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CN110445715B - Method and device for monitoring and deploying flow in autonomous domain network - Google Patents

  • ️Tue Nov 16 2021

CN110445715B - Method and device for monitoring and deploying flow in autonomous domain network - Google Patents

Method and device for monitoring and deploying flow in autonomous domain network Download PDF

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Publication number
CN110445715B
CN110445715B CN201910622942.6A CN201910622942A CN110445715B CN 110445715 B CN110445715 B CN 110445715B CN 201910622942 A CN201910622942 A CN 201910622942A CN 110445715 B CN110445715 B CN 110445715B Authority
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node
path
deployment
routers
information table
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2019-07-11
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CN110445715A (en
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陈文龙
周媛媛
唐晓岚
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Capital Normal University
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  • 238000000034 method Methods 0.000 title claims abstract description 24
  • 230000007246 mechanism Effects 0.000 claims abstract description 43
  • 239000011159 matrix material Substances 0.000 claims abstract description 29
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/08Configuration management of networks or network elements
    • H04L41/0803Configuration setting
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L43/00Arrangements for monitoring or testing data switching networks
    • H04L43/08Monitoring or testing based on specific metrics, e.g. QoS, energy consumption or environmental parameters
    • H04L43/0876Network utilisation, e.g. volume of load or congestion level
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L45/00Routing or path finding of packets in data switching networks
    • H04L45/12Shortest path evaluation

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
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Abstract

本发明公开了一种自治域网络内流量监测部署方法及装置,方法包括:S1,获取自治域网络内的多个路由器,以多个路由器中的多个接入路由器中两个不同的接入路由器作为源节点和目的节点,求解源节点到目的节点的所有最短路径;S2,将所有最短路径记录在路径节点信息表,根据路径节点信息表生成多个路径关系矩阵;S3,对多个路径关系矩阵进行列求和,将和值最大的路径关系矩阵对应的节点作为部署节点来生成部署集合;S4,判断部署节点是否覆盖所有最短路径,不是,则在所有最短路径中移除包含部署节点的最短路径执行S2,是则S5;S5,在所有部署节点部署监测机制。该方法可以减小部署监测机制的路由器数量,减小内存开销与资源消耗。

Figure 201910622942

The invention discloses a flow monitoring deployment method and device in an autonomous area network. The method includes: S1, acquiring multiple routers in the autonomous area network, and using the multiple access routers in the multiple routers to access two different access routers. As the source node and the destination node, the router solves all the shortest paths from the source node to the destination node; S2, records all the shortest paths in the path node information table, and generates multiple path relationship matrices according to the path node information table; S3, for multiple paths The relationship matrix is column summed, and the node corresponding to the path relationship matrix with the largest sum value is used as the deployment node to generate the deployment set; S4, determine whether the deployment node covers all the shortest paths, if not, remove the deployment nodes from all the shortest paths. If the shortest path is S2, then S5; S5, deploy the monitoring mechanism on all deployment nodes. This method can reduce the number of routers deploying the monitoring mechanism, and reduce memory overhead and resource consumption.

Figure 201910622942

Description

Method and device for monitoring and deploying flow in autonomous domain network

Technical Field

The invention relates to the technical field of data monitoring, in particular to a method and a device for monitoring and deploying flow in an autonomous domain network.

Background

The monitoring of the network data flow can not only check the data flow condition between any two access routers in the network, but also judge network abnormity and attack, thereby ensuring the high-efficiency and reliable operation of the network.

Deploying a monitoring mechanism on a router within an autonomous domain network is an effective way to perform a comprehensive network traffic analysis. The data flow in a monitoring area can be achieved by deploying a monitoring mechanism on the routers in the autonomous domain network, and the work of extracting and monitoring the data flow is realized.

Disclosure of Invention

The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.

Therefore, an object of the present invention is to provide a method for deploying traffic monitoring in an autonomous domain network, which can reduce the number of routers deploying a monitoring mechanism, thereby reducing resource consumption.

The invention also aims to provide a flow monitoring deployment device in the autonomous domain network.

In order to achieve the above object, an embodiment of the present invention provides a method for monitoring and deploying traffic in an autonomous domain network, including:

s1, acquiring a plurality of routers in the autonomous domain network, and solving all shortest paths from a source node to a destination node by taking two different access routers in a plurality of access routers in the plurality of routers as the source node and the destination node;

s2, recording all the shortest paths in a path node information table, and generating a plurality of path relation matrixes according to the path node information table;

s3, performing column summation on the multiple path relation matrixes respectively, and generating a deployment set by taking the node corresponding to the path relation matrix with the maximum summation value as a deployment node;

s4, judging whether the deployment nodes in the deployment set cover all the shortest paths, if not, removing the shortest paths containing the deployment nodes from all the shortest paths, executing S2, and if so, executing S5;

s5, deploying monitoring mechanism at all deployment nodes of the deployment set.

