A method and system for evaluating connectivity elasticity of a local area network system

Abstract

The present invention discloses a method and system for evaluating the connectivity elasticity of a local area network system. The method includes: formalizing modeling of the local area network system according to all nodes and their connectivity relationships in the local area network system; establishing a probabilistic reliability model to describe the hardware in the local area network system, and using a binary decision diagram method to calculate the probabilistic reliability of the hardware in the local area network system; calculating the probabilistic reliability of the software in the local area network system; and combining the probabilistic reliability of the hardware and software to calculate the connectivity opportunity reliability of each minimum path, and then calculating the upper bound of the connectivity opportunity reliability of the local area network system, and using it as the connectivity opportunity reliability of the local area network system; calculating the maximum flow of each minimum path, and then obtaining the maximum flow of the local area network system; and establishing a connectivity elasticity model for the local area network system. The present invention takes into account the functional failures of hardware devices and software in the local area network, and is helpful for quantitatively analyzing the random process of fluctuations in network task capabilities under the influence of connectivity failures.

Description

Technical Field

[0001] The present invention relates to the field of reliability assessment of local area network systems, and in particular to a method and system for assessing connectivity elasticity of a local area network system. Background Art

[0002] With the advent of the information age, local area network systems are playing an increasingly important role. In order to achieve rapid and accurate interaction of large amounts of information, it is necessary to build a local area network system with high reliability and timeliness. When a local area network is impacted, the amount of network data may be much greater than the design level, resulting in network congestion and system performance will inevitably decline. In addition, during the use of network equipment, various hardware components of the network will age and degrade, which will also lead to the loss of network redundancy, thereby affecting the normal operation of the local area network system.

[0003] System resilience can characterize the performance of a local area network system. The system is often impacted during stable operation and recovers after a period of time by restarting switches, servers, etc. The definition of network system connectivity resilience is: the system is impacted, and the system tasks can resist the impact within a specified time so that the tasks issued by the nodes in the system can still be transmitted to the target node, and the system connectivity performance can quickly recover to the original level after the impact ends. By analyzing the connectivity resilience of the local area network system when a connectivity failure occurs, the performance of the local area network system can be quantitatively evaluated.

[0004] Therefore, it is necessary to consider the connectivity resilience of the local area network system when a connectivity failure occurs, and to master the evaluation method of the connectivity resilience of the local area network system, which is of great significance and role in predicting failures of the local area network system and thus ensuring that the local area network system can complete the prescribed tasks normally.

[0005] The present invention is to solve the following technical problems:

[0006] (1) To solve the problem of comprehensively analyzing the reliability model of the hardware connectivity of the local area network system based on probability measurement while considering the hardware failure mechanism.

[0007] (2) Solve the problem of establishing the connectivity elasticity model of the system when the network system traffic input meets the uncertainty measurement. Summary of the invention

[0008] The technical problem to be solved by the present invention is to provide a method and system for evaluating the connectivity elasticity of a local area network system in view of the defects in the prior art.

[0009] The technical solution adopted by the present invention to solve its technical problem is:

[0010] The present invention provides a method for evaluating the connectivity elasticity of a local area network system, the method comprising:

[0011] Step 1: Based on all nodes and their connectivity in the local area network system, the local area network system is formally modeled, and the local area network system, nodes and connectivity are abstractly represented as a finite set; nodes include hardware and software; connectivity is the edge composed of nodes;

[0012] Step 2: Establish a probabilistic reliability model to describe the hardware in the local area network system, and use a binary decision diagram method to calculate the probabilistic reliability of the hardware in the local area network system;

[0013] Step 3: According to the topological relationship of the local area network system, the minimum path set and adjacency matrix of the local area network system are obtained; the relationship between the software probability reliability of the first k+1 nodes and the software probability reliability of the first k nodes is analyzed to obtain the software probability reliability of the local area network system; and the connectivity opportunity reliability of each minimum path is calculated by combining the hardware and software probability reliability, and then the upper bound of the connectivity opportunity reliability of the local area network system is calculated, which is used as the connectivity opportunity reliability of the local area network system;

[0014] Step 4: Based on the obtained minimum path set, obtain the point path matrix, calculate the maximum flow of each minimum path, and then obtain the maximum flow of the local area network system; calculate the task capacity and average task capacity of the local area network system based on the maximum flow, and then establish the connectivity elasticity model of the local area network system to achieve the characterization and measurement of the connectivity elasticity of the local area network system.

[0015] Furthermore, the method of step 1 of the present invention comprises:

[0016] For an arbitrary local area network system, it is represented as G(V,E), where V = {v1,v2,v3,...}, represents the set of all nodes, E represents all edges, and:

[0017] E={e ij |e ij =v i →v j},v i ,v j ∈V

[0018] In the time dimension, we have:

[0019] G(t)={V(t),E(t)}

[0020] In which, t represents time, and any local network system is abstracted as a finite set of nodes V = (v1, v2, ...) and edges E = (e1, e2, ...). (V, E) constitutes a system connectivity graph G, and the elements in E are the edges of G.

