CN110752990A - Time-varying network shortest routing method for guaranteeing elasticity - Google Patents

Time-varying network shortest routing method for guaranteeing elasticity Download PDF

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CN110752990A
CN110752990A CN201911017082.XA CN201911017082A CN110752990A CN 110752990 A CN110752990 A CN 110752990A CN 201911017082 A CN201911017082 A CN 201911017082A CN 110752990 A CN110752990 A CN 110752990A
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node
betweenness
nodes
network
link
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CN110752990B (en
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李红艳
夏茹敏
谷聚娟
张亚生
杨光祥
张顺
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CETC 54 Research Institute
Xian University of Electronic Science and Technology
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Xian University of Electronic Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L45/00—Routing or path finding of packets in data switching networks
    • H04L45/12—Shortest path evaluation
    • H04L45/123—Evaluation of link metrics
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L45/00—Routing or path finding of packets in data switching networks
    • H04L45/12—Shortest path evaluation
    • H04L45/124—Shortest path evaluation using a combination of metrics

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Abstract

The invention discloses a time-varying network shortest routing method for guaranteeing elasticity, which mainly solves the problem that a certain node frequently participates in path construction in the traditional shortest routing method to cause the criticality of the node in a time-varying network to be too high. The scheme is as follows: 1) marking node betweenness on the time expansion graph and initializing the node betweenness; 2) constructing node betweenness-time delay normalization indexes; 3) randomly selecting any node as a current source node, and constructing an betweenness-time delay shortest path tree; 4) judging whether nodes which do not construct the betweenness-time delay shortest path tree still exist or not: if yes, updating the betweenness information and the betweenness-time delay normalization index information of the network nodes, and returning to step 3); otherwise, outputting the betweenness-time delay shortest path between the network nodes. The invention can reserve more residual communication service capability for the time-varying network when the node fails, improves the network elasticity performance, and can be used in satellite networks with time-varying attributes, such as small satellite formation, remote sensing satellites and small constellation.

Description

Time-varying network shortest routing method for guaranteeing elasticity
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a time-varying network shortest routing method for guaranteeing elasticity, which can be used in satellite networks with time-varying attributes, such as small satellite formation, remote sensing satellites and small constellation groups.
Background
Satellite networks are now rapidly growing and dominate over their wide coverage, and it is desirable to provide fast and convenient communication services to users worldwide.
A time-varying network refers to a network in which the network topology or bandwidth resources available for traffic transmission in the network dynamically change over time.
In a time-varying network, when a traditional Dijkstra algorithm is used for solving paths between network nodes, link delay is taken as weight on a time expansion graph and the shortest delay is taken as an optimization target of routing, so that a certain node is positioned in the shortest transmission path of multiple pairs of nodes, the node becomes a key node of the network, and the failure of the node can cause the time-varying network to lose most communication capacity and even cause paralysis of the whole network.
In order to avoid the above situations, the criticality of the time-varying network node needs to be identified on the time expansion diagram, the routing method of the time-varying network is limited, the positions of the nodes in the time-varying network are balanced, and the problem that a certain node has high participation in point-to-point path construction is avoided.
In order to avoid that the network traffic may be concentrated in a certain part of key nodes, which causes the resource of the part of key nodes to be over-consumed and invalid, thereby causing the network service capability to be reduced. The prior art proposes related research on methods for avoiding critical node routing in networks.
An internet, huang jia qi, luozi, wangchin, et al, in 2014, proposed a node betweenness-based congestion sensing routing algorithm, which calculates multiple alternative paths with the minimum delay overhead among nodes through a space-time evolution diagram of a network topology, and introduces a node betweenness to identify the load condition of the nodes. The algorithm calculates a plurality of shortest paths by taking time delay as an index, and selects an actual forwarding path by taking an betweenness as the index during forwarding, thereby effectively reducing the condition that the flow is concentrated on a certain key node for forwarding. However, in the algorithm, the link delay and the betweenness are split into two parts, the path is constructed and selected respectively, and the betweenness does not participate in the calculation of the route, so that a routing scheme combining the delay and the betweenness cannot be provided in one step in the route calculation process.
