CN109039706B - Fog wireless access network collaboration content deployment method based on graph theory - Google Patents

Fog wireless access network collaboration content deployment method based on graph theory Download PDF

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CN109039706B
CN109039706B CN201810717808.XA CN201810717808A CN109039706B CN 109039706 B CN109039706 B CN 109039706B CN 201810717808 A CN201810717808 A CN 201810717808A CN 109039706 B CN109039706 B CN 109039706B
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wireless access
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CN109039706A (en
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蒋雁翔
崔潇婷
郑福春
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Southeast University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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Abstract

The invention discloses a method for deploying cooperation contents of a fog wireless access network based on graph theory, which comprises the following steps: (1) cooperative caching according to access stratumThe cluster set is used for constructing a popular content set of each cooperative cache cluster and a popular content set of each non-cluster node; (2) constructing a connection edge set of the fog wireless nodes of the access layer according to the distance and the load difference between the fog wireless nodes and the affiliated cooperative cache cluster
Figure DDA0001717967540000011
(3) According to connected edge sets
Figure DDA0001717967540000012
Constructing access layer adjacency list set
Figure DDA0001717967540000013
(4) According to collections
Figure DDA0001717967540000014
Obtaining
Figure DDA0001717967540000015
Redundant content set corresponding to each edge in the content
Figure DDA0001717967540000016
(5) From redundant content sets
Figure DDA0001717967540000017
Computing
Figure DDA0001717967540000018
The cache decision correction indicating quantity of the redundant content corresponding to each edge; (6) calculating a cache decision correction indicating quantity of each cooperative cache cluster; (7) calculating a cache decision correction indicating quantity of each non-cluster fog wireless access node; (8) a final caching decision is calculated. The method and the device determine the caching decision of the F-AP in the fog wireless access network in a cooperative mode, and have low calculation complexity and higher total front-loading capacity.

Description

Fog wireless access network collaboration content deployment method based on graph theory
Technical Field
The invention relates to a content deployment method, in particular to a fog wireless access network collaborative content deployment method based on graph theory.
Background
As a novel system architecture of a 5G communication system, a Fog-Radio Access Network (F-RAN) has attracted wide attention in the field of communication with its great advantages in relieving forward congestion and reducing communication delay. A Fog-radio Access node F-AP (Fog-Access Point) in the F-RAN can cache popular content in advance at off-peak times, which is the key to achieving fronthaul offload. But the storage space of the F-AP is limited, and the content popularity distribution over the coverage area of the F-AP is more dispersed, and the edge cache performance gain of the F-RAN is thus greatly limited. The adjacent cooperative nodes are considered, the content is deployed in a cooperative mode, the content diversity is improved, the cache redundancy is eliminated, the locally acquired requested content is increased, and the cooperative cache can bring great help for further improving the performance gain of the 5G system.
The problem of cooperative content deployment is an NP-hard problem, a global optimal solution can be obtained by using a dynamic programming method, but the time complexity of the method is exponential time complexity. The approximate solution proposed in the past mainly converts the content deployment optimization problem into a monotone sub-model function optimization problem limited by pseudo-array constraint, and then proposes a greedy algorithm to solve the converted problem. When the method is applied, a complex calculation process is needed to evaluate the marginal value of the objective function, and the time complexity of the method is high-order polynomial time complexity related to the number of cache nodes and the size of the content library. Since the content library size is usually very large, in the fog wireless access network, the F-APs are distributed more densely, and therefore, it is necessary to provide a more efficient collaborative content deployment method.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a method for deploying the cooperative content of the fog wireless access network based on the graph theory.
The technical scheme is as follows: the invention discloses a method for deploying cooperation contents of a fog wireless access network based on graph theory, which comprises the following steps:
(1) according to the cooperative cache cluster set of the access layer, constructing the popular content set of each cooperative cache cluster n
Figure GDA0002885227770000011
And a popular content set for each non-clustered fog wireless access node i
Figure GDA0002885227770000012
N is 1, …, N, I is 1, …, I, N, I respectively represent the number of the cooperative cache cluster and the non-cluster fog wireless access nodes;
(2) constructing a connection edge set epsilon of the fog wireless nodes of the access layer according to the distance and the load difference between the fog wireless nodes and the cooperative cache cluster to which the fog wireless nodes belongr；
(3) According to the connection edge set epsilonrBuilding access layer adjacency list set
Figure GDA0002885227770000013
(4) According to access layer adjacency list set
Figure GDA0002885227770000021
Obtaining epsilonrRedundant content set corresponding to each edge in the content
Figure GDA0002885227770000022
(5) From redundant content sets
Figure GDA0002885227770000023
Calculating epsilonrThe cache decision correction indicating quantity of the redundant content corresponding to each edge;
(6) calculating a cache decision correction indicating quantity corresponding to each cooperative cache cluster n according to the updated popular content set of the cooperative cache clusters in the step (5);
(7) calculating a cache decision correction indicating quantity corresponding to each non-cluster fog wireless access node according to the cache decision correction indicating quantity obtained in the step (5);
(8) and (5) calculating a final cache decision according to the cache decision correction indicating quantity obtained in the steps (5) to (7).
Further, the step (1) specifically comprises:
(1.1) Aggregating access stratum fog wireless access points
Figure GDA0002885227770000024
The nodes in the cluster are divided into N cooperative cache clusters, and non-clustered fog wireless nodes form a non-cluster fog wireless node set
Figure GDA0002885227770000025
(1.2) selecting the nth cooperative cache cluster, and calculating the content library
Figure GDA0002885227770000026
Per content to a cooperative cache cluster nnfAnd according to the intra-cluster request probability pnfSorting in descending order by SnKmThe individual content serves as a popular content collection of a cooperative cache cluster n
Figure GDA0002885227770000027
Wherein the probability of requests p in a clusternfThe calculation formula of (A) is as follows:
Figure GDA0002885227770000028
in the formula (I), the compound is shown in the specification,
Figure GDA0002885227770000029
representing a set of fog wireless access nodes, p, comprised in a cooperative cache cluster nmfF-AP (radio access node) for representing fogmThe probability of a request for content f over the coverage area,
Figure GDA00028852277700000210
λmF-AP (radio access node) for representing fogmRequest arrival rate of SnRepresenting the number of misty wireless access nodes, K, in a cooperative cache cluster nmF-AP (radio access node) for representing fogmThe number of contents that can be cached;
(1.3) repeatedly executing other cooperative cache clusters according to the step (1.2) until a popular content set of each cooperative cache cluster is obtained;
(1.4) selecting the ith non-cluster fog wireless access node
Figure GDA00028852277700000211
Computing content library
Figure GDA00028852277700000212
For each non-cluster-fog wireless access node F-APiRequest probability p ofifAnd according to the request probability pifSorting in descending order, the first KiA set of most popular content
Figure GDA00028852277700000213
Wherein, KiF-AP (radio access node) for representing fogiThe number of contents that can be cached;
and (1.5) repeatedly executing other non-cluster-fog wireless access nodes according to the step (1.4) until the popular content set of each non-cluster-fog wireless access node is obtained.