[0021] Furthermore, in the node of step 1 of the present invention, the hardware includes: terminal equipment, central switch, router, central computing server, and the software includes: basic performance software and transmission performance software.

[0022] Furthermore, the information transmission in the local area network system of step 1 of the present invention satisfies the following conditions simultaneously:

[0023] 1) Information enters from the terminal device and outputs from the terminal device during transmission;

[0024] 2) Information cannot pass through the same hardware component repeatedly;

[0025] 3) Information passes through the central switch at most once before being transmitted to the central computing server;

[0026] 4) The buffer of the central computing server is large enough.

[0027] Furthermore, the method of step 2 of the present invention comprises:

[0028] For a hardware connected network G(V,E), V is the point set contained in the network, and E is the edge set contained in the network; the number of nodes in the network is represented by |V, and the number of edges is represented by |E;

[0029] Suppose there are n nodes and edges in a local area network system, and any node and any edge has a failure probability q i , the normal operation probability of nodes and edges is p i , where q i =1-p i , and whether each node and edge fails is independent of each other;

[0030] Then for this network, a network state vector X=(X1,X2,...,X n ) represents all the states of the network, where one network state is represented by x=(x1,x2,...,x n ), x i Indicates the working status of the working nodes or edges in the network, x i Can only take 0 or 1;

[0031] When x i =1, it means that the working status of the node or edge is normal. i =0 means the working status of the node or edge is faulty;

[0032] Assume that there are n nodes in the network G(V,E), and define the n-order matrix C = [C ij ], where if there is no direct edge connecting nodes i and j, then C ij= 0; if there is an edge directly connecting nodes i and j, then C ij =1, the matrix C is called the adjacency matrix of the network G(V,E); for the adjacency matrix C, the following calculation method is defined:

[0033]

[0034] Among them, r represents all the paths with a distance r from node i to node j in the local area network system; when the number of nodes is n, it is easy to know that the distance of the longest path will not be greater than n-1; so C r＝n = 0 is always true, so let r = 1, 2, ... n-1, calculate C r , we can get all the minimum path sets MP={L k ,k=1,2,…};

[0035] After obtaining the minimum path set, the Boolean function f(x1,x2,…,x n ) describes the minimum path set; for any minimum path L∈MP, it must contain the corresponding Boolean element in X, and the product of all corresponding elements is denoted by φ(L)=Π x∈L x, then:

[0036] f(x1,x2,…,x n )=Σ L∈MP φ(L)

[0037] From the Boolean function f(x1,x2,…,x n ) and select a Boolean variable x from the function i , this Boolean variable is the root node of the function. There are two paths to this root node. One of the paths is the expression converted by the Boolean function when the Boolean variable takes the value of 0. This expression is called the function at x i = 0, and the other way is that the Boolean variable takes the value of 1. The transformed expression is called the function at x i = 1 component under 1; if we start from x1, we have:

[0038]

[0039] Use these two transformed expressions to select any of the remaining variables x again j , x j ≠x i , repeat the operation until the expression of the 0 component is 0, the expression of the 1 component is 1, or the two components are 0 or 1 at the same time, at which point the decomposition of the Boolean function is considered complete;

[0040] Find all the paths from the root node to the leaf node with a value of 1, which is the disjoint minimum path set of f, denoted as MP2 = {NL k, k=1,2,…}; any disjoint minimum path NL contains x i Take the direction of 0 or 1, when x i When NL∈MP2 takes 0, it is recorded as Otherwise, it is recorded as x i ; and let the disjoint product be:

[0041]

[0042] Add up all the disjoint products to get the disjoint product sum of the local area network system with respect to X:

[0043]

[0044] In the above formula, x i Replaced with the reliability of the corresponding node or edge or Get the network connectivity reliability:

[0045]

[0046] Furthermore, the method for calculating the software probability reliability in step 3 of the present invention includes:

[0047] The software probability reliability is related to the link in which the node is located. In a link, if there are k nodes before a node in the link, the software probability reliability of the node is related to its own probability reliability and the first k nodes; the software probability reliability of the first k+1 nodes in the link satisfies the following relationship:

[0048]

[0049] Among them, the software probability reliability of the first k+1 nodes is the intersection of the software probability reliability of the first k nodes and the software probability reliability of the k+1th node; the software probability reliability of the first k nodes is The software probability reliability of the k+1th node is

[0050] Furthermore, the method of step 3 of the present invention comprises:

[0051] The hardware probability reliability of each node in the local area network system is R Pi , the software probability reliability of each node is R Ui ; The hardware probability reliability of terminal device 1 is R PS , the software probability reliability is R US , the hardware probability reliability of terminal device 2 is R PT , the software probability reliability is R UT; According to the topological structure of the local area network system, the minimum path set MP and adjacency matrix C of the system are obtained; represents the hardware probability reliability of the i-th node in the link within the system, represents the software probabilistic reliability of the i-th node in the link within the system;

[0052] Calculate the hardware probability reliability and software probability reliability of each node in the link; calculate the connectivity opportunity reliability R of each minimum path based on the minimum path set MP MP for:

[0053]

[0054] Then the connectivity opportunity reliability of the local area network system is R All-C The upper bound of is:

[0055]

[0056] The reliability of the connection opportunity R All-C The upper bound of is regarded as the connectivity opportunity reliability of the system.