The method for monitoring and deploying the flow in the autonomous domain network can consider the problem of cost required by deploying the monitoring mechanism, deploy the mechanism in routers which are as few as possible in the autonomous domain network, save resources, ensure that at least one router in an optimal path between any two access routers connected with an end system deploys the flow monitoring mechanism, effectively monitor the flow between any two access routers in the autonomous domain network, and ensure that the number of the routers which deploy the flow monitoring mechanism is minimum. Compared with the monitoring mechanism deployed in all routers, the number of routers for deploying the monitoring mechanism can be greatly reduced, and therefore resource consumption is reduced.

In addition, the traffic monitoring deployment method in the autonomous domain network according to the above embodiment of the present invention may further have the following additional technical features:

further, in an embodiment of the present invention, each row of the path information table corresponds to a different node, and each column represents a different shortest path P(i,j)When node rmExisting in the shortest path P(i,j)And when the path information table is in the middle, filling 1 in the cell corresponding to the path information table, otherwise, filling 0 in the cell.

Further, in an embodiment of the present invention, the path relation matrix is a single-row multi-column matrix generated for each row of digital values of the path node information table.

Further, in an embodiment of the present invention, when row and column sums are performed on the plurality of path relationship matrices, if there are a plurality of nodes with the largest sum, any one node is selected as the deployment node to join the deployment set.

Further, in one embodiment of the present invention, the plurality of routers within the autonomous domain network include the plurality of access routers and a plurality of intermediate nodes, and the shortest path is the shortest path from any access router to another access router through the plurality of intermediate nodes.

In order to achieve the above object, an embodiment of another aspect of the present invention provides an apparatus for monitoring and deploying traffic in an autonomous domain network, including:

the system comprises an acquisition module, a routing module and a routing module, wherein the acquisition module is used for acquiring a plurality of routers in an autonomous domain network, taking two different access routers in a plurality of access routers in the plurality of routers as a source node and a destination node, and solving all shortest paths from the source node to the destination node;

the generating module is used for recording all the shortest paths in a path node information table and generating a plurality of path relation matrixes according to the path node information table;

the summation module is used for carrying out column summation on the path relation matrixes respectively, and taking the node corresponding to the path relation matrix with the maximum summation value as a deployment node to generate a deployment set;

a judging module, configured to judge whether the deployment nodes in the deployment set cover all shortest paths;

a loop module, configured to remove a shortest path including the deployment node from all shortest paths when the deployment node in the deployment set does not cover all shortest paths, and then execute the generation module;

and the deployment module is used for deploying the monitoring mechanism at all the deployment nodes of the deployment set.

The traffic monitoring and deploying device in the autonomous domain network can consider the cost problem required by deploying the monitoring mechanism, deploy the mechanism in routers as few as possible in the autonomous domain network, save resources, ensure that at least one router in an optimal path between any two access routers connected with an end system deploys the traffic monitoring mechanism, effectively monitor the traffic between any two access routers in the autonomous domain network, and ensure that the number of the routers deploying the traffic monitoring mechanism is minimum. Compared with the monitoring mechanism deployed in all routers, the number of routers for deploying the monitoring mechanism can be greatly reduced, and therefore resource consumption is reduced.

In addition, the traffic monitoring deployment device in the autonomous domain network according to the above embodiment of the present invention may further have the following additional technical features:

further, in an embodiment of the present invention, each row of the path information table corresponds to a different node, and each column represents a different shortest path P(i,j)When node rmExisting in the shortest path P(i,j)And when the path information table is in the middle, filling 1 in the cell corresponding to the path information table, otherwise, filling 0 in the cell.

Further, in an embodiment of the present invention, the path relation matrix is a single-row multi-column matrix generated for each row of digital values of the path node information table.

Further, in an embodiment of the present invention, when row and column sums are performed on the plurality of path relationship matrices, if there are a plurality of nodes with the largest sum, any one node is selected as the deployment node to join the deployment set.

Further, in one embodiment of the present invention, the plurality of routers within the autonomous domain network include the plurality of access routers and a plurality of intermediate nodes, and the shortest path is the shortest path from any access router to another access router through the plurality of intermediate nodes.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

fig. 1 is a flowchart of a method for monitoring and deploying traffic in an autonomous domain network according to an embodiment of the present invention;

FIG. 2 is an exemplary topology diagram of an autonomous domain according to one embodiment of the invention;

fig. 3 is a flow chart of a method for monitoring and deploying traffic in an autonomous domain network according to an embodiment of the present invention;

fig. 4 is a schematic structural diagram of a flow monitoring deployment device in an autonomous domain network according to an embodiment of the present invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.