Further, the step (2) specifically comprises:
(2.1) initializing the connected edge set εrIs an empty set;
(2.2) selecting a set of Access stratum fog wireless Access points
Figure GDA0002885227770000031
Middle mth node F-APmPerforming the following operations:
obtaining the m' th node F-APm'M', M ═ M + 1., M denotes the number of the fog wireless access points, and it is determined whether the following conditions are satisfied:
a、Dmm'≤γd，Lmm'≥γl(ii) a Wherein D ismm′＝||dm-dm′||2，dmAnd dm′Respectively represent fog wireless access nodes F-APmAnd F-APm'Coordinates in Euclidean space, Lmm′＝||λm-λm′||2，λmAnd λm′Respectively representing fog wireless accessNode F-APmAnd F-APm'Request arrival rate, gamma, over coverage areadThreshold, gamma, representing the distance between the fog radio access nodeslA threshold representing a load difference, | · | | non-conducting phosphor2Represents the L2 norm operator;
b. node F-APmAnd node F-APm'Not in the same cooperative cache cluster;
if conditions a and b are satisfied simultaneously, the edges (F-AP) will be connectedm,F-APm') Adding to the set εrPerforming the following steps;
(2.3) for fog Wireless Access Point set
Figure GDA0002885227770000032
And (5) repeatedly executing other nodes according to the step (2.2) until the fog wireless access point set is traversed
Figure GDA0002885227770000033
All the nodes are in the state of being in order to obtain the final connection edge set epsilonr。
Further, the step (3) specifically comprises:
(3.1) set of Wireless Access points to Access stratum fog
Figure GDA0002885227770000034
M-th node in (F-AP)mBuilding its neighbor list set
Figure GDA0002885227770000035
(3.2) eliminating the adjacent table sets with the element number of 1 from the adjacent table sets of all F-AP nodes, and sequencing the rest adjacent table sets in a descending order according to the element number in the sets to obtain sets
Figure GDA0002885227770000036
Wherein H is
Figure GDA0002885227770000037
The number of the elements in the Chinese character 'Zhongqin'.
Further, the step (4) specifically comprises:
(4.1) for adjacency list set
Figure GDA0002885227770000038
The k element of (1)
Figure GDA0002885227770000039
The following steps are carried out:
A. obtaining
Figure GDA00028852277700000310
J element of F-APk,jWith the first element F-APk,1The repeated popular content set corresponding to the connection edge e is obtained according to the following criteria
Figure GDA00028852277700000311
Figure GDA0002885227770000041
In the formula (I), the compound is shown in the specification,
Figure GDA0002885227770000042
representing a set of fog wireless access nodes included in the cooperative cache cluster n,
Figure GDA0002885227770000043
representing a non-clustered fog set of wireless nodes
Figure GDA0002885227770000044
Figure GDA0002885227770000045
Denotes F-APk,jJ2, …, Jk，JkTo represent
Figure GDA0002885227770000046
The number of middle elements;
B. for adjacency list set
Figure GDA0002885227770000047
Is repeatedly executed (4.1), thereby obtaining a repeated popular content set corresponding to each connecting edge
Figure GDA0002885227770000048
(4.2) for adjacency list set
Figure GDA0002885227770000049
The k element of (1)
Figure GDA00028852277700000410
The following steps are carried out:
for the
Figure GDA00028852277700000411
J element of F-APk,jInitialization of Kk,j＝KmK, where J is 1, …, Jk，JkTo represent
Figure GDA00028852277700000412
The number of medium elements, m represents a fog wireless access node F-APk,jIn the collection
Figure GDA00028852277700000413
The sequence number in (1), M belongs to { 1.,. M }, M denotes the number of the fog wireless access nodes, K denotes the number of the fog wireless access nodes, andk,jand KmAll represent fog wireless access node F-APk,jK represents the maximum available storage space size of the fog wireless access node;
(4.3) for adjacency list set
Figure GDA00028852277700000414
The k element of (1)
Figure GDA00028852277700000415
The following steps are carried out:
A. cumulative calculation
Figure GDA00028852277700000416
J element of F-APk,jWith the first element F-APk,1The intersection of the sets of repeated popular content corresponding to the connecting edges of
Figure GDA00028852277700000417
B. If it is
Figure GDA00028852277700000418
Then for the collection
Figure GDA00028852277700000419
J element of F-APk,jWith the first element F-APk,1E, from the set
Figure GDA00028852277700000420
In random selection of Kk,1The content forms a redundant content set corresponding to the edge e
Figure GDA00028852277700000421
And based on redundant content sets
Figure GDA00028852277700000422
Updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmAnd updating the connection F-APk,jE' ≠ e corresponding repeated popular content set
Figure GDA00028852277700000423
Wherein J is 2, …, Jk；
C. If it is
Figure GDA00028852277700000424
Then for the collection
Figure GDA00028852277700000425
J element of F-APk,jWith the first element F-APk,1E, from the set
Figure GDA00028852277700000426
In the random selection
Figure GDA00028852277700000427
Content, together with collections
Figure GDA00028852277700000428
All contents in (1) constitute a redundant content set corresponding to the edge e
Figure GDA00028852277700000429
And based on redundant content sets
Figure GDA00028852277700000430
Updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmAnd updating the connection F-APk,jE' ≠ e corresponding repeated popular content set
Figure GDA0002885227770000051
Wherein J is 2, …, Jk；
D. For adjacency list set
Figure GDA0002885227770000052
Repeat (4.3) to obtain a redundant content set corresponding to each connecting edge
Figure GDA0002885227770000053
Further, the step (5) specifically comprises:
(5.1) for adjacency list set
Figure GDA0002885227770000054
The k element of (1)
Figure GDA0002885227770000055
The following steps are carried out:
for the
Figure GDA0002885227770000056
J element of F-APk,jReset Kk,j＝KmK, where J is 1, …, Jk，JkTo represent
Figure GDA0002885227770000057
The number of medium elements, m represents a fog wireless access node F-APk,jIn the collection
Figure GDA0002885227770000058
The sequence number in (1), M belongs to { 1.,. M }, M denotes the number of the fog wireless access nodes, K denotes the number of the fog wireless access nodes, andk,jand KmAll represent fog wireless access node F-APk,jK represents the maximum available storage space size of the fog wireless access node;
(5.2) for adjacency list set
Figure GDA0002885227770000059
The k element of (1)
Figure GDA00028852277700000510
The following steps are carried out:
to the collection
Figure GDA00028852277700000511
Middle j element F-APk,jWith the first element F-APk,1Redundant content set corresponding to the connecting edge e of
Figure GDA00028852277700000512
The following four-step operation is performed, J is 2, …, and Jk，JkTo represent
Figure GDA00028852277700000513
The number of the medium elements is as follows:
is in the collection
Figure GDA00028852277700000514
Wherein the cache location is found in the F-APk,1The content of (1), the content of the part is not allowed to be cached in the F-APk,jTo avoid cache redundancy, the F-AP is switched onk,jCorresponding cache decision correction indicator Δ xk,j,fSet to-1, i.e.: Δ xk,j,f＝-1,
Figure GDA00028852277700000515
And to aggregate such content from collections
Figure GDA00028852277700000516
Wherein the cache decision correction indicator Δ xk,j,f1 indicates that the buffer location of the content F is in the F-APk,j；
② in the collection
Figure GDA00028852277700000517
Does not allow for finding a cache location in the F-APk,1The part of the content has to be cached in the F-APk,jThen F-AP is setk,jCorresponding cache decision correction indicator Δ xk,j,fSet to 1, namely: Δ xk,j.f＝1,
Figure GDA00028852277700000518
And is arranged at
Figure GDA00028852277700000519
When it is time to assemble these contents from the collection
Figure GDA00028852277700000520
Removing and updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmFrom the collection of these contents