[0057] Furthermore, the method of step 4 of the present invention comprises:

[0058] The point-path matrix is:

[0059]

[0060] Among them, each column vector in A(i,j) represents each minimum path of the local area network system, and each row vector represents whether the i-th node is in the minimum path set. The matrix A(i,j) is a point path matrix;

[0061] Given the maximum processing capacity C of each node in the local area network system i , then the column vector C represents the vector of the maximum processing capacity of each node, that is:

[0062]

[0063] In solving the maximum flow F of the local network max When , the maximum flow b of each minimum path is calculated i , then the maximum flow F of the system max is the sum of the maximum flows that can flow through each minimum path; that is:

[0064]

[0065] The constraints are:

[0066]

[0067] When the system is disturbed, a node V i Stop working, and the new point-path matrix A - (i, j) is the original matrix A(i, j) with the row of the node eliminated and the column where the element in the row is 1;

[0068] Calculate the maximum flow of the system after the disturbance Then the connectivity critical mission capability MC(t) of the system is:

[0069]

[0070] For any node V i , we can get a maximum flow after disturbance Assuming that the disturbance in the system is equally likely to occur at any node, the average connectivity task capability of the system is for:

[0071]

[0072] In order to obtain the average connectivity task capability Then, the connectivity elasticity of the local area network system is calculated; the connectivity elasticity of the local area network is The specific expression is:

[0073]

[0074] Among them, t0 is the initial time, t a The moment when the network began to be impacted, t d is the time when the network impact is completed, t r is the time when the system starts to recover, t s is the moment when the system recovery is completed and the performance is stable, t e The moment when the impact is complete.

[0075] The present invention provides a connectivity elasticity evaluation system for a local area network system, the evaluation system comprising:

[0076] The formal modeling unit is used to formally model the local area network system according to all nodes and their connectivity relationships in the local area network system, and abstractly represent the local area network system, nodes and connectivity relationships as a finite set; nodes include hardware and software; connectivity relationships are edges composed of nodes;

[0077] The hardware reliability modeling unit is used to establish a probabilistic reliability model to describe the hardware in the local area network system and calculate the probabilistic reliability of the hardware in the local area network system using a binary decision diagram method;

[0078] The connectivity opportunity reliability modeling unit is used to obtain the minimum path set and adjacency matrix of the local area network system according to the topological relationship of the local area network system; analyze the relationship between the software probability reliability of the first k+1 nodes and the software probability reliability of the first k nodes to obtain the software probability reliability of the local area network system; and calculate the connectivity opportunity reliability of each minimum path in combination with the hardware and software probability reliability, and then calculate the upper bound of the connectivity opportunity reliability of the local area network system, which is used as the connectivity opportunity reliability of the local area network system;

[0079] The connectivity elasticity analysis model modeling unit is used to obtain the point path matrix based on the obtained minimum path set, calculate the maximum flow of each minimum path, and then obtain the maximum flow of the local area network system; calculate the task capability and average task capability of the local area network system based on the maximum flow, and then establish the connectivity elasticity model of the local area network system to realize the characterization and measurement of the connectivity elasticity of the local area network system.

[0080] The beneficial effects produced by the present invention are:

[0081] The present invention considers the hardware equipment and software function failures in the local area network, proposes a local area network connectivity elasticity characterization and measurement model, provides an analysis method for the impact mechanism of local area network failure anomalies on network system tasks based on time-varying elasticity measurement, and establishes a local area network system elasticity model, which is helpful to quantitatively analyze the random process of network task capacity fluctuations under the influence of connectivity failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0083] Figure 1 is a local area network system connectivity topology model of an embodiment of the present invention;

[0084] Figure 2 It is a simplified model of the local area network system connectivity topology of an embodiment of the present invention;

[0085] Figure 3 It is a BDD decomposition diagram of the local area network system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0087] Embodiment 1

[0088] The method for evaluating the connectivity elasticity of a local area network system according to an embodiment of the present invention includes:

[0089] (1) Formal modeling of local area network systems

[0090] The local network system is represented as G(V,E), and the system is abstracted as a finite set of nodes V = (v1, v2, ..., v7) and edges E = (e1, e2, ..., e12), such as Figure 1 The local area network system connectivity topology model shown is used to establish a formal model of the local area network system.

[0091] (2) LAN system hardware reliability modeling

[0092] A probabilistic reliability model is established to describe the hardware in the local area network system, and the binary decision diagram method (BDD) is used to calculate the probabilistic reliability of the local area network system. By calculating the probability of hardware failure in the local area network system, the minimum path set of the local area network system is solved, and the Boolean function is obtained and decomposed based on the minimum path set to obtain the hardware connectivity reliability of the local area network system. in They are node reliability and edge reliability, respectively, and are statistical results.