The following describes a method and a device for monitoring and deploying traffic in an autonomous domain network according to an embodiment of the present invention with reference to the accompanying drawings.

First, a traffic monitoring deployment method in an autonomous domain network according to an embodiment of the present invention will be described with reference to the drawings.

Before introducing the method, the meaning of the formula symbol is defined:

g (R, E): the autonomous domain network comprises an autonomous domain network, wherein R is a router set, and E is a node set.

P(i,j): access router riTo another access router rjThe shortest path of (2).

U: a collection of nodes (routers) deploying a detection mechanism.

Fig. 1 is a flowchart of a method for monitoring and deploying traffic in an autonomous domain network according to an embodiment of the present invention.

As shown in fig. 1, the method for monitoring and deploying the flow rate in the autonomous domain network includes the following steps:

step S1, acquiring multiple routers in the autonomous domain network, and solving all shortest paths from the source node to the destination node by using two different access routers in multiple access routers in the multiple router nodes as the source node and the destination node.

Further, all routers within the autonomous domain network are obtained, the routers within the autonomous domain network may be represented as including a plurality of access routers (edge nodes) and a plurality of intermediate nodes, and the shortest path is the shortest path from an access router (edge node) to another access router (another edge node) through the plurality of intermediate nodes.

It can be understood that many routers are included in the autonomous domain network, the access router is a router capable of directly performing data packet transmission with routers in other autonomous domain networks, the access router may also be referred to as an edge node, and first obtains all the access routers in the autonomous domain network, and respectively uses any two of the access routers riAnd rjFor the source node and the destination node, and finding the shortest path from all possible source nodes to possible destination nodes, using P(i,j)Is shown byWhere i ≠ j.

As shown in fig. 2, A, B, C, D, E, F are routers in an autonomous domain network, wherein A, C, D, F four routers are access routers (also called edge nodes), and B, E are intermediate nodes. Calculating all shortest paths using A, C, D, F different two of four access routers as source node and destination node, and using P(i,j)And (4) showing. For example, when access router A is the source node and access router D is the destination node, the shortest path is represented as P(A,D)

Step S2, record all shortest paths in the path node information table, and generate a plurality of path relationship matrices according to the path node information table.

Further, in one embodiment of the present invention, each row of the path information table corresponds to a different node, and each column represents a different shortest path P(i,j)When node rmExisting in the shortest path P(i,j)And when the path information table is in the middle, filling 1 in the corresponding cell of the path information table, otherwise, filling 0 in the corresponding cell of the path information table.

In particular, all shortest paths P to be calculated(i,j)The passed routing nodes are recorded respectively and filled in the path node information table. All shortest path information recorded according to fig. 2 is shown in table 1, and table 1 is a path information node table.

TABLE 1

Figure BDA0002126106360000051

As shown in FIG. 2, the optimal path P is calculated for all 4 access routers (edge nodes) as the source node and the destination node(i,j)Simultaneously obtaining each P(i,j)And fills it in table 1. For example, the shortest path from access router a to access router C is: A-B-C. Thus, with P(A,C)The corresponding node A, B, C is filled with 1 and D, E, F is filled with 0.

Further, in one embodiment of the present invention, the path relation matrix is a single row and multiple column matrix generated for each row digital value of the path node information table.

The path relation matrix of node A, C can be expressed as P according to Table 1A=(1 1 1 1 0 0 1 0 0 1 0 0);PC= (100111010010). The path relation matrix is a matrix with a single row and multiple columns.

Step S3, performing column summation on each of the plurality of path relation matrices, and generating a deployment set using the node corresponding to the path relation matrix with the largest sum as a deployment node.

After the path relation matrix of each node is obtained according to the path node information table, column summation is carried out on the path relation matrix corresponding to each node, the node corresponding to the path relation matrix with the maximum sum value is taken as a deployment node to be placed in a deployment set, and the deployment node can be an edge node or an intermediate node.

Further, in an embodiment of the present invention, when row and column sums are performed on a plurality of path relationship matrices, if a plurality of nodes with the largest sum value are provided, any one node is selected as a deployment node to join in a deployment set.

