CN114500296A - 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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CN114500296A
CN114500296A CN202210087697.5A CN202210087697A CN114500296A CN 114500296 A CN114500296 A CN 114500296A CN 202210087697 A CN202210087697 A CN 202210087697A CN 114500296 A CN114500296 A CN 114500296A
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CN114500296B (en
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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; 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

Communication, storage and computing resource unified characterization method based on function expansion diagram
Technical Field
The invention belongs to the technical field of information, and particularly relates to a communication, storage and computing resource unified characterization method based on a function expansion diagram, which can be used for communication, storage and computing resource analysis and management of time-varying networks such as public transport, communication and supply chains.
Background
In order to model the influence of network topology on data transmission, Fulkerson et al propose a time expansion diagram, and connect discrete time snapshots by introducing a storage link, thereby implementing joint characterization of communication resources and storage resources of network nodes. Time expansion maps are widely used to characterize dynamic networks that change over time, such as multi-commodity problems, evacuation planning problems, spatial information networks, and communication networks. However, the network node has other computing processing functions in addition to the communication function and the storage function. For example, for a communication network, a network node may have an image processing function, and an original image flowing into the node may be compressed into a compressed image and then flows out from the node; for data flow problems, a network node may have processing functionality that converts incoming raw material into product after processing, such as processing apples into apple juice, and flows out of the node. However, such time-expansion diagrams do not characterize the computational processing functions of the nodes in the dynamic network.
For example, in a "Maximum flow routing protocol for space information network with service function constraints" article by husting Yang, a time-varying spatial information network is represented by using a time expansion diagram, and discrete time snapshots are connected by introducing a storage link, so that joint representation of communication resources and storage resources of network nodes is realized. However, nodes in the spatial information network, such as satellites, have other computing processing functions, such as image compression, in addition to communication and storage functions. The time expansion graph cannot take the corresponding computing resources of the spatial information network nodes into account, and therefore cannot be used for joint planning of communication, storage and computation in the spatial information network.
Disclosure of Invention
The invention aims to provide a unified characterization method of communication, storage and computing resources based on a function expansion diagram aiming at the defect that the prior art cannot jointly characterize the communication, storage and computing resources, so as to form a unified function diagram model, describe the connection and transformation relation among different resources and realize the analysis and management of the communication, storage and computing resources in a time-varying network.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
(1) initializing a set of network nodes to
Figure BDA0003487692200000011
The number of the network nodes is N;
(2) dividing network nodes, namely dividing nodes which can not provide a task computing function and only play a role in communication and storage in a network into non-functional nodes, and dividing nodes which can not only provide the communication and storage functions but also provide the computing function in the network into functional nodes; aggregating network nodes according to the partitioning
Figure BDA0003487692200000021
Expressed as:
Figure BDA0003487692200000022
wherein
Figure BDA0003487692200000023
Is a collection of non-functional nodes that,
Figure BDA0003487692200000024
in the form of a collection of functional nodes,
Figure BDA0003487692200000025
denotes the jth non-functional node, N1The number of non-functional nodes is,
Figure BDA0003487692200000026
denotes the ith functional node, N2Is the number of functional nodes, N ═ N1+N2；
(3) Decomposing the network nodes according to the functions of the network nodes:
if function node
Figure BDA0003487692200000027
Can provide MiA computing function, then decomposing the node intoA virtual child node viAnd MiA virtual computing node
Figure BDA0003487692200000028
And two virtual transmission links
Figure BDA0003487692200000029
And
Figure BDA00034876922000000210
wherein M isiAs a functional node
Figure BDA00034876922000000211
The total number of computing functions can be provided,
Figure BDA00034876922000000212
functional node of a representation
Figure BDA00034876922000000213
The mth virtual compute node of the decomposition,
Figure BDA00034876922000000214
representing a slave virtual child node viTo virtual computing node
Figure BDA00034876922000000215
The directional line segment of (a) is,
Figure BDA00034876922000000216
representing slave virtual computing nodes
Figure BDA00034876922000000217
To virtual child node viIs directed line segment of (M ∈ [1, M)i]；
(4) Planning the network period according to the connectivity of the network node
Figure BDA00034876922000000218
Divided into T time intervals
Figure BDA00034876922000000219
Wherein
Figure BDA00034876922000000220
And at a time interval tauqThe internal network topology is kept unchanged, and q belongs to [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 tauq；
(5b) At each time interval τ of the directed graphqAdding 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 BDA00034876922000000221
Figure BDA00034876922000000222
Figure BDA00034876922000000223
wherein,
Figure BDA00034876922000000224
is a set of non-functional nodes of a functional node map,
Figure BDA00034876922000000225
is a set of virtual child nodes of the functional node map,
Figure BDA00034876922000000226
is a virtual compute node set of a functional node map,
Figure BDA00034876922000000227
is expressed in time interval tauqNon-functional node of internal network
Figure BDA00034876922000000228
A copy of (a) is made of,
Figure BDA00034876922000000229
for a virtual sub-node viA copy of (a) is made of,
Figure BDA00034876922000000230
is expressed in time interval tauqIntra-network virtual compute node
Figure BDA00034876922000000231
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 τqThe jth non-functional node in the internal and external network
Figure BDA0003487692200000031
Can give the kth non-functional node
Figure BDA0003487692200000032
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure BDA0003487692200000033
And the kth non-functional node
Figure BDA0003487692200000034
Adding a directed line segment between
Figure BDA0003487692200000035
If at time interval τqInner, j th non-functional node
Figure BDA0003487692200000036
Can give the ith functional node
Figure BDA0003487692200000037