The patent application published in 2013 by Zunwei, Zhao Zhilong, Tianchun mountain, Yanhan, Zhang hong and the like provides a heuristic routing method for avoiding key nodes in a complex network. The method reduces the maximum node betweenness in the network by changing the weight on the edge of the connected key node, and reduces the flow of the key node by redistributing the flow load between the key node and the non-key node by using the shortest path algorithm. However, the algorithm only considers betweenness as an index to construct the shortest path, neglects the influence of link delay in the process of constructing the shortest path, and has poor applicability in a time-varying network with time-varying characteristics.
Therefore, how to find a time-varying network shortest routing method which comprehensively considers two important indexes of time delay and betweenness to ensure elasticity becomes a research difficulty and a hotspot in the technical field of time-varying network routing.
Disclosure of Invention
The invention aims to provide a shortest routing method for guaranteeing elasticity of a time-varying network, comprehensively considering the influence of betweenness and time delay, giving a shortest routing scheme of betweenness-time delay combined constraint in a routing calculation process by one step, constructing a point-to-point path with smaller time delay and relatively equal node positions, avoiding the occurrence of nodes with extremely high key in the shortest path of the time-varying network, and preventing the network service capability from being greatly reduced due to failure of the nodes.
The technical scheme of the invention is that node betweenness and link time delay of a time-varying network are respectively normalized and jointly converted into new link weight, and the new link weight is marked on a time expansion diagram representing a time interval communication relation of the time-varying network; and then solving the betweenness-time delay shortest path between the node pairs by utilizing a Dijsktra algorithm. The shortest path between the node pairs obtained through calculation can guarantee time delay and prevent a certain node from frequently appearing in the shortest paths, so that the network is ensured not to lose most routing service capacity due to the failure of the certain node, and the elasticity performance of the network is improved. The method comprises the following implementation steps:
(1) and (V, E) representing the time interval connectivity relation of the time-varying network by using a time expansion graph G, and respectively marking the link time delay T on the link of GjAnd node betweenness BiWherein i belongs to V, j belongs to E, V represents a node in the network, and E represents a link in the network; node betweenness BiInitializing 0, which indicates that the median value of the node i is 0;
(2) constructing a node betweenness-time delay normalization index on a time expansion diagram:
(2a) the betweenness B of the node iiAnd (3) marking the maximum value on the time expansion diagram, and obtaining the maximum value of the betweenness of the current network node according to the following rules: b ismax＝max{Bi|i∈V}；
(2b) Using B obtained in step (2a)maxBetweenness to nodes in networkiNormalization is carried out to obtain normalized node index bi，
Figure BDA0002246039860000021
(2c) Marking the time delay of the link j on a time expansion diagram, and obtaining the maximum value of the current network link time delay according to the following rules: t ismax＝max{Tj|j∈E}；
(2d) Using T obtained in step (2c)maxDelay T for linkjNormalization is carried out to obtain normalized network link time delay tj，
Figure BDA0002246039860000031
(2e) Using normalized betweenness biAnd normalized link delay tjObtaining the betweenness-time delay normalization index w of the link jj：
wj＝bi+tj，i∈V,j∈E
Wherein, the node i is a terminal node of the link j;
(2f) normalizing the index w of the betweenness and the time delay obtained in the step (2e)jMarked on the link j;
(3) defining a source node set S ═ { i | i ∈ V }, setting the initial number N of the set elements to be 0, and counting the total number N of the network nodes;
(4) randomly selecting a node as a current source node;
(5) judging whether the current source node belongs to a source node set S:
if the current node does not belong to the source node set S, adding the current node into the source node set S, and updating the number n of elements of the source node set to be n + 1;
otherwise, returning to the step (4) to reselect the node;
(6) judging the element number N in the source node set S and the total number N of the network nodes: if N is less than N, executing the step (7); otherwise, executing step (9);
(7) starting with a current node as a source node, taking an betweenness-time delay normalization index w on a link as a link weight, and solving a betweenness-time delay shortest path tree T to other nodes in the network by utilizing a Dijkstra algorithm;
(8) updating the betweenness information of nodes on each path l on the shortest path tree T and the betweenness-time delay index information on the link:
(8a) updating intermediate node betweenness information B on betweenness-time delay shortest path liIs Bi'；
(8b) Updating the betweenness-time delay normalization information w of the link j on the betweenness-time delay shortest path ljIs wj'；
(9) Judging whether all nodes in the network are added into the source node set S: if the number of the current S set elements is less than the total number N of the network nodes, namely N is less than N, all the node nodes in the network are not added into the set S, and the step (4) is returned; otherwise, the nodes are all added into S, the construction of the betweenness-delay shortest paths among all the points of the network is completed, and the betweenness-delay shortest paths among the nodes of the network are output.