For example, as can be seen from the topology of fig. 2 and the path node information table of table 1, the sum of the path relationship matrices corresponding to node a is 6, the sum of the path relationship matrices corresponding to node B is 6, the sum of the path relationship matrices corresponding to node C is 6, the sum of the path relationship matrices corresponding to node D is 6, the sum of the path relationship matrices corresponding to node E is 10, and the sum of the path relationship matrices corresponding to node F is 6, so that the node with the largest sum is E. Therefore, node E is added to deployment set U.

Step S4, determine whether the deployment nodes in the deployment set cover all shortest paths, if not, remove the shortest paths including the deployment nodes from all shortest paths, execute S2, if yes, execute S5.

And judging the deployment nodes in the deployment set, and judging whether all the deployment nodes cover all the shortest paths, namely, each shortest path at least comprises one deployment node, if the deployment nodes do not cover all the shortest paths, namely, no deployment node exists in the shortest paths, removing the shortest paths containing the deployment nodes from all the shortest paths, and returning to execute S2 until the deployment nodes cover all the shortest paths.

In the topology shown in fig. 2, if the deployment node calculated in step S3 is E, and there is no deployment node in the shortest paths, the shortest paths included in the node E are removed from all the shortest paths, and the remaining shortest paths are performed in steps S2-S4.

Specifically, the path node information table is updated after the shortest path including the node E is removed, as shown in table 2.

TABLE 2

Figure BDA0002126106360000061

For example, after removing the path where the node E is located in table 1, the path node information table is shown in table 2. The path relation matrix of each node is re-represented. At this point, the path relationship matrix for node A, B, C may be updated as: and P is (11). And the path relation matrix for node D, E, F may be updated to P ═ 00. Any one of the three nodes may be selected A, B, C to join in the set U at this point.

Step S5, a monitoring mechanism is deployed at all deployment nodes of the deployment set.

After the deployment nodes cover all shortest paths through the steps of steps S1-S4, the monitoring mechanism is deployed at all deployment nodes.

The deployed monitoring mechanism may be a traffic monitoring mechanism, such as a NetFlow mechanism, or other monitoring mechanism.

As shown in fig. 3, a process for deploying a traffic monitoring mechanism within an autonomous domain network is shown. The number of routers for deploying the monitoring mechanism can be reduced to a great extent through the process, so that the resource consumption is reduced.

According to the method for monitoring and deploying the flow in the autonomous domain network, which is provided by the embodiment of the invention, the problem of cost required by deploying the monitoring mechanism can be considered, the mechanism is deployed in the routers which are as few as possible in the autonomous domain network, resources are saved, and at least one router in the optimal path between any two access routers connected with an end system is ensured to deploy the flow monitoring mechanism, so that the flow between any two access routers in the autonomous domain network can be effectively monitored, and the quantity of the routers which deploy the flow monitoring mechanism is ensured to be minimum. Compared with the monitoring mechanism deployed in all routers, the number of routers for deploying the monitoring mechanism can be greatly reduced, and therefore resource consumption is reduced.

Next, a traffic monitoring deployment device in an autonomous domain network according to an embodiment of the present invention is described with reference to the drawings.

Fig. 4 is a schematic structural diagram of a flow monitoring deployment device in an autonomous domain network according to an embodiment of the present invention.

As shown in fig. 4, the device for monitoring and deploying traffic in an autonomous domain network includes: an

acquisition module

100, a

generation module

200, a

summation module

300, a

determination module

400, a

loop module

500, and a

deployment module

600.

The obtaining

module

100 is configured to obtain a plurality of routers in an autonomous domain network, and solve all shortest paths from a source node to a destination node by using two different access routers in a plurality of access routers in the plurality of routers as the source node and the destination node.

The

generating module

200 is configured to record all shortest paths in a path node information table, and generate a plurality of path relationship matrices according to the path node information table.

And a summing

module

300, configured to perform column summation on the multiple path relation matrices, and generate a deployment set by using a node corresponding to the path relation matrix with the largest sum value as a deployment node.

The determining

module

400 is configured to determine whether deployment nodes in the deployment set cover all shortest paths.

The

loop module

500 is configured to remove the shortest paths including the deployment nodes from all the shortest paths and then execute the generation module when the deployment nodes in the deployment set do not cover all the shortest paths.

A

deployment module

600 configured to deploy the monitoring mechanism at all deployment nodes of the deployment set.

Further, in one embodiment of the present invention, each row of the path information table corresponds to a different node, and each column represents a different shortest path P(i,j)When node rmExisting in the shortest path P(i,j)And when the path information table is in the middle, filling 1 in the corresponding cell of the path information table, otherwise, filling 0 in the corresponding cell of the path information table.

Further, in one embodiment of the present invention, the path relation matrix is a single row and multiple column matrix generated for each row digital value of the path node information table.