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure BDA0003487692200000038
And the ith virtual child node
Figure BDA0003487692200000039
Adding a directed line segment between
Figure BDA00034876922000000310
If at time interval τqInner, i-th function node
Figure BDA00034876922000000311
Can give the kth function node
Figure BDA00034876922000000312
When data is transmitted, the ith virtual child node in the functional node diagram
Figure BDA00034876922000000313
And the kth virtual child node
Figure BDA00034876922000000314
Adding a directed line segment between
Figure BDA00034876922000000315
If at time interval τqInner, i-th function node
Figure BDA00034876922000000316
Can give the jth non-functional node
Figure BDA00034876922000000317
When data is transmitted, the ith virtual child node in the functional node diagram
Figure BDA00034876922000000318
And the jth non-functional node
Figure BDA00034876922000000319
Adding a directed line segment between
Figure BDA00034876922000000320
(5c2) Adding a storage link:
adding a slave node between adjacent time intervals of each non-functional node of the functional node map
Figure BDA00034876922000000321
To the node
Figure BDA00034876922000000322
Directed line segment of
Figure BDA00034876922000000323
Adding a slave node between adjacent time intervals of each virtual child node of the functional node graph
Figure BDA00034876922000000324
To the node
Figure BDA00034876922000000325
Directed line segment of
Figure BDA00034876922000000326
(5c3) Adding a virtual transmission link: at each virtual child node of the functional node map
Figure BDA00034876922000000327
Virtual sub-computing node corresponding thereto
Figure BDA00034876922000000328
Adding two directed line segments in between
Figure BDA00034876922000000329
And
Figure BDA00034876922000000330
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 amount 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 BDA00034876922000000331
Streaming virtual compute nodes
Figure BDA00034876922000000332
The consumed computing capacity cannot exceed the virtual computing node
Figure BDA0003487692200000041
Provided computing power, wherein
Figure BDA0003487692200000042
To calculate the function for the upcoming reception
Figure BDA0003487692200000043
The data stream of (a) is transmitted,
Figure BDA0003487692200000044
m∈[1,Mi]，
Figure BDA0003487692200000045
shown is a virtual flow into the functional expansion diagram through the transmission link and the storage linkPseudo child node
Figure BDA0003487692200000046
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 BDA0003487692200000047
Streaming virtual compute nodes
Figure BDA0003487692200000048
Is multiplied by the amount of data of
Figure BDA0003487692200000049
Equaling data streams
Figure BDA00034876922000000410
Egress virtual compute node
Figure BDA00034876922000000411
The amount of data of (a), wherein,
Figure BDA00034876922000000412
computing functions for received
Figure BDA00034876922000000413
The data stream of (2);
(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.
Compared with the prior art, the invention has the following advantages:
1) the invention uniformly represents communication, storage and computing capabilities through the function expansion diagram framework, thereby solving the problem that a plurality of computing functions in one node cannot be represented in the traditional time expansion diagram. Specifically, each node with a computing function is virtually decomposed into three virtual components based on a conventional time expansion graph: the system comprises a sub-virtual node, a virtual computing node and a virtual transmission link, wherein the sub-virtual node maintains the communication and storage capacity of the original node, the virtual computing node provides the computing capacity of the original node, and the virtual transmission link connects the sub-virtual node and the virtual computing node. Meanwhile, the function expansion diagram of the invention can represent a plurality of parallel or a plurality of continuous computing functions in one node.
2) In the invention, the problem that the data processing process of the computing function unit of the node cannot be represented in the traditional time expansion diagram is solved by introducing the virtual transmission link in the construction of the function expansion diagram. The invention uses the transmission link, the storage link and the virtual transmission link in the function expansion diagram to represent communication, storage and calculation resources in the time-varying network, provides a uniform representation for the joint communication, storage and calculation resources, and the position relationship among different links in the function expansion diagram represents the connection and transformation relationship among different resources.
3) The invention sets communication capacity constraint, storage capacity constraint, calculation capacity constraint and flow conservation constraint on data flow in the function expansion diagram, overcomes the problem that the flow conservation constraint is difficult to quantify caused by the possible change of the type of the data flow and the proportion of the input data flow and the output data flow for a node with a plurality of parallel calculation functions or a plurality of continuous functions, and can uniformly represent dynamic network communication, storage and calculation resources changing along with time through the function expansion diagram.
Drawings
FIG. 1 is a schematic view of a scenario in which the present invention is used;
FIG. 2 is a general flow chart of an implementation of the present invention;
FIG. 3 is a schematic diagram illustrating the connection relationship between nodes in a network during a planning period according to the present invention;
FIG. 4 is a schematic diagram of different nodes and virtual transmission links obtained by decomposing functional nodes in the present invention;
FIG. 5 is a blank directed graph initialized in the present invention;
FIG. 6 is a functional node diagram constructed in the present invention.
Fig. 7 is a function expansion diagram constructed in the present invention.
Detailed Description
The invention is described in detail below with reference to the drawings and examples, which are only for the purpose of illustrating the invention and do not constitute any limitation to the invention.
Referring to fig. 1, the network scenario of the present example consists of 6 network nodes
Figure BDA0003487692200000051
Are formed of network nodes
Figure BDA0003487692200000052
And
Figure BDA0003487692200000053
the three nodes can not provide task computing function and only play roles of communication and storage, but
Figure BDA0003487692200000054
And
Figure BDA0003487692200000055
the three network nodes can not only provide communication and storage functions, but also can respectively provide M1,M2And M3A computing function. The planning period of the network is
Figure BDA0003487692200000056
Connectivity between nodes in a planning period is shown in fig. 3, and each abscissa and ordinate in fig. 3 corresponds to a connection relationship between a pair of nodes, where the abscissa represents time, the ordinate represents connectivity, state 1 represents connection, and state 0 represents disconnection.
Referring to fig. 2, the specific implementation steps of the present example under the above scenario conditions are as follows:
step 1, initializing network parameters and dividing network nodes.