[0093] (3) Modeling the reliability of hardware and software network connectivity opportunities

[0094] Calculate the minimum path set of the local area network system, analyze the relationship between the probability reliability of the first k+1 nodes and the probability reliability of the first k nodes, calculate the connectivity chance reliability of each minimum path, calculate the upper bound of the connectivity chance reliability of the local area network system, and use it as the connectivity chance reliability of the local area network system.

[0095] (4) Modeling of local area network system connectivity elasticity analysis model

[0096] Use the column vectors in A(i,j) to represent each minimum path of the local network system, that is, the point path matrix, and calculate the maximum flow b of each minimum path i , then the maximum flow of the system Calculate the mission capability MC(t) and average mission capability of the local area network system Establish a connectivity resilience model for local area network systems.

[0097] Embodiment 2

[0098] The method for evaluating the connectivity elasticity of a local area network system according to an embodiment of the present invention includes:

[0099] 1. Formal modeling of local area network systems

[0100] The hardware equipment of the local area network system includes terminal equipment, switches, routers, and central computing servers, and the software includes basic performance software, transmission performance software, etc.

[0101] In general, for any network system, it can be expressed as G(V,E), where V = {v1,v2,v3,v4}, represents the set of all functional nodes, E represents all edges, and

[0102] E={e ij |e ij =v i →v j},v i ,v j ∈V (5)

[0103] In the time dimension, we have:

[0104] G(t)={V(t),E(t)} (6)

[0105] Abstract the topology model of the local area network system, such as Figure 1 shown.

[0106] In the device, the system is abstracted as nodes V = (v1, v2, ..., v7) and edges E = (e1, e2, ..., e 12 ). (V,E) forms a system connected graph G, the elements in E are the edges of G, and the following conditions are met when information is transmitted in the system:

[0107] 1) Information enters from the terminal device and outputs from the terminal device during transmission;

[0108] 2) Information cannot pass through the same component repeatedly;

[0109] 3) Information passes through the central switch at most once before being delivered to the computing server;

[0110] 4) The computing server's buffer is large enough.

[0111] In order to examine whether the system can reach a steady state after being subjected to a certain impact, it is assumed that the total flow input from the terminal device is always less than the total processing capacity of the computing server, thereby exploring the steady state of the system after the impact and obtaining the connectivity elasticity of the system.

[0112] 2. LAN system hardware reliability modeling

[0113] The hardware and software devices in the architecture are considered as nodes that can fail, and the randomness and uncertainty of network connectivity are studied. Generally, in a network system, except for devices with redundant performance such as switches and servers, which will not directly cause hardware circuit failures, all other hardware will fail to complete the system's tasks, so these hardware will cause hardware circuit failures.

[0114] For a hardware connected network G(V,E), V is the point set contained in the network, and E is the edge set contained in the network. The number of nodes in the network is represented by |V|, and the number of edges is represented by |E|. Suppose there are n nodes and edges in a network system, and any node and any edge have a failure probability q i , the normal operation probability of nodes and edges is p i , where q i =1-p i , and the failure of each node and edge is independent of each other. Then for this network, a network state vector X=(X1,X2,…,X n ) represents all the states of the network, where a network state can be represented as x = (x1, x2, .., x n ), x i Indicates the working status of nodes or edges in the network, x i It can only be 0 or 1. i =1, it means that the working status of the node or edge is normal. i =0 means that the working status of the node or the edge is faulty.

[0115] Assume that there are n nodes in the network G(V,E), and define the n-order matrix C = [C ij ], where if there is no direct edge connecting nodes i and j, then C ij = 0; if there is an edge directly connecting nodes i and j, then C ij =1, the matrix C is called the adjacency matrix of the network G(V,E). For the adjacency matrix C, the following calculation method is defined:

[0116]

[0117] r represents all paths with a distance of r from node i to node j in the network system. When the number of nodes is n, it is easy to know that the distance of the longest path will not be greater than n-1. So C r＝n = 0 is always true, so let r = 1, 2, ... n-1, calculate C r , we can get all the minimum path sets MP={L k ,k=1,2,…}.

[0118] After obtaining the minimum path set, we can use the Boolean function f(x1,x2,...,x n ) describes the minimum path set. For any minimum path L∈MP, it must contain the corresponding Boolean elements in X. The product of all corresponding elements is denoted by φ(L)=Π x∈ L x, then:

[0119] f(x1,x2,...,xn )=∑ L∈MP φ(L) (9)

[0120] From the Boolean function f(x1,x2,...,x n ) and select a Boolean variable x from the function i , this Boolean variable is the root node of the function. There are two paths to this root node. One of the paths is the expression converted by the Boolean function when the Boolean variable takes the value of 0. This expression is called the function at x i = 0, and the other way is that the Boolean variable takes the value of 1. The transformed expression is called the function at x i = 1. If we start from x1, we have

[0121]

[0122] Use these two transformed expressions to select any of the remaining variables x again j , x j ≠x i , repeat the above operation until the expression of the 0 component is 0, the expression of the 1 component is 1, or the two components are 0 or 1 at the same time. We believe that the decomposition of the Boolean function is completed at this time.