Figure GDA00028852277700000521
Removing; wherein, the cache decision correction indication quantity Deltaxk,1,fCache location of presentation content F at-1 is not allowed at F-APk,1；
Respectively calculating the sets
Figure GDA0002885227770000061
In (3) caching in the F-APk,1Available fronthaul unload capacity
Figure GDA0002885227770000062
And will aggregate
Figure GDA0002885227770000063
In (3) caching in the F-APk,jAvailable fronthaul unload capacity
Figure GDA0002885227770000064
Wherein:
Figure GDA0002885227770000065
Figure GDA0002885227770000066
in the formula (II)
Figure GDA0002885227770000067
Represents all satiations (F-AP)m,F-APk，1)∈εrOr (F-AP)k，1,F-APm)∈εrFog wireless access node F-APmSet of constructs, set
Figure GDA0002885227770000068
Represents all satiations (F-AP)m,F-APk，j)∈εrOr (F-AP)k，j,F-APm)∈εrFog wireless access node F-APmSet of formations, λm'F-AP (radio access node) for representing fogm'Request arrival rate of (p)m'fF-AP (radio access node) for representing fogm'Probability of request for content f over the coverage area, L representing the size of each content;
fourthly if
Figure GDA0002885227770000069
Then set up
Figure GDA00028852277700000610
The remaining content is cached in the F-APk,1Higher forward unload capacity can be obtained, F-APk,1Setting the corresponding cache decision correction indication quantity to be 1, F-APk,jThe corresponding cache decision correction indication quantity is set to-1, namely: Δ xk,1.f＝1,Δxk,j.f＝-1,
Figure GDA00028852277700000611
And is arranged at
Figure GDA00028852277700000612
When it is time to assemble these contents from the collection
Figure GDA00028852277700000613
Removing and updating Kk,1Update the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to Km(ii) a If it is
Figure GDA00028852277700000614
Then set up
Figure GDA00028852277700000615
The remaining content is cached in the F-APk,jHigher forward unload capacity can be obtained, F-APk,1Setting the corresponding cache decision correction indication quantity to-1, F-APk,jThe corresponding cache decision correction indication amount is set to 1, that is: Δ xk,j.1＝-1,Δxk,j.f＝1,
Figure GDA00028852277700000616
And is arranged at
Figure GDA00028852277700000617
When it is time to assemble these contents from the collection
Figure GDA00028852277700000618
Removing and updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to Km；
(5.3) for adjacency list set
Figure GDA00028852277700000619
Repeating the step (5.2) to obtain epsilonrAnd correcting the indication quantity of the cache decision of the redundant content corresponding to each edge.
Further, the step (6) specifically comprises:
(6-1) for the nth cooperative cache cluster, performing the following steps:
A. F-AP for the ith fog wireless access node in the nth cooperation cache clustern,lIf, if
Figure GDA0002885227770000071
Then will be
Figure GDA0002885227770000072
All the cache positions are selected in the F-APn,lCorresponding cache decision correction indicator Δ xn,l,fSet to 1, namely:
Figure GDA0002885227770000073
if it is
Figure GDA0002885227770000074
Then from
Figure GDA0002885227770000075
Medium random selectionLet Kn,lAnd then F-APn,lCorresponding cache decision correction indicator Δ xn,l,fSetting as 1; updating Kn,lAnd selecting the selected content from the collection
Figure GDA0002885227770000076
Removing; wherein, Δ xn,l,f0 indicates that it is impossible to determine whether or not the cache position of the content F is in the foggy wireless access node F-APn,l，Kn,lDenotes F-APn,lL is 1, …, Ln represents the number of nodes in the cooperative cache cluster n;
B. for F-APn,lIf K isn,l> 0, then from the set
Figure GDA0002885227770000077
In random selection of Kn,lAnd correcting the corresponding cache decision by the indicated quantity delta xn,l,fSet to 1, update Kn,lAnd selecting the selected content from the collection
Figure GDA0002885227770000078
Removing; otherwise, not processing; wherein, l is 1, …, Ln;
and (6.2) repeatedly executing other cooperative cache clusters according to the step (6.1) until the cache decision correction indicating quantity corresponding to each cooperative cache cluster is obtained.
Further, the step (7) specifically comprises:
(7.1) for non-cluster fog wireless node set
Figure GDA0002885227770000079
The ith element F-AP of (1)iThe following steps are carried out:
if KiIf > 0, then assemble
Figure GDA00028852277700000710
According to the request probability pifSorting in descending order, selecting top KiAccording to the content, the corresponding cache decision is corrected by the indication quantity delta xifSetting as 1; otherwise, the operation is not executed; wherein the content of the first and second substances,Kidenotes F-APiThe available storage space of (a) is,
Figure GDA00028852277700000711
representing the entire content set, Δ xm′fThe cache position of the content F is shown in the F-APm'，
Figure GDA00028852277700000712
Indicates all the satisfaction (AP)m,APi)∈εrOr (AP)i,APm)∈εrFog wireless access node APmA set of constructs;
(7.2) for non-clustered fog Wireless node sets
Figure GDA00028852277700000713
And (7.1) repeatedly executing other elements to obtain the corresponding cache decision correction indication quantity of each non-cluster fog wireless access node.
Further, the step (8) specifically comprises:
(8.1) selecting a set of access stratum fog wireless access points
Figure GDA00028852277700000714
M-th node in (F-AP)mThe following steps are executed:
finding cache location is at F-APmIn the F-AP, the contents are stored in the F-APmThe final caching decision of (1) is set to 1, that is: x is the number ofmf＝1,f∈{f|Δxmf1} and the rest is in the F-APmIs set to 0, i.e.:
Figure GDA0002885227770000081
wherein the content of the first and second substances,
Figure GDA0002885227770000082
representing the entire content set, xmfRepresentative content F at F-APmFinal caching decision;
(8.2) Wireless Access Point set for Access stratum fog
Figure GDA0002885227770000083
And (8.1) repeating the steps so as to obtain the final caching decision of each fog wireless access node.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages:
1. by constructing the adjacency list set of the vertexes, the situation that the same edge is repeatedly constructed in different vertex pair sequences is avoided, and the subsequent large amount of calculation related to the edge can be avoided from being repeated, so that the calculation is simplified from the source;
2. on the basis of determining the repeated popular content set corresponding to each edge, the redundant content set corresponding to each edge is further determined by combining the storage space size of the fog wireless access node, so that the content which does not cause cache redundancy in the repeated popular content is indirectly eliminated, and the calculation is further simplified;
3. when the redundant content set of one edge is determined, the contents are removed from the repeated popular content sets corresponding to the other edges connected with the top points of the edge, so that twice caching decision correction on the same content on the same fog wireless access node is guaranteed, and the calculation is further simplified;
4. in a staged mode, firstly, an intra-cluster content set and a non-cluster node popular content set which can enable the uploading unloading increment of the intra-cluster cooperation to be maximum are found, then the caching decision of the repeated popular content which affects the uploading unloading amount of the inter-cluster cooperation and the non-cluster node cooperation is corrected, at the moment, the cache decision correction indicating amount can be simultaneously determined by a plurality of repeated popular contents meeting the characteristics of the cache position, the cache position of each content does not need to be calculated iteratively, and the whole process greatly simplifies the calculation of the collaborative content deployment with the maximum total uploading unloading amount.