Further, in an embodiment of the present invention, when row and column sums are performed on a plurality of path relationship matrices, if a plurality of nodes with the largest sum value are provided, any one node is selected as a deployment node to join in a deployment set.

Further, in one embodiment of the present invention, the plurality of routers within the autonomous domain network include a plurality of access routers and a plurality of intermediate nodes, and the shortest path is the shortest path from any access router to another access router through the plurality of intermediate nodes.

It should be noted that the explanation of the embodiment of the traffic monitoring deployment method in the autonomous domain network is also applicable to the device of the embodiment, and details are not described here.

According to the traffic monitoring deployment device in the autonomous domain network provided by the embodiment of the invention, the problem of cost required by the deployment of the monitoring mechanism can be considered, the mechanism is deployed in the routers which are as few as possible in the autonomous domain network, resources are saved, and at least one router in the optimal path between any two access routers connected with an end system is ensured to deploy the traffic monitoring mechanism, so that the traffic between any two access routers in the autonomous domain network can be effectively monitored, and the quantity of the routers which deploy the traffic monitoring mechanism is ensured to be minimum. Compared with the monitoring mechanism deployed in all routers, the number of routers for deploying the monitoring mechanism can be greatly reduced, and therefore resource consumption is reduced.

Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.

Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (6)

1. A method for monitoring and deploying flow in an autonomous domain network is characterized by comprising the following steps:

s1, acquiring a plurality of routers in the autonomous domain network, and solving all shortest paths from a source node to a destination node by taking two different access routers in a plurality of access routers in the plurality of routers as the source node and the destination node;

s2, recording all the shortest paths in a path node information table, and generating a plurality of path relation matrixes according to the path node information table; wherein each row of the path node information table corresponds to a different node, and each column represents a different nodeShortest path P of(i,j)When node rmExisting in the shortest path P(i,j)When the path node information table is in the middle, filling 1 in the cell corresponding to the path node information table, otherwise, filling 0 in the cell; the path relation matrix is a single-row multi-column matrix generated by each row of digital values of the path node information table;

s3, performing column summation on the multiple path relation matrixes respectively, and generating a deployment set by taking the node corresponding to the path relation matrix with the maximum summation value as a deployment node;

s4, judging whether the deployment nodes in the deployment set cover all the shortest paths, if not, removing the shortest paths containing the deployment nodes from all the shortest paths, executing S2, and if so, executing S5;

s5, deploying monitoring mechanism at all deployment nodes of the deployment set.

2. The method of claim 1,

and when row-column summation is carried out on the path relation matrixes, if the node with the maximum summation value is a plurality of nodes, selecting any node as the deployment node to join the deployment set.

3. The method of claim 1,

the plurality of routers in the autonomous domain network comprise the plurality of access routers and a plurality of intermediate nodes, and the shortest path is the shortest path from any access router to another access router through the plurality of intermediate nodes.

4. A flow monitoring deployment device in an autonomous domain network is characterized by comprising:

the system comprises an acquisition module, a routing module and a routing module, wherein the acquisition module is used for acquiring a plurality of routers in an autonomous domain network, taking two different access routers in a plurality of access routers in the plurality of routers as a source node and a destination node, and solving all shortest paths from the source node to the destination node;

the generating module is used for recording all the shortest paths in a path node information table and generating a plurality of path relation matrixes according to the path node information table; wherein each row of the path node information table corresponds to a different node, and each column represents a different shortest path P(i,j)When node rmExisting in the shortest path P(i,j)When the path node information table is in the middle, filling 1 in the corresponding cell of the path node information table, otherwise, filling 0 in the corresponding cell of the path node information table; the path relation matrix is a single-row multi-column matrix generated by each row of digital values of the path node information table;

the summation module is used for carrying out column summation on the path relation matrixes respectively, and taking the node corresponding to the path relation matrix with the maximum summation value as a deployment node to generate a deployment set;

a judging module, configured to judge whether the deployment nodes in the deployment set cover all shortest paths;

a loop module, configured to remove a shortest path including the deployment node from all shortest paths when the deployment node in the deployment set does not cover all shortest paths, and then execute the generation module;

and the deployment module is used for deploying the monitoring mechanism at all the deployment nodes of the deployment set.

5. The apparatus of claim 4,

and when row-column summation is carried out on the path relation matrixes, if the node with the maximum summation value is a plurality of nodes, selecting any node as the deployment node to join the deployment set.

6. The apparatus of claim 4,

the plurality of routers in the autonomous domain network comprise the plurality of access routers and a plurality of intermediate nodes, and the shortest path is the shortest path from any access router to another access router through the plurality of intermediate nodes.

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