The number of the initialized network nodes is N, N is 6, and the initialized network nodes are aggregated into
Figure BDA0003487692200000057
I.e. the set is composed of
Figure BDA0003487692200000058
Six network nodes, wherein the network nodes
Figure BDA0003487692200000059
And
Figure BDA00034876922000000510
the three nodes can not provide task computing function and only play roles of communication and storage, but
Figure BDA00034876922000000511
And
Figure BDA00034876922000000512
the three network nodes can not only provide communication and storage functions, but also can respectively provide M1,M2And M3A computing function.
Dividing nodes which can not provide task computing function and only play communication and storage roles in the network into non-functional nodes, and dividing nodes which can not only provide communication and storage functions but also provide computing function in the network into functional nodes;
aggregating network nodes according to the partitioning
Figure BDA00034876922000000513
Expressed as:
Figure BDA00034876922000000514
wherein
Figure BDA00034876922000000515
Is a collection of non-functional nodes that,
Figure BDA0003487692200000061
in the form of a collection of functional nodes,
Figure BDA0003487692200000062
represents the jth nonfunctional node, j ∈ [1, N)1]，N 13 is the number of non-functional nodes,
Figure BDA0003487692200000063
represents the ith functional node, i ∈ [1, N2]，N 23 is the number of functional nodes, N is N1+N2。
And 2, decomposing the network nodes according to the functions of the network nodes.
If function node
Figure BDA00034876922000000640
Can provide MiA computing function, then decomposing the node into a virtual child node viAnd MiA virtual computing node
Figure BDA0003487692200000064
And two virtual transmission links
Figure BDA0003487692200000065
And
Figure BDA0003487692200000066
as shown in FIG. 4, wherein MiAs a functional node
Figure BDA0003487692200000067
The total number of computing functions can be provided,
Figure BDA0003487692200000068
functional node of a representation
Figure BDA0003487692200000069
The mth virtual compute node of the decomposition,
Figure BDA00034876922000000610
representing slave virtual child node viTo virtual computing node
Figure BDA00034876922000000611
The directional line segment of (a) is,
Figure BDA00034876922000000612
representing slave virtual computing nodes
Figure BDA00034876922000000613
To virtual child node viIs directed line segment of (M ∈ [1, M)i]Virtual child node viVirtual computing node implementing communication and storage functions
Figure BDA00034876922000000614
Implementing a computing function
Figure BDA00034876922000000615
And data flow
Figure BDA00034876922000000616
Streaming virtual compute nodes
Figure BDA00034876922000000617
Will be processed and converted into a new type of data stream
Figure BDA00034876922000000618
From the virtual computing node
Figure BDA00034876922000000619
And the water flows out, wherein,
Figure BDA00034876922000000620
to calculate the function for the upcoming reception
Figure BDA00034876922000000621
The data stream of (a) is transmitted,
Figure BDA00034876922000000622
computing functions for received
Figure BDA00034876922000000623
The data stream of (2).
And 3, dividing a network planning period into T continuous unequal time intervals according to the connectivity of the network nodes.
As shown in fig. 3, it comprises three time intervals, i.e. a first time interval τ1Second time interval τ2Third time interval τ3Wherein:
first time interval τ1Inner, 1 st non-functional node
Figure BDA00034876922000000624
Can give the 1 st functional node
Figure BDA00034876922000000625
Transmitting data, 1 st functional node
Figure BDA00034876922000000626
Can give the 2 nd functional node
Figure BDA00034876922000000627
Transmitting data, 2 nd non-functional node
Figure BDA00034876922000000628
Can give the 3 rd non-functional node
Figure BDA00034876922000000629
Transmitting data;
second time interval tau2Inner, 1 st non-functional node
Figure BDA00034876922000000630
Can give the 1 st functional node
Figure BDA00034876922000000631
Transmitting data, 2 ndFunction node
Figure BDA00034876922000000632
Can give the 3 rd function node
Figure BDA00034876922000000633
Transmitting data, 3 rd function node
Figure BDA00034876922000000634
Can give the 2 nd non-functional node
Figure BDA00034876922000000635
Transmitting data;
third time interval τ3Inner, 1 st function node
Figure BDA00034876922000000641
Can give the 2 nd functional node
Figure BDA00034876922000000636
Transmitting data, 2 nd functional node
Figure BDA00034876922000000637
Can give the 3 rd function node
Figure BDA00034876922000000638
Transmitting data, 3 rd function node
Figure BDA00034876922000000642
Can give the 2 nd non-functional node
Figure BDA00034876922000000639
Transmitting data, 2 nd non-functional node
Figure BDA0003487692200000071
Can give the 3 rd non-functional node
Figure BDA0003487692200000072
And transmitting the data.
Planning the network period according to the connectivity of the 6 network nodes
Figure BDA0003487692200000073
Divided into 3 time intervals { tau1,τ2,τ3Where T is 3, τq＝[tq-1,tq) And at a time interval tauqThe internal network topology is kept unchanged, and q belongs to [1, T ]]。
And 4, constructing a function expansion diagram.