Drawings
FIG. 1 is a diagram of an application scenario of the present invention;
FIG. 2 is a schematic flow chart of the present invention.
Detailed Description
The embodiment provides a graph theory-based fog wireless access network cooperationThe application scenario of the content deployment method is shown in fig. 1, H F-APs exist in an access layer of a fog wireless access network, and all the F-APs form a set
Figure GDA0002885227770000084
As shown in fig. 2, the method comprises the steps of:
(1) according to the cooperative cache cluster set of the access layer, constructing the popular content set of each cooperative cache cluster n
Figure GDA0002885227770000085
And a popular content set for each non-clustered fog wireless access node i
Figure GDA0002885227770000086
N is 1, …, N, I is 1, …, I, N, I respectively indicate the number of cooperative cache clusters and non-cluster-misty wireless access nodes. The method specifically comprises the following steps:
(1.1) aggregating access stratum fog wireless access points
Figure GDA0002885227770000091
The nodes in the cluster are divided into N cooperative cache clusters, and non-clustered fog wireless nodes form a non-cluster fog wireless node set
Figure GDA0002885227770000092
(1.2) selecting the nth cooperative cache cluster, and calculating the content library
Figure GDA0002885227770000093
Per content to a cooperative cache cluster nnfAnd according to the intra-cluster request probability pnfSorting in descending order by SnKmThe individual content serves as a popular content collection of a cooperative cache cluster n
Figure GDA0002885227770000094
Wherein the probability of requests p in a clusternfThe calculation formula of (A) is as follows:
Figure GDA0002885227770000095
in the formula (I), the compound is shown in the specification,
Figure GDA0002885227770000096
representing a set of fog wireless access nodes, p, comprised in a cooperative cache cluster nmfF-AP (radio access node) for representing fogmThe probability of a request for content f over the coverage area,
Figure GDA0002885227770000097
λmF-AP (radio access node) for representing fogmRequest arrival rate of SnRepresenting the number of misty wireless access nodes, K, in a cooperative cache cluster nmF-AP (radio access node) for representing fogmThe number of contents that can be cached;
(1.3) repeatedly executing other cooperative cache clusters according to the step (1.2) until a popular content set of each cooperative cache cluster is obtained;
(1.4) selecting the ith non-cluster fog wireless access node
Figure GDA0002885227770000098
Computing content library
Figure GDA0002885227770000099
For each non-cluster-fog wireless access node F-APiRequest probability p ofifAnd according to the request probability pifSorting in descending order, the first KiA set of most popular content
Figure GDA00028852277700000910
Wherein, KiF-AP (radio access node) for representing fogiThe number of contents that can be cached;
and (1.5) repeatedly executing other non-cluster-fog wireless access nodes according to the step (1.4) until the popular content set of each non-cluster-fog wireless access node is obtained.
(2) Constructing an access layer according to the distance and the load difference between the fog wireless nodes and the cooperative cache cluster to which the fog wireless nodes belongConnection edge set epsilon of fog wireless noder。
The method specifically comprises the following steps:
(2.1) initializing the connected edge set εrIs an empty set;
(2.2) selecting a set of Access stratum fog wireless Access points
Figure GDA00028852277700000911
Middle mth node F-APmPerforming the following operations:
obtaining the m' th node F-APm'M', M ═ M + 1., M denotes the number of the fog wireless access points, and it is determined whether the following conditions are satisfied:
a、Dmm'≤γd，Lmm'≥γl(ii) a Wherein D ismm′＝||dm-dm′||2，dmAnd dm′Respectively represent fog wireless access nodes F-APmAnd F-APm'Coordinates in Euclidean space, Lmm′＝||λm-λm′||2，λmAnd λm′Respectively represent fog wireless access nodes F-APmAnd F-APm'Request arrival rate, gamma, over coverage areadThreshold, gamma, representing the distance between the fog radio access nodeslA threshold representing a load difference, | · | | non-conducting phosphor2Represents the L2 norm operator;
b. node F-APmAnd node F-APm'Not in the same cooperative cache cluster;
if conditions a and b are satisfied simultaneously, the edges (F-AP) will be connectedm,F-APm') Adding to the set εrPerforming the following steps;
(2.3) for fog Wireless Access Point set
Figure GDA0002885227770000101
And (5) repeatedly executing other nodes according to the step (2.2) until the fog wireless access point set is traversed
Figure GDA0002885227770000102
All the nodes are in the state of being in order to obtain the final connection edge set epsilonr。
(3) According to the connection edge set epsilonrBuilding access layer adjacency list set
Figure GDA0002885227770000103
The method specifically comprises the following steps:
(3.1) set of Wireless Access points to Access stratum fog
Figure GDA0002885227770000104
M-th node in (F-AP)mBuilding its neighbor list set
Figure GDA0002885227770000105
(3.2) eliminating the adjacent table sets with the element number of 1 from the adjacent table sets of all F-AP nodes, and sequencing the rest adjacent table sets in a descending order according to the element number in the sets to obtain
Figure GDA0002885227770000106
Wherein H is
Figure GDA0002885227770000107
The number of the elements in the Chinese character 'Zhongqin'.
