over a network
Figure FDA00039978345900000418
The number of types of data streams on the network,
Figure FDA00039978345900000419
representing slave non-functional nodes
Figure FDA00039978345900000420
To the virtual child node
Figure FDA00039978345900000421
Is transmitted over a network
Figure FDA00039978345900000422
The number of types of data streams on the network,
Figure FDA00039978345900000423
representing slave virtual child nodes
Figure FDA00039978345900000424
To the virtual child node
Figure FDA00039978345900000425
Is transmitted to
Figure FDA00039978345900000426
The number of types of data streams on the network,
Figure FDA00039978345900000427
representing slave virtual child nodes
Figure FDA00039978345900000428
To non-functional nodes
Figure FDA00039978345900000429
Is transmitted over a network
Figure FDA00039978345900000430
The number of types of data streams on the network,
Figure FDA00039978345900000431
and
Figure FDA00039978345900000432
are respectively provided withRepresenting a data stream xi n In a transmission link
Figure FDA00039978345900000433
Figure FDA00039978345900000434
And
Figure FDA00039978345900000435
the amount of data to be transmitted over the network,
Figure FDA00039978345900000436
and
Figure FDA00039978345900000437
are respectively transmission links
Figure FDA00039978345900000438
And
Figure FDA00039978345900000439
the communication capacity of the mobile communication terminal (c),
Figure FDA00039978345900000440
is a collection of transmission links in the function expansion diagram.
4. The method according to claim 1, wherein the sum of the data amount transmitted on the virtual transmission link for the data streams defined in the communication capacity constraint in (6) cannot exceed the communication capacity of the virtual transmission link, and the formula is as follows:
Figure FDA00039978345900000441
Figure FDA0003997834590000051
wherein,
Figure FDA0003997834590000052
as a stream xi n In virtual transmission links
Figure FDA0003997834590000053
The amount of data to be transmitted over the network,
Figure FDA0003997834590000054
data stream xi of new type converted for received computing function n ' in a virtual transmission link
Figure FDA0003997834590000055
The amount of data to be transmitted over the network,
Figure FDA0003997834590000056
as a stream xi n In virtual transmission links
Figure FDA0003997834590000057
A transmission capacity of (a), which represents the maximum amount of data that can be transmitted;
Figure FDA0003997834590000058
data stream xi of new type converted for received computing function n ' in a virtual transmission link
Figure FDA0003997834590000059
The transmission capacity of (a);
Figure FDA00039978345900000510
a set of virtual transmission links from the virtual child nodes to the virtual compute nodes in the function expansion graph;
Figure FDA00039978345900000511
is a set of virtual transmission links from a virtual child compute node to a virtual child node in a functional expansion graph.
5. The method of claim 1, wherein the sum of the amounts of data stored on the storage links for all data streams defined in (6) under the storage capacity constraint cannot exceed the storage capacity of its storage link, and the formula is expressed as follows:
Figure FDA00039978345900000512
Figure FDA00039978345900000513
wherein,
Figure FDA00039978345900000514
and
Figure FDA00039978345900000515
respectively representing data streams xi n In a memory link
Figure FDA00039978345900000516
And
Figure FDA00039978345900000517
the amount of data stored on the memory device,
Figure FDA00039978345900000518
and
Figure FDA00039978345900000519
respectively representing memory links
Figure FDA00039978345900000520
And
Figure FDA00039978345900000521
the storage capacity of (a) of (b),
Figure FDA00039978345900000522
representing non-functional nodes flowing into a functional expansion graph over transport links and storage links
Figure FDA00039978345900000523
The number of types of different data streams of (2),
Figure FDA00039978345900000524
representing flow into a virtual child node in a function extension graph through transport links, storage links, and virtual transport links
Figure FDA00039978345900000525
The number of types of different data streams of (2),
Figure FDA0003997834590000061
the set of links is stored for the function expansion diagram.
6. The method of claim 1 wherein the receive-soon-to-compute function defined in (6) in the constraint on computing capacity
Figure FDA0003997834590000062
Data stream of
Figure FDA0003997834590000063
Streaming virtual compute nodes
Figure FDA0003997834590000064
The consumed computing capacity cannot exceed the virtual computing node
Figure FDA0003997834590000065
The computational power provided, the formula is as follows:
Figure FDA0003997834590000066
wherein,
Figure FDA0003997834590000067
to calculate the function for the upcoming reception
Figure FDA0003997834590000068
The data stream of (a) is transmitted,
Figure FDA0003997834590000069
computing functions for received
Figure FDA00039978345900000610
The data stream of (a) is transmitted,
Figure FDA00039978345900000611
as a stream of data
Figure FDA00039978345900000612
In virtual transmission links
Figure FDA00039978345900000613
The amount of data to be transmitted over the network,
Figure FDA00039978345900000614
for calculating the factor, what is indicated is that the data stream per unit is processed
Figure FDA00039978345900000615
And converted into a data stream
Figure FDA00039978345900000616
The amount of computing power that needs to be consumed,
Figure FDA00039978345900000617
representing virtual computing nodes
Figure FDA00039978345900000618
The computing power of the device.
7. The method of claim 1, wherein the data stream ξ as defined in the conservation of flow constraint in (6) n The amount of data flowing into a non-functional node is equal to the amount of data it flows out of the non-functional node, and the formula is as follows:
Figure FDA00039978345900000619
wherein,
Figure FDA00039978345900000620
and
Figure FDA00039978345900000621
respectively representing data streams xi n In a transmission link
Figure FDA00039978345900000622
And
Figure FDA00039978345900000623
the amount of data to be transmitted over the network,
Figure FDA00039978345900000624
and
Figure FDA00039978345900000625
respectively representing data streams xi n In a memory link
Figure FDA00039978345900000626
And
Figure FDA00039978345900000627
the amount of data stored on the memory device,
Figure FDA00039978345900000628
for streaming to non-functional nodes via transmission and storage links
Figure FDA00039978345900000629
Of the different data streams of (a) to (b),
Figure FDA00039978345900000630
the set of transmission links in the diagram is extended for functionality.
8. The method of claim 1, wherein the data stream ξ as defined in the conservation of flow constraint in (6) n The amount of data flowing into a virtual child is equal to the amount of data it flows out of the virtual child, and the formula is as follows:
Figure FDA0003997834590000071
wherein,
Figure FDA0003997834590000072
and
Figure FDA0003997834590000073
respectively representing data streams xi n In a transmission link
Figure FDA0003997834590000074
And
Figure FDA0003997834590000075
the amount of data to be transmitted over the network,
Figure FDA0003997834590000076
and
Figure FDA0003997834590000077
respectively representing data streams xi n In a virtual transmission link
Figure FDA0003997834590000078
And
Figure FDA0003997834590000079
the amount of data to be transmitted over the network,
Figure FDA00039978345900000710
and
Figure FDA00039978345900000711
respectively representing data streams xi n In a memory link
Figure FDA00039978345900000712
And
Figure FDA00039978345900000713
the amount of data stored on the memory device,
Figure FDA00039978345900000714
for streaming to virtual sub-nodes via transport links, storage links and virtual transport links
Figure FDA00039978345900000715
Of the different data streams of (a) to (b),
Figure FDA00039978345900000716
a set of transmission links in the function expansion diagram;
Figure FDA00039978345900000717
a set of virtual transmission links from the virtual child nodes to the virtual compute nodes in the function expansion graph;
Figure FDA00039978345900000718
is a set of virtual transmission links from a virtual child compute node to a virtual child node in a functional expansion graph.
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