4.1) initializing a blank T-3 layer directed graph, wherein the time interval of the q-th layer directed graph is tauqQ is more than or equal to 1 and less than or equal to 3, as shown in figure 5;
4.2) at each time interval τ of the directed graphqAll non-functional nodes, all virtual sub-nodes decomposed by functional nodes, and all virtual computing nodes decomposed by functional nodes in the network are added to form a functional node diagram, as shown in fig. 6, where:
set of non-functional nodes of a functional node map as
Figure BDA0003487692200000074
I.e. the set is composed of
Figure BDA0003487692200000075
Nine non-functional nodes, as shown by the pentagonal nodes of fig. 6, wherein,
Figure BDA0003487692200000076
indicating the jth network non-functional node
Figure BDA0003487692200000077
At the qth time interval τqInner copy, j is more than or equal to 1 and less than or equal to N1，1≤q≤T，N1＝3，T＝3；
Set of virtual child nodes of functional node graph as
Figure BDA0003487692200000078
I.e. the set is composed of
Figure BDA0003487692200000079
Nine virtual child nodes, as shown by the circle node in fig. 6, wherein,
Figure BDA00034876922000000710
representing the ith network virtual child node viAt the qth time interval τqInner copy, i is more than or equal to 1 and less than or equal to N2，1≤q≤T，N2＝3，T＝3；
The virtual computing node set of the functional node graph is
Figure BDA00034876922000000711
The set consists of virtual compute nodes in three time intervals, as shown by the rectangle of nodes in fig. 6, i.e.,
at a first time interval tau1Therein is provided with
Figure BDA00034876922000000712
Figure BDA00034876922000000713
In total of M1+M2+M3A plurality of virtual compute nodes;
at a second time interval tau2Therein is provided with
Figure BDA00034876922000000714
Figure BDA00034876922000000715
In total of M1+M2+M3A plurality of virtual compute nodes;
at a third time interval tau3Therein is provided with
Figure BDA00034876922000000716
Figure BDA0003487692200000081
In total of M1+M2+M3A plurality of virtual compute nodes; wherein,
Figure BDA0003487692200000082
representing the ith network virtual compute node
Figure BDA0003487692200000083
At the qth time interval τqInner copy, i is more than or equal to 1 and less than or equal to N2，1≤m≤Mi，1≤q≤T，N2＝3，T＝3；
4.3) adding links in the functional node graph, as shown in FIG. 7:
4.3.1) adding transmission links according to connectivity of the node, as shown by the solid line in fig. 7:
if at time interval τqThe jth non-functional node in the internal and external network
Figure BDA0003487692200000084
Can give the kth non-functional node
Figure BDA0003487692200000085
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure BDA0003487692200000086
And the kth non-functional node
Figure BDA0003487692200000087
Adding a directed line segment between
Figure BDA0003487692200000088
If at time interval τqInner, j th non-functional node
Figure BDA0003487692200000089
Can give the ith functional node
Figure BDA00034876922000000810
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure BDA00034876922000000811
And the ith virtual child node
Figure BDA00034876922000000833
Adding a directed line segment between
Figure BDA00034876922000000812
If at time interval τqInner, i-th function node
Figure BDA00034876922000000813
Can give the kth function node
Figure BDA00034876922000000814
When data is transmitted, the ith virtual child node in the functional node diagram
Figure BDA00034876922000000815
And the kth virtual child node
Figure BDA00034876922000000816
Adding a directed line segment between
Figure BDA00034876922000000817
If at time interval τqInner, i-th function node
Figure BDA00034876922000000818
Can give the jth non-functional node
Figure BDA00034876922000000819
When data is transmitted, the ith virtual child node in the functional node diagram
Figure BDA00034876922000000820
And the jth non-functional node
Figure BDA00034876922000000821
Adding a directed line betweenSegment of
Figure BDA00034876922000000822
4.3.2) add storage links as shown by the dashed lines in FIG. 7:
adding a node from the q-th time interval between adjacent time intervals of each non-functional node of the functional node map
Figure BDA00034876922000000823
Node to the q +1 time interval
Figure BDA00034876922000000824
Directed line segment of
Figure BDA00034876922000000825
Adding a node from the q-th time interval between adjacent time intervals of each virtual child node of the functional node graph
Figure BDA00034876922000000826
Node to qth time interval
Figure BDA00034876922000000827
Directed line segment of
Figure BDA00034876922000000828
4.3.3) adding virtual transmission links: at each virtual child node of the functional node map
Figure BDA00034876922000000829
Virtual sub-computing node corresponding thereto
Figure BDA00034876922000000830
Adding two directed line segments in between
Figure BDA00034876922000000831
And
Figure BDA00034876922000000832
as shown by the dotted line of fig. 7, the function expansion diagram shown in fig. 7 is obtained.
And 5, setting a communication capacity constraint, a storage capacity constraint, a calculation capacity constraint and a flow conservation constraint.
5.1) setting a communication capacity constraint, namely limiting that the sum of the data amount transmitted by all data streams on a transmission link or a virtual transmission link cannot exceed the communication capacity of the transmission link or the virtual transmission link:
5.1.1) for a transmission link, the sum of the data amounts transmitted on the transmission link by all data streams defined by the communication capacity constraint of the transmission link cannot exceed the communication capacity of the transmission link, and the formula is as follows:
Figure BDA0003487692200000091
Figure BDA0003487692200000092
Figure BDA0003487692200000093
Figure BDA0003487692200000094
wherein,
Figure BDA0003487692200000095
representing a node from the jth non-function
Figure BDA0003487692200000096
To the kth non-functional node
Figure BDA0003487692200000097
Is transmitted over a network
Figure BDA0003487692200000098
The number of types of data streams on the network,
Figure BDA0003487692200000099
representing a node from the jth non-function
Figure BDA00034876922000000910
To the ith virtual child node
Figure BDA00034876922000000911
Is transmitted over a network
Figure BDA00034876922000000912
The number of types of data streams on the network,
Figure BDA00034876922000000913
representing the from the ith virtual child node
Figure BDA00034876922000000914
To the k-th virtual child node
Figure BDA00034876922000000915
Is transmitted over a network
Figure BDA00034876922000000916
The number of types of data streams on the network,
Figure BDA00034876922000000917
representing the from the ith virtual child node
Figure BDA00034876922000000918
To the jth non-functional node
Figure BDA00034876922000000919
Is transmitted over a network
Figure BDA00034876922000000920
The number of types of data streams on the network,
Figure BDA00034876922000000921
Figure BDA00034876922000000922
and
Figure BDA00034876922000000923
respectively representing data streams xinIn a transmission link
Figure BDA00034876922000000924
Figure BDA00034876922000000925
And
Figure BDA00034876922000000926
the amount of data to be transmitted over the network,
Figure BDA00034876922000000927
and
Figure BDA00034876922000000928
are respectively transmission links
Figure BDA00034876922000000929
And
Figure BDA00034876922000000930
the communication capacity of the mobile communication terminal (c),
Figure BDA00034876922000000931
a set of transmission links in the function expansion diagram;
5.1.2) for a virtual transmission link, the sum of the data amount transmitted on the virtual transmission link by the data flow defined in the restriction of the communication capacity of the virtual transmission link cannot exceed the communication capacity of the virtual transmission link, and the formula is as follows:
Figure BDA00034876922000000932
Figure BDA00034876922000000933
wherein,
Figure BDA00034876922000000934
as a stream xinIn virtual transmission links
Figure BDA00034876922000000935
The amount of data transmitted;
Figure BDA00034876922000000936
data stream xi of new type converted for received computing functionn' in a virtual transmission link
Figure BDA0003487692200000101
The amount of data transmitted;
Figure BDA0003487692200000102
as a stream xinIn virtual transmission links
Figure BDA0003487692200000103
A transmission capacity of (a), which represents the maximum amount of data that can be transmitted;
Figure BDA0003487692200000104
data stream xi of new type converted for received computing functionn' in a virtual transmission link
Figure BDA0003487692200000105
The transmission capacity of (a);
Figure BDA0003487692200000106
from virtual child nodes to virtual compute nodes in a function expansion diagramA set of virtual transmission links;
Figure BDA0003487692200000107
is a set of virtual transmission links from a virtual child compute node to a virtual child node in a functional expansion graph.