The invention has the following advantages:
1. because the time-varying characteristic of the time-varying network is considered, the shortest route which guarantees elasticity can be searched for satellite networks with time-varying attributes, such as small satellite formation, remote sensing satellites and small constellations;
2. because the node betweenness is converted into a part of the link weight, the network positions of the nodes can be balanced when the method is used for constructing the paths between the time-varying network node pairs;
3. because the normalized node betweenness and the link time delay are combined to form the link weight, the invention restricts the construction of the shortest path between the time-varying network node pairs, thereby avoiding the problem of overhigh node criticality while ensuring the low time delay of the path and reducing the influence on the time-varying network communication performance when the node fails.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a time expansion diagram based on betweenness in the present invention;
FIG. 3 is a time expansion diagram for the initialization of betweenness in the present invention;
FIG. 4 is a time expansion diagram of the midamble-delay normalization of the present invention;
FIG. 5 shows a node according to the present invention
Figure BDA0002246039860000042
An betweenness-delay shortest path tree graph;
FIG. 6 is a node in the present invention
Figure BDA0002246039860000043
The related betweenness information in the betweenness-time delay shortest path tree is updated;
FIG. 7 shows a node according to the present invention
Figure BDA0002246039860000045
The betweenness-time delay shortest path tree diagram;
FIG. 8 is a node in the present inventionThe related betweenness information in the betweenness-time delay shortest path tree is updated.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, the implementation steps of the invention are as follows:
step one, time interval communication relation and initialization of a time-varying network.
The time-varying network time-period connectivity is usually represented by a fast graph, a time expansion graph and a time aggregation graph, in this example, the time expansion graph G ═ (V, E) represents the time-varying network time-period connectivity, and the links of G are respectively labeled with link delays TjAnd node betweenness BiWhere i ∈ V, j ∈ E, V denotes a node in the network, and E denotes a link in the network, as shown in fig. 2;
node betweenness BiInitialized to 0, starting with a value representing the node i index, i.e. 0
Figure BDA0002246039860000041
As shown in fig. 3.
And step two, constructing a node betweenness-time delay normalization index on the time expansion graph G.
(2.1) obtaining the maximum value of the betweenness of the current network nodes on the time expansion graph G: b ismax＝max{Bi|i∈V}；
In this embodiment, the maximum betweenness B of network nodesmax＝0；
(2.2) utilizing maximum betweenness B of network nodesmaxBetweenness to nodes in networkiNormalization is carried out to obtain normalized node index bi：
In this embodiment, the maximum betweenness B of network nodesmaxB is 0i＝0；
(2.3) marking the time delay of the link j on a time expansion diagram, and obtaining the maximum value of the current network link time delay according to the following rules: t ismax＝max{Tj|j∈E}；
In this embodiment, the maximum link delay Tmax＝6；
(2.4) Using T obtained in step (2c)maxDelay T for linkjNormalization is carried out to obtain normalized network link time delay tj，
Figure BDA0002246039860000051
In this embodiment, the maximum link delay Tmax＝6，
Figure BDA0002246039860000052
To calculate the linkThe normalized link delay is taken as an example,
Figure BDA0002246039860000054
(2.5) Using the normalization index biAnd normalized link delay tjObtaining the betweenness-time delay normalization index w of the link jj：
wj＝bi+tj，i∈V,j∈E
Wherein, the node i is a terminal node of the link j;
this embodiment, using the formula wj＝bi+tjI belongs to V, j belongs to E and respectively calculates the betweenness-time delay normalization index of the link j so as to calculate the link
Figure BDA0002246039860000055
The betweenness-time delay normalization index is as follows:
Figure BDA0002246039860000056
similarly, calculating the betweenness-time delay normalization indexes of all links;
(2.6) normalizing the index w of the betweenness and the time delay obtained in the step (2.5)jMarked on the link j;
in this embodiment, the index w for normalization of the number of bits-delay is marked below or on the right side of the time expansion graph link jjAs shown in fig. 4.