[0123] Find all the paths from the root node to the leaf node with a value of 1, which is the disjoint minimum path set of f, denoted as MP2 = {NL k ,k=1,2,...}. Any disjoint minimum path NL contains x i Take the direction of 0 or 1, when x i When NL∈MP2 takes 0, it is recorded as Otherwise, it is recorded as x i . And let the non-intersection product be

[0124]

[0125] Add up all the disjoint products to get the disjoint product sum of the local area network system with respect to X

[0126]

[0127] In the above formula, x i Replaced with the reliability of the corresponding network node or edge or The network connectivity reliability can be obtained

[0128]

[0129] 3. Modeling the reliability of hardware and software network connectivity opportunities

[0130] The connectivity topology model of the local area network system is simplified. The connectivity topology model of the simplified local area network system is as follows: Figure 2 shown.

[0131] The hardware probability reliability of each node in the local area network system is R Pi (i=1,2,...8), the software probability reliability of each node is R Ui (i=1,2,...8). The hardware probability reliability of terminal device 1 is R PS , the software probability reliability is R US , the hardware probability reliability of terminal device 2 is R PT , the software probability reliability is R UT . Obtain the minimum path set MP of the system. According to the topological relationship of the local area network system, obtain the adjacency matrix C of the system.

[0132]

[0133] The minimum path set MP is obtained as {(V S ,V1,V5,V7,V T ), (V S ,V1,V5,V7,V8,V T ), (V S ,V1,V3,V6,V8,V T ), (V S ,V1,V3,V6,V8,V7,V T ), (V S ,V1,V4,V6,V8,V T ), (V S ,V1,V4,V6,V8,V7,V T ), (V S ,V2,V6,V8,V T ), (V S ,V2,V6,V8,V7,V T ), (V S ,V2,V3,V5,V7,V T ), (V S ,V2,V3,V5,V7,V8,V T ), (V S ,V2,V4,V5,V7,V T ), (V S ,V2,V4,V5,V7,V8,V T )}.

[0134] BDD decomposition diagram Figure 3 As shown, ● is the node of the local area network system, and ■ is the Boolean variable of the node.

[0135] represents the hardware probability reliability of the i-th node in the link within the system, Represents the software probability reliability of the i-th node in the link within the system. The hardware failure probability reliability of each node can be calculated by formula (9), and the software reliability is related to the link in which the node is located. In a link, if there are k nodes before a node in the link, the software probability reliability of the node is related to its own probability reliability and the first k nodes. In general, the more uncertain nodes there are in a link, the greater the total uncertainty of the link. The software probability reliability of the first k+1 nodes in the link satisfies the following relationship:

[0136]

[0137] That is, the software probability reliability of the first k+1 nodes is the intersection of the software probability reliability of the first k nodes and the software probability reliability of the k+1th node. The software probability reliability of the first k nodes is The software probability reliability of the k+1th node is

[0138] From formula (10), the hardware probability reliability and software probability reliability of each node in the link can be calculated as shown in the following formula:

[0139]

[0140] According to the minimum path set MP, calculate the connectivity reliability R of each minimum path MP for:

[0141]

[0142] Since the chance reliability of each link in the uncertain system and the chance reliability of the system satisfy subadditivity, the following relationship holds:

[0143]

[0144] Then the connectivity opportunity reliability of the local area network system is R All-C The upper bound of is:

[0145]

[0146] Among them, the reliability of each minimum path is based on Figure 3 In this intellectual achievement, the reliability of the connection opportunity R All-C The upper bound of is regarded as the connectivity opportunity reliability of the system.

[0147] 4. Connectivity elasticity modeling of local area network systems

[0148] According to the previous part, we get the minimum path set of the local area network. The following matrix can be given:

[0149]

[0150] Each column vector in A(i,j) represents each minimum path of the local network, and each row vector represents whether the i-th node is in the minimum path set. Such a matrix A(i,j) is called a point-path matrix.

[0151] After the point-path matrix is ​​determined, the maximum processing capacity C of each point in the local area network system is given. i , then the column vector C represents the vector of the maximum processing capacity of each node, that is:

[0152]

[0153] In solving the maximum flow F of the local network max When , the maximum flow b of each minimum path should be calculated i , then the maximum flow F of the system max is the sum of the maximum flows that can flow through each minimum path. Compared with the minimum cut algorithm, this calculation method can simplify the calculation complexity of the model, that is:

[0154]

[0155] The constraints are:

[0156]

[0157] Among them, A is the point path matrix, b is the maximum flow matrix of the minimum path, and H is the vector composed of the maximum processing capacity of each node, which is the same matrix as the previous n-order matrix.