5.2) setting a storage capacity constraint, namely limiting the sum of the data quantity stored on the storage link of all data streams to be not more than the storage capacity of the storage link, wherein the formula is as follows:
Figure BDA0003487692200000108
Figure BDA0003487692200000109
wherein,
Figure BDA00034876922000001010
and
Figure BDA00034876922000001011
respectively representing data streams xinIn a memory link
Figure BDA00034876922000001012
And
Figure BDA00034876922000001013
the amount of data stored on the memory device,
Figure BDA00034876922000001014
and
Figure BDA00034876922000001015
respectively representing memory links
Figure BDA00034876922000001016
And
Figure BDA00034876922000001017
the storage capacity of (a) of (b),
Figure BDA00034876922000001018
representing a flow through a transmission link and a storage link into a jth non-functional node in a functional expansion graph
Figure BDA00034876922000001019
The number of types of different data streams of (2),
Figure BDA00034876922000001020
representing the flow through the transport link, storage link and virtual transport link into the ith virtual child node in the function expansion graph
Figure BDA00034876922000001021
The number of types of different data streams of (2),
Figure BDA00034876922000001022
the set of links is stored for the function expansion map.
5.3) setting the computation capacity constraint, i.e. the defined function of the incoming computation
Figure BDA00034876922000001023
Of a data stream
Figure BDA00034876922000001024
Streaming virtual compute nodes
Figure BDA00034876922000001025
The consumed computing capacity cannot exceed the virtual computing node
Figure BDA00034876922000001026
The computational power provided is formulated as follows:
Figure BDA0003487692200000111
wherein,
Figure BDA0003487692200000112
to calculate the function for the upcoming reception
Figure BDA0003487692200000113
The data stream of (a) is transmitted,
Figure BDA0003487692200000114
computing functions for received
Figure BDA0003487692200000115
The data stream of (a) is transmitted,
Figure BDA0003487692200000116
as a stream of data
Figure BDA0003487692200000117
In virtual transmission links
Figure BDA0003487692200000118
The amount of data to be transmitted over the network,
Figure BDA0003487692200000119
for calculating the factor, what is indicated is that the data stream per unit is processed
Figure BDA00034876922000001110
And converted into a data stream
Figure BDA00034876922000001111
The amount of computing power that needs to be consumed,
Figure BDA00034876922000001112
representing virtual computing nodes
Figure BDA00034876922000001113
The computing power of the device.
5.4) setting flow conservation constraint:
the constraint comprises three aspects of non-functional nodes, virtual child nodes and virtual computing nodes, and is specifically realized as follows:
5.4.1) for non-functional nodes, define data stream xinThe 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 BDA00034876922000001114
wherein,
Figure BDA00034876922000001115
and
Figure BDA00034876922000001116
respectively representing data streams xinIn a transmission link
Figure BDA00034876922000001117
And
Figure BDA00034876922000001118
the amount of data to be transmitted over the network,
Figure BDA00034876922000001119
and
Figure BDA00034876922000001120
respectively representing data streams xinIn a memory link
Figure BDA00034876922000001121
And
Figure BDA00034876922000001122
the amount of data stored on the memory device,
Figure BDA00034876922000001123
for streaming to non-functional nodes via transmission and storage links
Figure BDA00034876922000001124
Different data ofThe set of the streams is then selected,
Figure BDA00034876922000001125
is a collection of transmission links in the function expansion diagram.
5.4.2) for a virtual child node, define a data stream ξnThe 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 BDA00034876922000001126
wherein,
Figure BDA0003487692200000121
and
Figure BDA0003487692200000122
respectively representing data streams xinIn a transmission link
Figure BDA0003487692200000123
And
Figure BDA0003487692200000124
the amount of data to be transmitted over the network,
Figure BDA0003487692200000125
and
Figure BDA0003487692200000126
respectively representing data streams xinIn virtual transmission links
Figure BDA0003487692200000127
And
Figure BDA0003487692200000128
the amount of data to be transmitted over the network,
Figure BDA0003487692200000129
and
Figure BDA00034876922000001210
respectively representing data streams xinIn a memory link
Figure BDA00034876922000001211
And
Figure BDA00034876922000001212
the amount of data stored on the memory device,
Figure BDA00034876922000001213
for streaming into the ith virtual sub-node over a transport link, a storage link and a virtual transport link
Figure BDA00034876922000001214
Of the different data streams of (a) to (b),
Figure BDA00034876922000001215
a set of transmission links in the function expansion diagram;
Figure BDA00034876922000001216
a set of virtual transmission links from the virtual child nodes to the virtual compute nodes in the function expansion graph;
Figure BDA00034876922000001217
is a set of virtual transmission links from a virtual child compute node to a virtual child node in a functional expansion graph.