(4) According to access layer adjacency list set
Figure GDA0002885227770000108
Obtaining epsilonrRedundant content set corresponding to each edge in the content
Figure GDA0002885227770000109
The method specifically comprises the following steps:
(4.1) for adjacency list set
Figure GDA00028852277700001010
The k element of (1)
Figure GDA00028852277700001011
The following steps are carried out:
A. obtaining
Figure GDA00028852277700001012
J element of F-APk,jWith the first element F-APk,1The repeated popular content set corresponding to the connection edge e is obtained according to the following criteria
Figure GDA00028852277700001013
Figure GDA00028852277700001014
In the formula (I), the compound is shown in the specification,
Figure GDA00028852277700001015
representing a set of fog wireless access nodes included in the cooperative cache cluster n,
Figure GDA00028852277700001016
representing a non-clustered fog set of wireless nodes
Figure GDA00028852277700001017
Figure GDA00028852277700001018
Denotes F-APk,jJ2, …, Jk，JkTo represent
Figure GDA00028852277700001019
The number of middle elements;
B. for adjacency list set
Figure GDA0002885227770000111
Is repeatedly executed (4.1), thereby obtaining a repeated popular content set corresponding to each connecting edge
Figure GDA0002885227770000112
(4.2) for adjacency list set
Figure GDA0002885227770000113
The k element of (1)
Figure GDA0002885227770000114
The following steps are carried out:
for the
Figure GDA0002885227770000115
J element of F-APk,jInitialization of Kk,j＝KmK, where J is 1, …, Jk，JkTo represent
Figure GDA0002885227770000116
The number of medium elements, m represents a fog wireless access node F-APk,jIn the collection
Figure GDA0002885227770000117
The sequence number in (1), M belongs to { 1.,. M }, M denotes the number of the fog wireless access nodes, K denotes the number of the fog wireless access nodes, andk,jand KmAll represent fog wireless access node F-APk,jK represents the maximum available storage space size of the fog wireless access node;
(4.3) for adjacency list set
Figure GDA0002885227770000118
The k element of (1)
Figure GDA0002885227770000119
The following steps are carried out:
A. cumulative calculation
Figure GDA00028852277700001110
J element of F-APk,jWith the first element F-APk,1The intersection of the sets of repeated popular content corresponding to the connecting edges of
Figure GDA00028852277700001111
B. If it is
Figure GDA00028852277700001112
Then for the collection
Figure GDA00028852277700001113
J element of F-APk,jWith the first element F-APk,1E, from the set
Figure GDA00028852277700001114
In random selection of Kk,1The content forms a redundant content set corresponding to the edge e
Figure GDA00028852277700001115
And based on redundant content sets
Figure GDA00028852277700001116
Updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmAnd updating the connection F-APk,jE' ≠ e corresponding repeated popular content set
Figure GDA00028852277700001117
Wherein J is 2, …, Jk；
C. If it is
Figure GDA00028852277700001118
Then for the collection
Figure GDA00028852277700001119
J element of F-APk,jWith the first element F-APk,1E, from the set
Figure GDA00028852277700001120
In the random selection
Figure GDA00028852277700001121
Content, together with collections
Figure GDA00028852277700001122
All contents in (1) constitute a redundant content set corresponding to the edge e
Figure GDA00028852277700001123
And based on redundant content sets
Figure GDA00028852277700001124
Updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmAnd updating the connection F-APk,jE' ≠ e corresponding repeated popular content set
Figure GDA00028852277700001125
Wherein J is 2, …, Jk；
D. For adjacency list set
Figure GDA00028852277700001126
Repeat (4.3) to obtain a redundant content set corresponding to each connecting edge
Figure GDA00028852277700001127
(5) From redundant content sets
Figure GDA0002885227770000121
Calculating epsilonrAnd correcting the indication quantity of the cache decision of the redundant content corresponding to each edge. The method specifically comprises the following steps:
(5-1) for adjacency list set
Figure GDA0002885227770000122
The k element of (1)
Figure GDA0002885227770000123
The following steps are carried out:
for the
Figure GDA0002885227770000124
J element of F-APk,jReset Kk,j＝KmK, where J is 1, …, Jk，JkTo represent
Figure GDA0002885227770000125
The number of medium elements, m represents a fog wireless access node F-APk,jIn the collection
Figure GDA0002885227770000126
The sequence number in (1), M belongs to { 1.,. M }, M denotes the number of the fog wireless access nodes, K denotes the number of the fog wireless access nodes, andk,jand KmAll represent fog wireless access node F-APk,jK represents the maximum available storage space size of the fog wireless access node;
(5-2) for adjacency list set
Figure GDA0002885227770000127
The k element of (1)
Figure GDA0002885227770000128
The following steps are carried out:
to the collection
Figure GDA0002885227770000129
Middle j element F-APk,jWith the first element F-APk,1Redundant content set corresponding to the connecting edge e of
Figure GDA00028852277700001210
The following four-step operation is performed, J is 2, …, and Jk，JkTo represent
Figure GDA00028852277700001211
The number of the medium elements is as follows:
is in the collection
Figure GDA00028852277700001212
Wherein the cache location is found in the F-APk,1The content of (1), the content of the part is not allowed to be cached in the F-APk,jTo avoid cache redundancy, the F-AP is switched onk,jCorresponding cache decision correction indicator Δ xk,j,fSet to-1, i.e.: Δ xk,j,f＝-1,
Figure GDA00028852277700001213
And to aggregate such content from collections
Figure GDA00028852277700001214
Wherein the cache decision correction indicator Δ xk,j,f1 indicates that the buffer location of the content F is in the F-APk,j；
② in the collection
Figure GDA00028852277700001215
Does not allow for finding a cache location in the F-APk,1The part of the content has to be cached in the F-APk,jThen F-AP is setk,jCorresponding cache decision correction indicator Δ xk,j,fSet to 1, namely: Δ xk,j.f＝1,
Figure GDA00028852277700001216
And is arranged at
Figure GDA00028852277700001217
When it is time to assemble these contents from the collection
Figure GDA00028852277700001218
Removing and updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmFrom the collection of these contents
Figure GDA00028852277700001219
Removing; wherein, the cache decision correction indication quantity Deltaxk,1,fCache location of presentation content F at-1 is not allowed at F-APk,1；
Respectively calculating the sets
Figure GDA00028852277700001220
In (3) caching in the F-APk,1Available fronthaul unload capacity
Figure GDA00028852277700001221
And will aggregate
Figure GDA00028852277700001222
In (3) caching in the F-APk,jAvailable fronthaul unload capacity
Figure GDA00028852277700001223
Wherein:
Figure GDA0002885227770000131
Figure GDA0002885227770000132
in the formula (II)
Figure GDA0002885227770000133
Represents all satiations (F-AP)m,F-APk，1)∈εrOr (F-AP)k，1,F-APm)∈εrFog wireless access node F-APmSet of constructs, set
Figure GDA0002885227770000134
Represents all satiations (F-AP)m,F-APk，j)∈εrOr (F-AP)k，j,F-APm)∈εrFog wireless access node F-APmSet of formations, λm'F-AP (radio access node) for representing fogm'Request arrival rate of (p)m'fF-AP (radio access node) for representing fogm'Probability of request for content f over the coverage area, L representing the size of each content;
fourthly if
Figure GDA0002885227770000135
Then set up
Figure GDA0002885227770000136
The remaining content is cached in the F-APk,1Higher forward unload capacity can be obtained, F-APk,1Setting the corresponding cache decision correction indication quantity to be 1, F-APk,jThe corresponding cache decision correction indication quantity is set to-1, namely: Δ xk,j.1＝1,Δxk,j.f＝-1,
Figure GDA0002885227770000137
And is arranged at
Figure GDA0002885227770000138
When it is time to assemble these contents from the collection
Figure GDA0002885227770000139
In the process of removing and updating the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to Km(ii) a If it is
Figure GDA00028852277700001310
Then set up
Figure GDA00028852277700001311
The remaining content is cached in the F-APk,jHigher forward unload capacity can be obtained, F-APk,1Setting the corresponding cache decision correction indication quantity to-1, F-APk,jThe corresponding cache decision correction indication amount is set to 1, that is: Δ xk,j.1＝-1,Δxk,j.f＝1,
Figure GDA00028852277700001312
And is arranged at
Figure GDA00028852277700001313
When it is time to assemble these contents from the collection
Figure GDA00028852277700001314
Removing and updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to Km；
(5-3) for adjacency list set
Figure GDA00028852277700001315
Repeating the step (5-2) to obtain epsilonrAnd correcting the indication quantity of the cache decision of the redundant content corresponding to each edge.