[0158] When the system is disturbed, a node V i Stop working, and the new point-path matrix A - (i, j) is the original matrix A(i, j) with the row of the node eliminated, and the column where the element in the row is 1.

[0159] Calculate the maximum flow of the system after the disturbance Then the connectivity critical mission capability MC(t) of the system is:

[0160]

[0161] For any node V i , we can get a maximum flow after disturbance We believe that the disturbance in the system is equally likely to occur at any node, so the average connectivity task capability of the system is for:

[0162]

[0163] In order to obtain the average connectivity task capability Then, by combining equations (7) to (15), we can calculate the connectivity elasticity of the local area network system. The connectivity elasticity of the local area network is The specific expression is:

[0164]

[0165] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A method for evaluating connectivity elasticity of a local area network system, characterized in that: The method includes: Step 1: Based on all nodes and their connectivity in the local area network system, the local area network system is formally modeled, and the local area network system, nodes and connectivity are abstractly represented as a finite set; nodes include hardware and software; connectivity is the edge composed of nodes; Step 2: Establish a probabilistic reliability model to describe the hardware in the local area network system, and use a binary decision diagram method to calculate the probabilistic reliability of the hardware in the local area network system; Step 3: According to the topological relationship of the local area network system, the minimum path set and adjacency matrix of the local area network system are obtained; the relationship between the software probability reliability of the first k+1 nodes and the software probability reliability of the first k nodes is analyzed to obtain the software probability reliability of the local area network system; and the connectivity opportunity reliability of each minimum path is calculated by combining the hardware and software probability reliability, and then the upper bound of the connectivity opportunity reliability of the local area network system is calculated, which is used as the connectivity opportunity reliability of the local area network system; Step 4: Based on the obtained minimum path set, a point path matrix is ​​obtained, and the maximum flow of each minimum path is calculated, thereby obtaining the maximum flow of the local area network system; the task capability and average task capability of the local area network system are calculated based on the maximum flow, and then a connectivity elasticity model of the local area network system is established to achieve the characterization and measurement of the connectivity elasticity of the local area network system; The method of step 2 comprises: For a hardware connected network G(V,E), V is the point set contained in the network, and E is the edge set contained in the network; the number of nodes in the network is represented by |V|, and the number of edges is represented by |E|; Suppose there are n nodes and edges in a local area network system, and any node and any edge has a failure probability q i , the normal operation probability of nodes and edges is p i , where q i =1-p i , and whether each node and edge fails is independent of each other; Then for the network, a network state vector X = (X1, X2, ..., X n ) represents all network states, where one network state is represented by x = (x1, x2, .., x n ), x i Indicates the working status of the working nodes or edges in the network, x i Can only take 0 or 1; When x i =1, it means that the working status of the node or edge is normal. i =0 means the working status of the node or edge is faulty; Assume that there are n nodes in the network G(V, E), and define the n-order matrix C = [C ij ], where if there is no direct edge connecting nodes i and j, then C ij = 0; if there is an edge directly connecting nodes i and j, then C ij =1, the matrix C is called the adjacency matrix of the network G(V, E); for the adjacency matrix C, the following calculation method is defined: Where r represents all the paths with a distance r from node i to node j in the local area network system. When the number of nodes is n, it is easy to know that the distance of the longest path will not be greater than n--1. Therefore, Cr=n=0 always holds true. So let r=1, 2, ...n-1, and calculate C. r , we can get all the minimum path sets MP={L k , k = 1, 2, ...}; After obtaining the minimum path set, the Boolean function f(x1, x2, ..., x n ) describes the minimum path set; for any minimum path L∈MP, it must contain the corresponding Boolean element in X, and the product of all corresponding elements is denoted by φ(L)=Π x∈L x, then: f(x1,x2,...,x n )=∑ L∈MP φ(L) From the Boolean function f(x1, x2, ..., x n ) and select a Boolean variable x from the function i , this Boolean variable is the root node of the function. There are two paths to this root node. One of the paths is the expression converted by the Boolean function when the Boolean variable takes the value of 0. This expression is called the function at x i = 0, and the other way is that the Boolean variable takes the value of 1. The transformed expression is called the function at x i = 1 component under 1; if we start from x1, we have: Use these two transformed expressions to select any of the remaining variables x again j , x j ≠x i , repeat the operation until the expression of the 0 component is 0, the expression of the 1 component is 1, or the two components are 0 or 1 at the same time, at which point the decomposition of the Boolean function is considered complete; Find all the paths from the root node to the leaf node with a value of 1, which is the disjoint minimum path set of f, denoted as MP2 = {NL k , k=1,2,...}; any disjoint minimum path NL contains x i Take the direction of 0 or 1, when x i When NL∈MP2 takes 0, it is recorded as Otherwise, it is recorded as x i ; and let the disjoint product be: Add up all the disjoint products to get the disjoint product sum of the local area network system with respect to X: In the above formula, x i Replaced with the reliability of the corresponding node or edge or Get the network connectivity reliability: The method for calculating the software probability reliability in step 3 includes: The software probability reliability is related to the link in which the node is located. In a link, if there are k nodes before a node in the link, the software probability reliability of the node is related to its own probability reliability and the first k nodes; the software probability reliability of the first k+1 nodes in the link satisfies the following relationship: Among them, the software probability reliability of the first k+1 nodes is the intersection of the software probability reliability of the first k nodes and the software probability reliability of the k+1th node; the software probability reliability of the first k nodes is The software probability reliability of the k+1th node is The method of step 3 comprises: The hardware probability reliability of each node in the local area network system is R Pi , the software probability reliability of each node is R Ui ; The hardware probability reliability of terminal device 1 is R PS , the software probability reliability is R US , the hardware probability reliability of terminal device 2 is R PT , the software probability reliability is R UT ; According to the topological structure of the local area network system, the minimum path set MP and adjacency matrix C of the system are obtained; represents the hardware probability reliability of the i-th node in the link within the system, represents the software probabilistic reliability of the i-th node in the link within the system; Calculate the hardware probability reliability and software probability reliability of each node in the link; calculate the connectivity opportunity reliability R of each minimum path based on the minimum path set MP MP for: Then the connectivity reliability of the local area network system is R All-C The upper bound of is: The reliability of the connection opportunity R All-C The upper bound of is regarded as the connectivity opportunity reliability of the system.