5.4.3) for virtual compute nodes, defining data flows
Figure BDA00034876922000001218
Streaming virtual compute nodes
Figure BDA00034876922000001219
Is multiplied by the amount of data of
Figure BDA00034876922000001220
Equal to another type of data stream
Figure BDA00034876922000001221
Egress virtual compute node
Figure BDA00034876922000001222
The formula is as follows:
Figure BDA00034876922000001223
wherein,
Figure BDA00034876922000001224
computing functions for imminent reception
Figure BDA00034876922000001225
The data stream of (a) is transmitted,
Figure BDA00034876922000001226
computing functions for received
Figure BDA00034876922000001227
The data stream of (a);
Figure BDA00034876922000001228
to calculate the function for the upcoming reception
Figure BDA00034876922000001229
Of a data stream
Figure BDA00034876922000001230
In virtual transmission links
Figure BDA00034876922000001231
The amount of data transmitted;
Figure BDA00034876922000001232
to be alreadyReceive computing functionality
Figure BDA00034876922000001233
Of a data stream
Figure BDA00034876922000001234
In a virtual transmission link
Figure BDA00034876922000001235
The amount of data transmitted;
Figure BDA00034876922000001236
indicating that a computing function is about to be received
Figure BDA00034876922000001237
Data stream of
Figure BDA00034876922000001238
And received computing function
Figure BDA00034876922000001239
Of a data stream
Figure BDA00034876922000001240
A scaling factor in between.
And 6, uniformly representing communication, storage and computing resources by using the function expansion diagram.
Because the transmission link, the storage link and the virtual transmission link in the function expansion diagram respectively represent communication, storage and calculation resources in the time-varying network, and the position relationship between different links in the function expansion diagram represents the bearing conversion relationship between different resources, and simultaneously, under the four constraints set in the step 5, the data stream in the function expansion diagram can meet the communication resource constraint, the storage resource constraint, the calculation constraint and the conversion relationship between various data streams in the network, so that the problem of joint management of the communication, storage and calculation resources can be converted into the problem of the data stream in the function expansion diagram, namely the problem of unified representation of dynamic network communication, storage and calculation resources changing along with time by using the function expansion diagram. The communication, storage and computing resources of the time-varying network can be uniformly analyzed and managed by using the function expansion diagram.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims (9)

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 FDA0003487692190000011
The number of the network nodes is N;
(2) dividing network nodes, namely dividing nodes which can not provide a task computing function and only play a role in communication and storage in a network into non-functional nodes, and dividing nodes which can not only provide the communication and storage functions but also provide the computing function in the network into functional nodes; aggregating network nodes according to the partitioning
Figure FDA0003487692190000012
Expressed as:
Figure FDA0003487692190000013
wherein
Figure FDA0003487692190000014
Is a collection of non-functional nodes that,
Figure FDA0003487692190000015
in the form of a collection of functional nodes,
Figure FDA0003487692190000016
denotes the jth non-functional node, N1The number of non-functional nodes is,
Figure FDA0003487692190000017
denotes the ith functional node, N2Is the number of functional nodes, N ═ N1+N2；
(3) Decomposing the network nodes according to the functions of the network nodes:
if function node
Figure FDA0003487692190000018
Can provide MiA computing function, then decomposing the node into a virtual child node viAnd MiA virtual computing node
Figure FDA0003487692190000019
And two virtual transmission links
Figure FDA00034876921900000110
And
Figure FDA00034876921900000111
wherein M isiAs a functional node
Figure FDA00034876921900000112
The total number of computing functions can be provided,
Figure FDA00034876921900000113
functional node of a representation
Figure FDA00034876921900000114
The mth virtual compute node of the decomposition,
Figure FDA00034876921900000115
representing a slave virtual child node viTo virtual computing node
Figure FDA00034876921900000116
The directional line segment of (a) is,
Figure FDA00034876921900000117
representing slave virtual computing nodes
Figure FDA00034876921900000118
To virtual child node viIs directed line segment of (M ∈ [1, M)i]；
(4) Planning the network period according to the connectivity of the network node
Figure FDA00034876921900000119
Divided into T time intervals
Figure FDA00034876921900000120
Wherein tau isq＝[tq-1,tq) And at a time interval tauqThe internal network topology is kept unchanged, and q belongs to [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 tauq；
(5b) At each time interval τ of the directed graphqAdding 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 FDA00034876921900000121
Figure FDA00034876921900000122
Figure FDA0003487692190000021
wherein,
Figure FDA0003487692190000022
is a set of non-functional nodes of a functional node map,
Figure FDA0003487692190000023
is a set of virtual child nodes of the functional node map,
Figure FDA0003487692190000024
is a virtual compute node set of a functional node map,
Figure FDA0003487692190000025
is expressed in time interval tauqNon-functional node of internal network
Figure FDA0003487692190000026
A copy of (a) is made of,
Figure FDA0003487692190000027
for a virtual sub-node viA copy of (a) is made of,
Figure FDA0003487692190000028
is expressed in time interval tauqIntra-network virtual compute node
Figure FDA0003487692190000029
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 τqThe jth non-functional node in the internal and external network
Figure FDA00034876921900000210
Can give the kth non-functional node
Figure FDA00034876921900000211
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure FDA00034876921900000212
And the kth non-functional node
Figure FDA00034876921900000213
Adding a directed line segment between
Figure FDA00034876921900000214
If at time interval τqInner, j th non-functional node
Figure FDA00034876921900000215
Can give the ith functional node
Figure FDA00034876921900000216
Transmitting data, and then transmitting the data in the jth non-functional node in the functional node diagram
Figure FDA00034876921900000217
And the ith virtual child node
Figure FDA00034876921900000218
Adding a directed line segment between
Figure FDA00034876921900000219
If at time interval τqInner, i-th function node
Figure FDA00034876921900000220
Can give the kth function node
Figure FDA00034876921900000221
When data is transmitted, the ith virtual child node in the functional node diagram
Figure FDA00034876921900000222
And the kth virtual child node
Figure FDA00034876921900000223
Adding a directed line segment between
Figure FDA00034876921900000224
If at time interval τqInner, i-th function node