And step three, defining a source node set and selecting the current source node.
Defining a source node set S ═ { i | i ∈ V }, setting the initial number N of the set elements to be 0, and counting the total number N of the network nodes;
and randomly selecting any one node as the current source node.
In this embodiment, a source node set S is defined, initiallyThe set number N is 0, and the total number N of the network nodes is counted to be 9; randomly selecting nodes
Figure BDA0002246039860000062
As the current source node.
Step four, judging whether the current source node belongs to a source node set S:
if the current node does not belong to the source node set S, adding the current node into the source node set S, and updating the number n of elements of the source node set to be n + 1;
otherwise, returning to the step three, and reselecting the current node.
In this embodiment, the currently selected source node
Figure BDA0002246039860000063
Then the node is connected
Figure BDA0002246039860000064
Into the source node set S, i.e.
Figure BDA0002246039860000065
And updates the number n +1 + 0+1 of elements of the source node set S to 1.
Step five, judging the element number N in the source node set S and the total number N of the network nodes: if N is less than N, executing step six; otherwise, executing step eight;
in this embodiment, if the number N of elements in the current source node set S is 1 and the total number N of network nodes is 9, step six is executed.
And step six, starting from the current node serving as a source node, and normalizing the index w by using the betweenness-time delay on the link jjAnd (4) solving the betweenness-time delay shortest path tree T to other nodes in the network by utilizing a Dijkstra algorithm for the link weight.
The solving process is as follows:
(6.1) initially, dividing nodes in the network into two parts, namely a selected node set P and a remaining node set U, respectively, and assuming that P only contains a current source node a, namely P ═ a };
in this embodiment, the current source node is
Figure BDA0002246039860000066
Therefore, it is not only easy to use
Figure BDA0002246039860000067
(6.2) normalization of the indicator w with an index of betweenness-time delayjThe value is used as a link weight between nodes and represents the distance between the nodes;
(6.3) forming a residual node set by nodes except the current source node A: and if any rest node B belongs to U, judging whether a link j exists between the node A and the node B:
if there is a link j, the distance between the node a and the node B is: w is a<A,B>＝wj；
Otherwise, the distance between the node A and the node B is infinity;
in this embodiment, the remaining node sets
Figure BDA0002246039860000068
Figure BDA0002246039860000071
At τ for nodes A, B, C, respectively1，τ2，τ3Characterization of the time period, because of the nodes
Figure BDA0002246039860000072
To the node
Figure BDA0002246039860000073
Presence link
Figure BDA0002246039860000074
Therefore, it is not only easy to use
Figure BDA0002246039860000075
And
Figure BDA0002246039860000076
at a distance of
Figure BDA0002246039860000077
Figure BDA0002246039860000078
In the same way, obtaining the node
Figure BDA0002246039860000079
Distances from other nodes in the remaining node set U;
(6.4) selecting a node K with the minimum distance A from the residual node set UtIs a reaction of KtAdding the obtained data into a selected node set P to obtain A to KtShortest path length of (2): w is a<A,Kt>；
In this embodiment, the distance is selected from the remaining node set U
Figure BDA00022460398600000710
Smallest node becauseTo
Figure BDA00022460398600000712
And
Figure BDA00022460398600000713
has the same and minimum distance of
Figure BDA00022460398600000714
Therefore, is at
Figure BDA00022460398600000715
And
Figure BDA00022460398600000716
optionally a node is added to the set P, assuming that it will be
Figure BDA00022460398600000717
Adding into the set P to obtain
Figure BDA00022460398600000718
To
Figure BDA00022460398600000719
Shortest path length of (2):
Figure BDA00022460398600000720
(6.5) with KtFor a new intermediate point, the distance from the node A to each node in the residual node set U is modified, and the node A is judged to be KtIs the distance from the intermediate point to the node B and does not pass through KtDistance of the nodes:
if passing KtIs not through KtIf the distance is small, the modified node B distance value is:
w<A,B>＝w<A,Kt>+w<Kt,B>；
otherwise, the distance value of the node B is not modified;
this embodiment is to
Figure BDA00022460398600000721
As a new intermediate point, the distance between each node in the set U is modifiedFrom due to
Figure BDA00022460398600000722
Is added only in such a way that
Figure BDA00022460398600000723
To
Figure BDA00022460398600000724
Is reduced from ∞ to 5/6, i.e.