(6) And (5) calculating the corresponding cache decision correction indication quantity of each cooperative cache cluster n according to the updated popular content set of the cooperative cache clusters. The method specifically comprises the following steps:
(6-1) for the nth cooperative cache cluster, performing the following steps:
A. F-AP for the ith fog wireless access node in the nth cooperation cache clustern,lIf, if
Figure GDA00028852277700001316
Then will be
Figure GDA00028852277700001317
All the cache positions are selected in the F-APn,lCorresponding cache decision correction indicator Δ xn,l,fSet to 1, namely:
Figure GDA0002885227770000141
if it is
Figure GDA0002885227770000142
Then from
Figure GDA0002885227770000143
In the random selection of Kn,lAnd then F-APn,lCorresponding cache decision correction indicator Δ xn,l,fSetting as 1; updating Kn,lAnd will be selectedContent slave collections
Figure GDA0002885227770000144
Removing; wherein, Δ xn,l,f0 indicates that it is impossible to determine whether or not the cache position of the content F is in the foggy wireless access node F-APn,l，Kn,lDenotes F-APn,lL is 1, …, Ln represents the number of nodes in the cooperative cache cluster n;
B. for F-APn,lIf K isn,l> 0, then from the set
Figure GDA0002885227770000145
In random selection of Kn,lAnd correcting the corresponding cache decision by the indicated quantity delta xn,l,fSet to 1, update Kn,lAnd selecting the selected content from the collection
Figure GDA0002885227770000146
Removing; otherwise, not processing; wherein, l is 1, …, Ln;
and (6.2) repeatedly executing other cooperative cache clusters according to the step (6.1) until the cache decision correction indicating quantity corresponding to each cooperative cache cluster is obtained.
(7) And (5) calculating the corresponding cache decision correction indication quantity of each non-cluster fog wireless access node according to the cache decision correction indication quantity obtained in the step (5). The method specifically comprises the following steps:
(7.1) for non-cluster fog wireless node set
Figure GDA0002885227770000147
The ith element F-AP of (1)iThe following steps are carried out:
if KiIf > 0, then assemble
Figure GDA0002885227770000148
According to the request probability pifSorting in descending order, selecting top KiAccording to the content, the corresponding cache decision is corrected by the indication quantity delta xifSetting as 1; otherwise, the operation is not executed; wherein, KiDenotes F-APiThe available storage space of (a) is,
Figure GDA0002885227770000149
representing the entire content set, Δ xm′fThe cache position of the content F is shown in the F-APm'，
Figure GDA00028852277700001410
Indicates all the satisfaction (AP)m,APi)∈εrOr (AP)i,APm)∈εrFog wireless access node APmA set of constructs;
(7.2) for non-clustered fog Wireless node sets
Figure GDA00028852277700001411
And (7.1) repeatedly executing other elements to obtain the corresponding cache decision correction indication quantity of each non-cluster fog wireless access node.
(8) And (5) calculating a final cache decision according to the cache decision correction indicating quantity obtained in the steps (5) to (7). The method specifically comprises the following steps:
(8.1) selecting a set of access stratum fog wireless access points
Figure GDA00028852277700001412
M-th node in (F-AP)mThe following steps are executed:
finding cache location is at F-APmIn the F-AP, the contents are stored in the F-APmThe final caching decision of (1) is set to 1, that is: x is the number ofmf＝1,f∈{fΔxmf1} and the rest is in the F-APmIs set to 0, i.e.:
Figure GDA0002885227770000151
wherein the content of the first and second substances,
Figure GDA0002885227770000152
representing the entire content set, xmfRepresentative content F at F-APmFinal caching decision;
(8.2) Wireless Access Point set for Access stratum fog
Figure GDA0002885227770000153
And (8.1) repeating the steps so as to obtain the final caching decision of each fog wireless access node.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (9)

1. A fog wireless access network collaboration content deployment method based on graph theory is characterized by comprising the following steps:
(1) according to the cooperative cache cluster set of the access layer, constructing the popular content set of each cooperative cache cluster n
Figure FDA0001717967510000011
And a popular content set for each non-clustered fog wireless access node i
Figure FDA0001717967510000012
N is 1, …, N, I is 1, …, I, N, I respectively represent the number of the cooperative cache cluster and the non-cluster fog wireless access nodes;
(2) constructing a connection edge set epsilon of the fog wireless nodes of the access layer according to the distance and the load difference between the fog wireless nodes and the cooperative cache cluster to which the fog wireless nodes belongr；
(3) According to the connection edge set epsilonrBuilding access layer adjacency list set
Figure FDA0001717967510000013
(4) According to access layer adjacency list set
Figure FDA0001717967510000014
Obtaining epsilonrRedundant content set corresponding to each edge in the content
Figure FDA0001717967510000015
(5) From redundant content sets
Figure FDA0001717967510000016
Calculating epsilonrThe cache decision correction indicating quantity of the redundant content corresponding to each edge;
(6) calculating a cache decision correction indicating quantity corresponding to each cooperative cache cluster n according to the updated popular content set of the cooperative cache clusters in the step (5);
(7) calculating a cache decision correction indicating quantity corresponding to each non-cluster fog wireless access node according to the cache decision correction indicating quantity obtained in the step (5);
(8) and (5) calculating a final cache decision according to the cache decision correction indicating quantity obtained in the steps (5) to (7).
2. The graph theory-based deployment method for the fog radio access network collaborative content, according to claim 1, is characterized in that: the step (1) specifically comprises the following steps:
(1.1) aggregating access stratum fog wireless access points
Figure FDA0001717967510000017
The nodes in the cluster are divided into N cooperative cache clusters, and non-clustered fog wireless nodes form a non-cluster fog wireless node set
Figure FDA0001717967510000018
(1.2) selecting the nth cooperative cache cluster, and calculating the content library
Figure FDA0001717967510000019
Per content to a cooperative cache cluster nnfAnd according to the intra-cluster request probability pnfSorting in descending order by SnKmThe individual content serves as a popular content collection of a cooperative cache cluster n
Figure FDA00017179675100000110
Wherein the probability of requests p in a clusternfThe calculation formula of (A) is as follows:
Figure FDA00017179675100000111
in the formula (I), the compound is shown in the specification,
Figure FDA00017179675100000112
representing a set of fog wireless access nodes, p, comprised in a cooperative cache cluster nmfF-AP (radio access node) for representing fogmThe probability of a request for content f over the coverage area,
Figure FDA00017179675100000113
λmF-AP (radio access node) for representing fogmRequest arrival rate of SnRepresenting the number of misty wireless access nodes, K, in a cooperative cache cluster nmF-AP (radio access node) for representing fogmThe number of contents that can be cached;
(1.3) repeatedly executing other cooperative cache clusters according to the step (1.2) until a popular content set of each cooperative cache cluster is obtained;
(1.4) selecting the ith non-cluster fog wireless access node
Figure FDA0001717967510000021
Computing content library
Figure FDA0001717967510000022
For each non-cluster-fog wireless access node F-APiRequest probability p ofifAnd according to the request probability pifSorting in descending order, the first KiA set of most popular content
Figure FDA0001717967510000023
Wherein, KiF-AP (radio access node) for representing fogiThe number of contents that can be cached;
and (1.5) repeatedly executing other non-cluster-fog wireless access nodes according to the step (1.4) until the popular content set of each non-cluster-fog wireless access node is obtained.