Figure FDA00034876921900000225
Can give the jth non-functional node
Figure FDA00034876921900000226
When data is transmitted, the ith virtual child node in the functional node diagram
Figure FDA00034876921900000227
And the jth non-functional node
Figure FDA00034876921900000228
Adding a directed line segment between
Figure FDA00034876921900000229
(5c2) Adding a storage link:
adding a slave node between adjacent time intervals of each non-functional node of the functional node map
Figure FDA00034876921900000230
To the node
Figure FDA00034876921900000231
Directed line segment of
Figure FDA00034876921900000232
Adding a slave node between adjacent time intervals of each virtual child node of the functional node graph
Figure FDA00034876921900000233
To the node
Figure FDA00034876921900000234
Directed line segment of
Figure FDA00034876921900000235
(5c3) Adding a virtual transmission link: at each virtual child node of the functional node map
Figure FDA00034876921900000236
Virtual sub-computing node corresponding thereto
Figure FDA00034876921900000237
Adding two directed line segments in between
Figure FDA00034876921900000238
And
Figure FDA00034876921900000239
thus 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 amount 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 FDA0003487692190000031
Streaming virtual compute nodes
Figure FDA0003487692190000032
The consumed computing capacity cannot exceed the virtual computing node
Figure FDA0003487692190000033
Provided computing power, wherein
Figure FDA0003487692190000034
To calculate the function for the upcoming reception
Figure FDA0003487692190000035
The data stream of (a) is transmitted,
Figure FDA0003487692190000036
m∈[1,Mi]，
Figure FDA0003487692190000037
showing the flow through the transport and storage links into virtual child nodes in a functional expansion graph
Figure FDA0003487692190000038
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; constrained data stream
Figure FDA0003487692190000039
Streaming virtual compute nodes
Figure FDA00034876921900000310
Is multiplied by the amount of data of
Figure FDA00034876921900000311
Equaling data streams
Figure FDA00034876921900000312
Egress virtual compute node
Figure FDA00034876921900000313
The amount of data of (a), wherein,
Figure FDA00034876921900000314
computing functions for received
Figure FDA00034876921900000315
The data stream of (2);
(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 viCommunication and storage functions are realized;
virtual computing node
Figure FDA00034876921900000316
Implementing a computing function
Figure FDA00034876921900000317
And data flow
Figure FDA00034876921900000318
Streaming virtual compute nodes
Figure FDA00034876921900000319
Will be processed and converted into a new type of data stream
Figure FDA00034876921900000320
From the virtual computing node
Figure FDA00034876921900000321
And the water flows out, wherein,
Figure FDA00034876921900000322
to calculate the function for the upcoming reception
Figure FDA00034876921900000323
The data stream of (a) is transmitted,
Figure FDA00034876921900000324
to calculate functions for received
Figure FDA00034876921900000325
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 FDA00034876921900000326
Figure FDA00034876921900000327
Figure FDA0003487692190000041
Figure FDA0003487692190000042
wherein,
Figure FDA0003487692190000043
representing slave non-functional nodes
Figure FDA0003487692190000044
To non-functional nodes
Figure FDA0003487692190000045
Is transmitted over a network
Figure FDA0003487692190000046
The number of types of data streams on the network,
Figure FDA0003487692190000047
representing slave non-functional nodes
Figure FDA0003487692190000048
To the virtual child node
Figure FDA0003487692190000049
Is transmitted over a network
Figure FDA00034876921900000410
The number of types of data streams on the network,
Figure FDA00034876921900000411
representing slave virtual child nodes
Figure FDA00034876921900000412
To the virtual child node
Figure FDA00034876921900000413
Is transmitted over a network
Figure FDA00034876921900000414
The number of types of data streams on the network,
Figure FDA00034876921900000415
representing slave virtual child nodes
Figure FDA00034876921900000416
To non-functional nodes
Figure FDA00034876921900000417
Is transmitted to
Figure FDA00034876921900000418
The number of types of data streams on the network,
Figure FDA00034876921900000419
and
Figure FDA00034876921900000420
respectively representing data streams xinIn a transmission link
Figure FDA00034876921900000421
Figure FDA00034876921900000422
And
Figure FDA00034876921900000423
the amount of data to be transmitted over the network,
Figure FDA00034876921900000424
and
Figure FDA00034876921900000425
are respectively transmission links
Figure FDA00034876921900000426
And
Figure FDA00034876921900000427
the communication capacity of the mobile communication terminal (c),
Figure FDA00034876921900000428
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 FDA00034876921900000429
Figure FDA00034876921900000430
wherein,
Figure FDA00034876921900000431
as a stream xinIn virtual transmission links
Figure FDA00034876921900000432
The amount of data to be transmitted over the network,
Figure FDA00034876921900000433
data stream xi of new type converted for received computing functionn' in a virtual transmission link
Figure FDA00034876921900000434
The amount of data to be transmitted over the network,
Figure FDA00034876921900000435
as a stream xinIn virtual transmission links
Figure FDA00034876921900000436
A transmission capacity of (a), which represents the maximum amount of data that can be transmitted;
Figure FDA00034876921900000437
data stream xi of new type converted for received computing functionn' in a virtual transmission link
Figure FDA0003487692190000051
The transmission capacity of (a);
Figure FDA0003487692190000052
a set of virtual transmission links from the virtual child nodes to the virtual compute nodes in the function expansion graph;
Figure FDA0003487692190000053
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) in the storage capacity constraint cannot exceed the storage capacity of its storage link, and the formula is expressed as follows:
Figure FDA0003487692190000054
Figure FDA0003487692190000055
wherein,
Figure FDA0003487692190000056
and
Figure FDA0003487692190000057
respectively representing data streams xinIn a memory link
Figure FDA0003487692190000058
And
Figure FDA0003487692190000059
the amount of data stored on the memory device,
Figure FDA00034876921900000510
and
Figure FDA00034876921900000511
respectively representing memory links
Figure FDA00034876921900000512
And
Figure FDA00034876921900000513
the storage capacity of (a) of (b),
Figure FDA00034876921900000514
representing non-functional nodes flowing into a functional expansion graph over transport links and storage links
Figure FDA00034876921900000515
The number of types of different data streams of (2),
Figure FDA00034876921900000516
representing flow into a virtual child node in a function extension graph through transport links, storage links, and virtual transport links
Figure FDA00034876921900000517
The number of types of different data streams of (2),
Figure FDA00034876921900000518
the set of links is stored for the function expansion map.