Figure BDA00022460398600000725
Therefore, modify
Figure BDA00022460398600000726
Distance of 5/6; the distance values of other nodes in the U are not modified;
(6.6) judging whether the selected node set P contains all the nodes:
if P already contains all nodes, the construction of the shortest path tree T of the node A is completed;
otherwise, repeating (6.4) to (6.5);
present embodiment, Current Collection
Figure BDA00022460398600000727
If not, repeating (6.4) to (6.5) until P contains all nodes, which means completion
Figure BDA00022460398600000728
The result of constructing the shortest path tree T of nodes is shown in fig. 5.
Step seven, updating the betweenness information of the nodes on each path l on the shortest path tree T and the betweenness-time delay index information on the link:
(7.1) updating the intermediate node betweenness information B on the betweenness-time delay shortest path liIs Bi'：
(7.1.1) obtaining an betweenness-delay shortest path set L ═ L from the source node A to the other m nodes according to the w shortest path tree T obtained in the step (6.6)1,l2,...,lx,...,lmIn which lxFor the xth IDT-DTX path, lx＝<A,K1,K2,...,Kt,...,B>Representing an betweenness-delay shortest path from node A to node B, K1K2…KtIs path lxX is e [1, m ∈)]M is less than or equal to N-1, t is less than or equal to N-2, and m and t are independent and are positive integers;
this embodiment is based on the node
Figure BDA00022460398600000811
The tree T of the shortest path between the number and the time delay is obtained
Figure BDA0002246039860000081
Set of betweenness-delay shortest paths L ═ L to the remaining 7 nodes1,l2,...,lx,...,l7And (c) the step of (c) in which,
Figure BDA0002246039860000082
Figure BDA0002246039860000083
(7.1.2) defining a set K for storing intermediate number-time delay shortest path intermediate nodes, and enabling a path L in a set L to be in a setxIntermediate node K oftAdding the intermediate nodes into the set K and counting each intermediate node K in the set KtThe number of occurrences of (c) is respectively used as a new node betweenness Bi'；
In this embodiment, a set K for storing intermediate nodes of the betweenness-delay shortest path is defined, and a path L in a set L is definedxIs added to the set K, i.e.
Figure BDA0002246039860000084
Counting the occurrence frequency of each intermediate node in the set K, and respectively taking the occurrence frequency as a new betweenness B of the nodei', i.e. that
Figure BDA0002246039860000085
Figure BDA0002246039860000086
As shown in fig. 6;
(7.2) updating the betweenness-time delay normalization information w of the link j on the betweenness-time delay shortest path ljIs wj'；
(7.2.1) according to the updated node betweenness Bi', updating the maximum value B of the node betweennessmax'：
Bmax'＝max{Bi'|i∈V}；
In this embodiment, the maximum value of the node betweenness is updated
Figure BDA0002246039860000087
(7.2.2) according to the updated Bi', updating the index b of normalized nodei'，
In this embodiment, the normalized node index is updated
Figure BDA0002246039860000089
In the same way, the method for preparing the composite material,
(7.2.3) based on the updated normalized betweenness bi' and normalized link delay tjUpdating the index wj'：
wj'＝bi'+tj，i∈V,j∈E
Wherein, the node i is a terminal node of the link j;
in this embodiment, the index w of the link j is updated according to the number-delay normalization indexj'＝bi'+tjIn a link
Figure BDA0002246039860000092
For the purpose of example only,
Figure BDA0002246039860000093
similarly, the betweenness-time delay normalization indexes of other links can be obtained;
(7.2.4) marking the updated index w on the link j of the time expansion graph G ═ V, E)j', as shown in FIG. 6.