3. The graph theory-based deployment method for the fog radio access network collaborative content, according to claim 1, is characterized in that: the step (2) specifically comprises the following steps:
(2.1) initializing the connected edge set εrIs an empty set;
(2.2) selecting a set of Access stratum fog wireless Access points
Figure FDA0001717967510000024
Middle mth node F-APmPerforming the following operations:
obtaining the m' th node F-APm'M', M ═ M + 1., M denotes the number of the fog wireless access points, and it is determined whether the following conditions are satisfied:
a、Dmm'≤γd，Lmm'≥γl(ii) a Wherein D ismm′＝||dm-dm′||2，dmAnd dm′Respectively represent fog wireless access nodes F-APmAnd F-APm'Coordinates in Euclidean space, Lmm′＝||λm-λm′||2，λmAnd λm′Respectively represent fog wireless access nodes F-APmAnd F-APm'Request arrival rate, gamma, over coverage areadThreshold, gamma, representing the distance between the fog radio access nodeslA threshold representing a load difference, | · | | non-conducting phosphor2Represents the L2 norm operator;
b. node F-APmAnd node F-APm'Not in the same cooperative cache cluster;
if conditions a and b are satisfied simultaneously, the edges (F-AP) will be connectedm,F-APm') Adding to the set εrPerforming the following steps;
(2.3) for fog Wireless Access Point set
Figure FDA0001717967510000025
And (5) repeatedly executing other nodes according to the step (2.2) until the fog wireless access point set is traversed
Figure FDA0001717967510000026
All the nodes are in the state of being in order to obtain the final connection edge set epsilonr。
4. The graph theory-based deployment method for the fog radio access network collaborative content, according to claim 1, is characterized in that: the step (3) specifically comprises the following steps:
(3.1) set of Wireless Access points to Access stratum fog
Figure FDA0001717967510000031
M-th node in (F-AP)mBuilding its neighbor list set
Figure FDA0001717967510000032
(3.2) eliminating the adjacent table sets with the element number of 1 from the adjacent table sets of all F-AP nodes, and sequencing the rest adjacent table sets in a descending order according to the element number in the sets to obtain sets
Figure FDA0001717967510000033
Wherein H is
Figure FDA0001717967510000034
The number of the elements in the Chinese character 'Zhongqin'.
5. The graph theory-based deployment method for the fog radio access network collaborative content, according to claim 1, is characterized in that: the step (4) specifically comprises the following steps:
(4.1) for adjacency list set
Figure FDA0001717967510000035
The k element of (1)
Figure FDA0001717967510000036
ExecuteThe method comprises the following steps:
A. obtaining
Figure FDA0001717967510000037
J element of F-APk,jWith the first element F-APk,1The repeated popular content set corresponding to the connection edge e is obtained according to the following criteria
Figure FDA0001717967510000038
Figure FDA0001717967510000039
In the formula (I), the compound is shown in the specification,
Figure FDA00017179675100000310
representing a set of fog wireless access nodes included in the cooperative cache cluster n,
Figure FDA00017179675100000311
representing a non-clustered fog set of wireless nodes
Figure FDA00017179675100000312
Figure FDA00017179675100000313
Denotes F-APk,jJ2, …, Jk，JkTo represent
Figure FDA00017179675100000314
The number of middle elements;
B. for adjacency list set
Figure FDA00017179675100000315
Is repeatedly executed (4.1), thereby obtaining a repeated popular content set corresponding to each connecting edge
Figure FDA00017179675100000316
(4.2) for adjacency list set
Figure FDA00017179675100000317
The k element of (1)
Figure FDA00017179675100000318
The following steps are carried out:
for the
Figure FDA00017179675100000319
J element of F-APk,jInitialization of Kk,j＝KmK, where J is 1, …, Jk，JkTo represent
Figure FDA00017179675100000320
The number of medium elements, m represents a fog wireless access node F-APk,jIn the collection
Figure FDA00017179675100000321
The sequence number in (1), M belongs to { 1.,. M }, M denotes the number of the fog wireless access nodes, K denotes the number of the fog wireless access nodes, andk,jand KmAll represent fog wireless access node F-APk,jK represents the maximum available storage space size of the fog wireless access node;
(4.3) for adjacency list set
Figure FDA00017179675100000322
The k element of (1)
Figure FDA00017179675100000323
The following steps are carried out:
A. cumulative calculation
Figure FDA00017179675100000324
J element of F-APk,jAnd firstAn element F-APk,1The intersection of the sets of repeated popular content corresponding to the connecting edges of
Figure FDA0001717967510000041
Figure FDA0001717967510000042
B. If it is
Figure FDA0001717967510000043
Then for the collection
Figure FDA0001717967510000044
J element of F-APk,jWith the first element F-APk,1E, from the set
Figure FDA0001717967510000045
In random selection of Kk,1The content forms a redundant content set corresponding to the edge e
Figure FDA0001717967510000046
And based on redundant content sets
Figure FDA0001717967510000047
Updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmAnd updating the connection F-APk,jE' ≠ e corresponding repeated popular content set
Figure FDA0001717967510000048
Wherein J is 2, …, Jk；
C. If it is
Figure FDA0001717967510000049
Then for the collection
Figure FDA00017179675100000410
J element of F-APk,jWith the first element F-APk,1E, from the set
Figure FDA00017179675100000411
In the random selection
Figure FDA00017179675100000412
Content, together with collections
Figure FDA00017179675100000413
All contents in (1) constitute a redundant content set corresponding to the edge e
Figure FDA00017179675100000414
And based on redundant content sets
Figure FDA00017179675100000415
Updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmAnd updating the connection F-APk,jE' ≠ e corresponding repeated popular content set
Figure FDA00017179675100000416
Wherein J is 2, …, Jk；
D. For adjacency list set
Figure FDA00017179675100000417
Repeat (4.3) to obtain a redundant content set corresponding to each connecting edge
Figure FDA00017179675100000418
6. The graph theory-based deployment method for the fog radio access network collaborative content, according to claim 1, is characterized in that: the step (5) specifically comprises the following steps:
(5.1) for adjacency list set
Figure FDA00017179675100000419
The k element of (1)
Figure FDA00017179675100000420
The following steps are carried out:
for the
Figure FDA00017179675100000421
J element of F-APk,jReset Kk,j＝KmK, where J is 1, …, Jk，JkTo represent
Figure FDA00017179675100000422
The number of medium elements, m represents a fog wireless access node F-APk,jIn the collection
Figure FDA00017179675100000423
The sequence number in (1), M belongs to { 1.,. M }, M denotes the number of the fog wireless access nodes, K denotes the number of the fog wireless access nodes, andk,jand KmAll represent fog wireless access node F-APk,jK represents the maximum available storage space size of the fog wireless access node;
(5.2) for adjacency list set
Figure FDA00017179675100000424
The k element of (1)
Figure FDA00017179675100000425
The following steps are carried out:
to the collection
Figure FDA00017179675100000426
Middle j element F-APk,jWith the first element F-APk,1Redundant content set corresponding to the connecting edge e of
Figure FDA0001717967510000051
The following four-step operation is performed, J is 2, …, and Jk，JkTo represent
Figure FDA0001717967510000052
The number of the medium elements is as follows:
is in the collection
Figure FDA0001717967510000053