6. The method of claim 1 wherein the receive-soon-to-compute function defined in (6) in the constraint on computing capacity
Figure FDA00034876921900000519
Of a data stream
Figure FDA00034876921900000520
Streaming virtual compute nodes
Figure FDA00034876921900000521
The consumed computing capacity cannot exceed the virtual computing node
Figure FDA00034876921900000522
The computational power provided, the formula is as follows:
Figure FDA00034876921900000523
wherein,
Figure FDA00034876921900000524
to calculate the function for the upcoming reception
Figure FDA00034876921900000525
Of a data stream，
Figure FDA00034876921900000526
Computing functions for received
Figure FDA00034876921900000527
The data stream of (a) is transmitted,
Figure FDA00034876921900000528
as a stream of data
Figure FDA00034876921900000529
In virtual transmission links
Figure FDA00034876921900000530
The amount of data to be transmitted over the network,
Figure FDA00034876921900000531
for calculating the factor, what is indicated is that the data stream per unit is processed
Figure FDA00034876921900000532
And converted into a data stream
Figure FDA00034876921900000533
The amount of computing power that needs to be consumed,
Figure FDA00034876921900000534
representing virtual computing nodes
Figure FDA0003487692190000061
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)nThe 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 FDA0003487692190000062
wherein,
Figure FDA0003487692190000063
and
Figure FDA0003487692190000064
respectively representing data streams xinIn a transmission link
Figure FDA0003487692190000065
And
Figure FDA0003487692190000066
the amount of data to be transmitted over the network,
Figure FDA0003487692190000067
and
Figure FDA0003487692190000068
respectively representing data streams xinIn a memory link
Figure FDA0003487692190000069
And
Figure FDA00034876921900000610
the amount of data stored on the memory device,
Figure FDA00034876921900000611
for streaming to non-functional nodes via transmission and storage links
Figure FDA00034876921900000612
Of the different data streams of (a) to (b),
Figure FDA00034876921900000613
is a collection of transmission links in the function expansion diagram.
8. The method of claim 1, wherein the data stream ξ as defined in the conservation of flow constraint in (6)nThe 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 FDA00034876921900000614
Figure FDA00034876921900000615
wherein,
Figure FDA00034876921900000616
and
Figure FDA00034876921900000617
respectively representing data streams xinIn a transmission link
Figure FDA00034876921900000618
And
Figure FDA00034876921900000619
the amount of data to be transmitted over the network,
Figure FDA00034876921900000620
and
Figure FDA00034876921900000621
respectively representing data streams xinIn virtual transmission links
Figure FDA00034876921900000622
And
Figure FDA00034876921900000623
the amount of data to be transmitted over the network,
Figure FDA00034876921900000624
and
Figure FDA00034876921900000625
respectively representing data streams xinIn a memory link
Figure FDA00034876921900000626
And
Figure FDA00034876921900000627
the amount of data stored on the memory device,
Figure FDA00034876921900000628
for streaming to virtual sub-nodes via transport links, storage links and virtual transport links
Figure FDA00034876921900000629
Of the different data streams of (a) to (b),
Figure FDA00034876921900000630
a set of transmission links in the function expansion diagram;
Figure FDA00034876921900000631
a set of virtual transmission links from the virtual child nodes to the virtual compute nodes in the function expansion graph;
Figure FDA0003487692190000071
is a set of virtual transmission links from a virtual child compute node to a virtual child node in a functional expansion graph.
9. The method of claim 1The method of (1), wherein the data stream defined in the conservation of flow constraint in (6)
Figure FDA0003487692190000072
Streaming virtual compute nodes
Figure FDA0003487692190000073
Is multiplied by the amount of data of
Figure FDA0003487692190000074
Equal to another type of data stream
Figure FDA0003487692190000075
Egress virtual compute node
Figure FDA0003487692190000076
The formula is as follows:
Figure FDA0003487692190000077
wherein,
Figure FDA0003487692190000078
to calculate the function for the upcoming reception
Figure FDA0003487692190000079
Of a data stream
Figure FDA00034876921900000710
In virtual transmission links
Figure FDA00034876921900000711
The amount of data transmitted;
Figure FDA00034876921900000712
for counting receivedComputing function
Figure FDA00034876921900000713
Of a data stream
Figure FDA00034876921900000714
In virtual transmission links
Figure FDA00034876921900000715
The amount of data transmitted;
Figure FDA00034876921900000716
indicating that a computing function is about to be received
Figure FDA00034876921900000717
Of a data stream
Figure FDA00034876921900000718
And received computing function
Figure FDA00034876921900000719
Of a data stream
Figure FDA00034876921900000720
A scaling factor in between.
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