2. The method for evaluating the connectivity elasticity of a local area network system according to claim 1, characterized in that: The method of step 1 comprises: For an arbitrary local area network system, it is represented as G(V,E), where V = {v1,v2,v3,...}, represents the set of all nodes, E represents all edges, and: E={e ij |e ij =v i →v j },v i ,v j ∈V In the time dimension, we have: G(t)={V(t),E(t)} Among them, t represents time, and any local area network system is abstracted as a finite set of nodes V = (v1, v2, ...) and edges E = (e1, e2, ...). (V, E) constitutes a system connectivity graph G, and the elements in E are the edges of G.

3. The method for evaluating the connectivity elasticity of a local area network system according to claim 2, characterized in that: In the node of step 1, the hardware includes: terminal equipment, central switch, router, central computing server, and the software includes: basic performance software and transmission performance software.

4. The method for evaluating the connectivity elasticity of a local area network system according to claim 3, characterized in that: The information transmission in the local area network system of step 1 satisfies the following conditions at the same time: 1) Information enters from the terminal device and outputs from the terminal device during transmission; 2) Information cannot pass through the same hardware component repeatedly; 3) Information passes through the central switch at most once before being transmitted to the central computing server; 4) The buffer of the central computing server is large enough.

5. The method for evaluating the connectivity elasticity of a local area network system according to claim 1, characterized in that: The method of step 4 comprises: The point-path matrix is: Among them, each column vector in A(i,j) represents each minimum path of the local area network system, and each row vector represents whether the i-th node is in the minimum path set. The matrix A(i,j) is a point path matrix; Given the maximum processing capacity H of each node in the local area network system i , then the column vector H represents the vector of the maximum processing capacity of each node, that is: In solving the maximum flow F of the local network max When , the maximum flow b of each minimum path is calculated i , then the maximum flow F of the system max is the sum of the maximum flows that can flow through each minimum path; that is: Among them, m is the number of minimum paths; The constraints are: Among them, A is the point-path matrix, b is the maximum flow matrix of the minimum path, and H is the vector composed of the maximum processing capacity of each node; When the system is disturbed, a node V i Stop working, and the new point-path matrix A - (i, j) is the original matrix A(i, j) with the row of the node eliminated and the column where the element in the row is 1; Calculate the maximum flow of the system after the disturbance Then the connectivity critical mission capability MC(t) of the system is: For any node V i , we can get a maximum flow after disturbance Assuming that the disturbance in the system is equally likely to occur at any node, the average connectivity task capability of the system is for: In order to obtain the average connectivity task capability Then, the connectivity elasticity of the local area network system is calculated; the connectivity elasticity of the local area network is The specific expression is: Among them, t0 is the initial time, t a The moment when the network began to be impacted, t d is the time when the network impact is completed, t r is the time when the system starts to recover, t s is the moment when the system recovery is completed and the performance is stable, t e The moment when the impact is complete.