And step eight, outputting the betweenness-time delay shortest path between the network nodes.
Judging whether all nodes in the network are added into the source node set S:
if the number of the current S set elements is less than the total number N of the network nodes, namely N is less than N, all the node nodes in the network are not added into the set S, and the step III is returned;
otherwise, the nodes are all added into S, the construction of the betweenness-delay shortest paths among all the points of the network is completed, and the betweenness-delay shortest paths among the nodes of the network are output.
In this embodiment, if the number num of the current S set elements is 1 and less than the total number N of the network nodes is 9, then all the node nodes in the network are not all added to the set S, the process returns to step three, and continues to find the betweenness-delay shortest path among the remaining nodes, and it is assumed that the next node to be selected as the source node is the next node
Figure BDA0002246039860000094
Will be provided withAdding the source node into the source node set S, and executing the source node set S
Figure BDA0002246039860000096
By the same operation, can obtain
Figure BDA0002246039860000097
The tree of the betweenness-delay shortest path, as shown in fig. 7;
in the same way, pair
Figure BDA0002246039860000098
The node betweenness related information of the path on the betweenness-time delay shortest path tree is updated to obtain
Figure BDA0002246039860000099
The related betweenness information in the betweenness-time delay shortest path tree is updated as shown in fig. 8;
repeating the source node selection operation until the node
Figure BDA00022460398600000910
And adding all nodes into the source node set S to obtain shortest path trees of all nodes, obtaining the betweenness-delay shortest paths between all the point pairs in the network according to the shortest path trees of all the nodes, and outputting the betweenness-delay shortest paths between the nodes of the network.

Claims (4)

1. A time-varying network shortest routing method for guaranteeing elasticity is characterized by comprising the following steps:
(1) and (V, E) representing the time interval connectivity relation of the time-varying network by using a time expansion graph G, and respectively marking the link time delay T on the link of GjAnd node betweenness BiWherein i belongs to V, j belongs to E, V represents a node in the network, and E represents a link in the network; node betweenness BiInitializing 0, which indicates that the median value of the node i is 0;
(2) constructing a node betweenness-time delay normalization index on a time expansion diagram:
(2a) the betweenness B of the node iiAnd (3) marking the maximum value on the time expansion diagram, and obtaining the maximum value of the betweenness of the current network node according to the following rules: b ismax＝max{Bi|i∈V}；
(2b) Using B obtained in step (2a)maxBetweenness to nodes in networkiNormalization is carried out to obtain normalized node index bi，
Figure FDA0002246039850000011
(2c) Marking the time delay of the link j on a time expansion diagram, and obtaining the maximum value of the current network link time delay according to the following rules: t ismax＝max{Tj|j∈E}；
(2d) Using T obtained in step (2c)maxDelay T for linkjNormalization is carried out to obtain normalized network link time delay tj，
Figure FDA0002246039850000012
(2e) Using normalized betweenness biAnd normalized link delay tjObtaining the index w of the betweenness-time delay normalizationj：
wj＝bi+tj，i∈V,j∈E
Wherein, the node i is a terminal node of the link j;
(2f) marking the betweenness-time delay normalization index obtained in the step (2e) on a link j;
(3) defining a source node set S ═ { i | i ∈ V }, setting the initial number N of the set elements to be 0, and counting the total number N of the network nodes;
(4) randomly selecting a node as a current source node;
(5) judging whether the current source node belongs to a source node set S:
if the current node does not belong to the source node set S, adding the current node into the source node set S, and updating the number n of elements of the source node set to be n + 1;
otherwise, returning to the step (4) to reselect the node;
(6) judging the element number N in the source node set S and the total number N of the network nodes: if N is less than N, executing the step (7); otherwise, executing step (9);
(7) starting from the current node as the source node, and normalizing the index w by the betweenness-time delay on the link jjSolving an betweenness-time delay shortest path tree T to other nodes in the network by utilizing a Dijkstra algorithm for link weight;
(8) updating the betweenness information of nodes on each path l on the shortest path tree T and the betweenness-time delay index information on the link:
(8a) updating intermediate node betweenness information B on betweenness-time delay shortest path liIs Bi'；
(8b) Updating the betweenness-time delay normalization information w of the link j on the betweenness-time delay shortest path ljIs wj'；
(9) Judging whether all nodes in the network are added into the source node set S: if the number of the current S set elements is less than the total number N of the network nodes, namely N is less than N, all the node nodes in the network are not added into the set S, and the step (4) is returned; otherwise, the nodes are all added into S, the construction of the betweenness-delay shortest paths among all the points of the network is completed, and the betweenness-delay shortest paths among the nodes of the network are output.