Wherein the cache location is found in the F-APk,1The content of (1), the content of the part is not allowed to be cached in the F-APk,jTo avoid cache redundancy, the F-AP is switched onk,jCorresponding cache decision correction indicator Δ xk,j,fSet to-1, i.e.: Δ xk,j,f＝-1,
Figure FDA0001717967510000054
And to aggregate such content from collections
Figure FDA0001717967510000055
Wherein the cache decision correction indicator Δ xk,j,f1 indicates that the buffer location of the content F is in the F-APk,j；
② in the collection
Figure FDA0001717967510000056
Does not allow for finding a cache location in the F-APk,1The part of the content has to be cached in the F-APk,jThen F-AP is setk,jCorresponding cache decision correction indicator Δ xk,j,fSet to 1, namely: Δ xk,j.f＝1,
Figure FDA0001717967510000057
And is arranged at
Figure FDA0001717967510000058
When it is time to assemble these contents from the collection
Figure FDA0001717967510000059
Removing and updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to KmFrom the collection of these contents
Figure FDA00017179675100000510
Removing; wherein, the cache decision correction indication quantity Deltaxk,1,fCache location of presentation content F at-1 is not allowed at F-APk,1；
Respectively calculating the sets
Figure FDA00017179675100000511
In (3) caching in the F-APk,1Available fronthaul unload capacity
Figure FDA00017179675100000512
And will aggregate
Figure FDA00017179675100000513
In (3) caching in the F-APk,jAvailable fronthaul unload capacity
Figure FDA00017179675100000514
Wherein:
Figure FDA00017179675100000515
Figure FDA00017179675100000516
in the formula (II)
Figure FDA00017179675100000517
Represents all satiations (F-AP)m,F-APk，1)∈εrOr (F-AP)k，1,F-APm)∈εrFog wireless access node F-APmSet of constructs, set
Figure FDA00017179675100000518
Represents all satiations (F-AP)m,F-APk，j)∈εrOr (F-AP)k，j,F-APm)∈εrFog wireless access node F-APmSet of formations, λm'F-AP (radio access node) for representing fogm'Request arrival rate of (p)m'fF-AP (radio access node) for representing fogm'Probability of request for content f over the coverage area, L representing the size of each content;
fourthly if
Figure FDA00017179675100000519
Then set up
Figure FDA00017179675100000520
The remaining content is cached in the F-APk,1Higher forward unload capacity can be obtained, F-APk,1Setting the corresponding cache decision correction indication quantity to be 1, F-APk,jThe corresponding cache decision correction indication quantity is set to-1, namely: Δ xk,1.f＝1,Δxk,j.f＝-1,
Figure FDA0001717967510000061
And is arranged at
Figure FDA0001717967510000062
When it is time to assemble these contents from the collection
Figure FDA0001717967510000063
Removing and updating Kk,1Update the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to Km(ii) a If it is
Figure FDA0001717967510000064
Then set up
Figure FDA0001717967510000065
The remaining content is cached in the F-APk,jHigher forward unload capacity can be obtained, F-APk,1Setting the corresponding cache decision correction indication quantity to-1, F-APk,jThe corresponding cache decision correction indication amount is set to 1, that is: Δ xk,j.1＝-1,Δxk,j.f＝1,
Figure FDA0001717967510000066
And is arranged at
Figure FDA0001717967510000067
When it is time to assemble these contents from the collection
Figure FDA0001717967510000068
Removing and updating Kk,jUpdate the corresponding KmAnd other fog wireless access nodes with the sequence number m are F-APk',j'(k'＞k,j'∈{1,...,Jk'}) available memory space Kk',j'Is updated to Km；
(5.3) for adjacency list set
Figure FDA0001717967510000069
Repeating the step (5.2) to obtain epsilonrAnd correcting the indication quantity of the cache decision of the redundant content corresponding to each edge.
7. The graph theory-based deployment method for the fog radio access network collaborative content, according to claim 1, is characterized in that: the step (6) specifically comprises the following steps:
(6-1) for the nth cooperative cache cluster, performing the following steps:
A. F-AP for the ith fog wireless access node in the nth cooperation cache clustern,lIf, if
Figure FDA00017179675100000610
Then will be
Figure FDA00017179675100000611
All the cache positions are selected in the F-APn,lCorresponding cache decision correction indicator Δ xn,l,fSet to 1, namely: Δ xn,l,f＝1,
Figure FDA00017179675100000612
If it is
Figure FDA00017179675100000613
Then from
Figure FDA00017179675100000614
In the random selection of Kn,lAnd then F-APn,lCorresponding cache decision correction indicator Δ xn,l,fSetting as 1; updating Kn,lAnd selecting the selected content from the collection
Figure FDA00017179675100000615
Removing; wherein, Δ xn,l,f0 indicates that it is impossible to determine whether or not the cache position of the content F is in the foggy wireless access node F-APn,l，Kn,lDenotes F-APn,lL is 1, …, Ln represents the number of nodes in the cooperative cache cluster n;
B. for F-APn,lIf K isn,l> 0, then from the set
Figure FDA00017179675100000616
In random selection of Kn,lAnd correcting the corresponding cache decision by the indicated quantity delta xn,l,fSet to 1, update Kn,lAnd will select the innerCollection of contents
Figure FDA00017179675100000617
Removing; otherwise, not processing; wherein, l is 1, …, Ln;
and (6.2) repeatedly executing other cooperative cache clusters according to the step (6.1) until the cache decision correction indicating quantity corresponding to each cooperative cache cluster is obtained.
8. The graph theory-based deployment method for the cooperative content in the fog radio access network, according to claim 1, wherein the step (7) specifically comprises:
(7.1) for non-cluster fog wireless node set
Figure FDA0001717967510000071
The ith element F-AP of (1)iThe following steps are carried out:
if KiIf > 0, then assemble
Figure FDA0001717967510000072
According to the request probability pifSorting in descending order, selecting top KiAccording to the content, the corresponding cache decision is corrected by the indication quantity delta xifSetting as 1; otherwise, the operation is not executed; wherein, KiDenotes F-APiThe available storage space of (a) is,
Figure FDA0001717967510000073
representing the entire content set, Δ xm′fThe cache position of the content F is shown in the F-APm'，
Figure FDA0001717967510000074
Indicates all the satisfaction (AP)m,APi)∈εrOr (AP)i,APm)∈εrFog wireless access node APmA set of constructs;
(7.2) for non-clustered fog Wireless node sets
Figure FDA0001717967510000075
And (7.1) repeatedly executing other elements to obtain the corresponding cache decision correction indication quantity of each non-cluster fog wireless access node.
9. The graph theory-based deployment method for the cooperative content in the fog radio access network, according to claim 1, wherein the step (8) specifically comprises:
(8.1) selecting a set of access stratum fog wireless access points
Figure FDA0001717967510000076
M-th node in (F-AP)mThe following steps are executed:
finding cache location is at F-APmIn the F-AP, the contents are stored in the F-APmThe final caching decision of (1) is set to 1, that is: x is the number ofmf＝1,f∈{f|Δxmf1} and the rest is in the F-APmIs set to 0, i.e.: x is the number ofmf＝0,
Figure FDA0001717967510000077
Wherein the content of the first and second substances,
Figure FDA0001717967510000078
representing the entire content set, xmfRepresentative content F at F-APmFinal caching decision;
(8.2) Wireless Access Point set for Access stratum fog
Figure FDA0001717967510000079
And (8.1) repeating the steps so as to obtain the final caching decision of each fog wireless access node.
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