6. A connectivity elasticity assessment system for a local area network system, characterized in that: The assessment system includes: The formal modeling unit is used to formally model the local area network system according to all nodes and their connectivity relationships in the local area network system, and abstractly represent the local area network system, nodes and connectivity relationships as a finite set; nodes include hardware and software; connectivity relationships are edges composed of nodes; The hardware reliability modeling unit is used to establish a probabilistic reliability model to describe the hardware in the local area network system and calculate the probabilistic reliability of the hardware in the local area network system using a binary decision diagram method; The connectivity opportunity reliability modeling unit is used to obtain the minimum path set and adjacency matrix of the local area network system according to the topological relationship of the local area network system; analyze the relationship between the software probability reliability of the first k+1 nodes and the software probability reliability of the first k nodes to obtain the software probability reliability of the local area network system; and calculate the connectivity opportunity reliability of each minimum path in combination with the hardware and software probability reliability, and then calculate the upper bound of the connectivity opportunity reliability of the local area network system, which is used as the connectivity opportunity reliability of the local area network system; The connectivity elasticity analysis model modeling unit is used to obtain a point path matrix based on the obtained minimum path set, calculate the maximum flow of each minimum path, and then obtain the maximum flow of the local area network system; calculate the task capability and average task capability of the local area network system based on the maximum flow, and then establish a connectivity elasticity model of the local area network system to achieve the characterization and measurement of the connectivity elasticity of the local area network system; The hardware reliability modeling unit comprises: For a hardware connected network G(V,E), V is the point set contained in the network, and E is the edge set contained in the network; the number of nodes in the network is represented by |V|, and the number of edges is represented by |E|; Suppose there are n nodes and edges in a local area network system, and any node and any edge has a failure probability q i , the normal operation probability of nodes and edges is p i , where q i =1-p i , and whether each node and edge fails is independent of each other; Then for this network, a network state vector X=(X1,X2,...,X n ) represents all the states of the network, where one network state is represented by x=(x1,x2,...,x n ), x i Indicates the working status of the working nodes or edges in the network, x i Can only take 0 or 1; When x i =1, it means that the working status of the node or edge is normal. i =0 means the working status of the node or edge is faulty; Assume that there are n nodes in the network G(V,E), and define the n-order matrix C = [C ij ], where if there is no direct edge connecting nodes i and j, then C ij = 0; if there is an edge directly connecting nodes i and j, then C ij =1, the matrix C is called the adjacency matrix of the network G(V,E); for the adjacency matrix C, the following calculation method is defined: Among them, r represents all the paths with a distance r from node i to node j in the local area network system; when the number of nodes is n, it is easy to know that the distance of the longest path will not be greater than n-1; so C r＝n = 0 is always true, so let r = 1, 2, ... n-1, calculate C r , we can get all the minimum path sets MP={L k ,k=1,2,…}; After obtaining the minimum path set, the Boolean function f(x1,x2,...,x n ) describes the minimum path set; for any minimum path L∈MP, it must contain the corresponding Boolean element in X, and the product of all corresponding elements is denoted by φ(L)=Π x∈L x, then: f(x1,x2,...,x n )=∑ L∈MP φ(L) From the Boolean function f(x1,x2,...,x n ) and select a Boolean variable x from the function i , this Boolean variable is the root node of the function. There are two paths to this root node. One of the paths is the expression converted by the Boolean function when the Boolean variable takes the value of 0. This expression is called the function at x i = 0, and the other way is that the Boolean variable takes the value of 1. The transformed expression is called the function at x i = 1 component under 1; if we start from x1, we have: Use these two transformed expressions to select any of the remaining variables x again j , x j ≠x i , repeat the operation until the expression of the 0 component is 0, the expression of the 1 component is 1, or the two components are 0 or 1 at the same time, at which point the decomposition of the Boolean function is considered complete; Find all the paths from the root node to the leaf node with a value of 1, which is the disjoint minimum path set of f, denoted as MP2 = {NL k , k=1,2,...}; any disjoint minimum path NL contains x i Take the direction of 0 or 1, when x i When NL∈MP2 takes 0, it is recorded as Otherwise, it is recorded as x i ; and let the disjoint product be: Add up all the disjoint products to get the disjoint product sum of the local area network system with respect to X: In the above formula, x i Replaced with the reliability of the corresponding node or edge or Get the network connectivity reliability: The method for calculating software probability reliability in the connectivity opportunity reliability modeling unit includes: The software probability reliability is related to the link in which the node is located. In a link, if there are k nodes before a node in the link, the software probability reliability of the node is related to its own probability reliability and the first k nodes; the software probability reliability of the first k+1 nodes in the link satisfies the following relationship: Among them, the software probability reliability of the first k+1 nodes is the intersection of the software probability reliability of the first k nodes and the software probability reliability of the k+1th node; the software probability reliability of the first k nodes is The software probability reliability of the k+1th node is The connectivity opportunity reliability modeling unit comprises: The hardware probability reliability of each node in the local area network system is R Pi , the software probability reliability of each node is R Ui ; The hardware probability reliability of terminal device 1 is R PS , the software probability reliability is R US , the hardware probability reliability of terminal device 2 is R PT , the software probability reliability is R UT ; According to the topological structure of the local area network system, the minimum path set MP and adjacency matrix C of the system are obtained; represents the hardware probability reliability of the i-th node in the link within the system, represents the software probabilistic reliability of the i-th node in the link within the system; Calculate the hardware probability reliability and software probability reliability of each node in the link; calculate the connectivity opportunity reliability R of each minimum path based on the minimum path set MP MP for: Then the connectivity reliability of the local area network system is R All-C The upper bound of is: The reliability of the connection opportunity R All-C The upper bound of is regarded as the connectivity opportunity reliability of the system.

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