2. The method of claim 1, wherein the Dijkstra algorithm is used in (7) to solve the betweenness-delay shortest path tree from the current source node to other nodes, and the following is implemented:
(7a) initially, dividing nodes in a network into two parts, namely a selected node set P and a residual node set U, and assuming that P only contains a current source node a, namely P is { a };
(7b) normalization of the indicator w by an index-delayjThe value is used as a link weight between nodes and represents the distance between the nodes;
(7c) and (3) forming a residual node set U (the rest nodes) by using nodes except the node A, assuming that the node B belongs to the U, and judging whether a link j exists between the node A and the node B:
if there is a link j, the distance between nodes a and B is: w is a<A,B>＝wj；
Otherwise, the distance between the nodes A and B is infinity;
(7d) selecting a node K with the minimum distance A from the residual node set UtIs a reaction of KtAdding to P to obtain A to KtShortest path length of (2): w is a<A,Kt>；
(7e) With KtFor a new intermediate point, the distance from the node A to each node in the set U is modified, and the node A is judged to be KtIs composed ofDistance between point and node B and not passing through KtDistance of the nodes:
if passing KtIs not through KtIf the distance is small, the modified node B distance value is:
w<A,B>＝w<A,Kt>+w<Kt,B>；
otherwise, the distance value of the node B is not modified;
(7f) judging whether the P contains all nodes:
if P already contains all nodes, the construction of the shortest path tree T of the node A is completed;
otherwise, repeating (7d) to (7 e).
3. The method of claim 1, wherein B is betweenness to nodes in (8a)iThe update is realized as follows:
(8a1) obtaining an betweenness-time delay shortest path set L from the source node A to the other m nodes according to the w shortest path tree T obtained in the step (7f)1,l2,...,lx,...,lmIn which lxFor the xth IDT-DTX path, lx＝<A,K1,K2,...,Kt,...,B>Representing an betweenness-delay shortest path from node A to node B, K1K2…KtIs path lxX is e [1, m ∈)]M is less than or equal to N-1, t is less than or equal to N-2, and m and t are independent and are positive integers;
(8a2) defining a set K for storing intermediate nodes of the betweenness-time delay shortest path, and combining the paths L in the set L (8a1)xIntermediate node K oftAdding the intermediate nodes into the set K and counting each intermediate node K in the set KtThe number of occurrences of (c) is respectively used as a new node betweenness Bi'；
(8a3) Marking a new node argument B on the time expansion graph G ═ V, Ei'。
4. The method of claim 1, wherein the step (8b) is performed by normalizing the indicator w for the betweenness and delay of the network nodesjUpdating and implementing methodThe following were used:
(8b1) according to the updated node betweenness Bi', obtaining the maximum value B of the updated node betweennessmax'：
Bmax'＝max{Bi'|i∈V}；
(8b2) According to updated Bmax' obtaining an updated normalized node betweenness index bi'，
Figure FDA0002246039850000041
(8b3) According to the updated normalized betweenness biNormalized link delay t of' and (2d)jObtaining an updated betweenness-time delay normalization index wj'：
wj'＝bi'+tj，i∈V,j∈E
Wherein, the node i is a terminal node of the link j;
(8b6) marking the updated betweenness-time delay normalization index w on the link j of the time expansion graph G ═ V, Ej'。
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