Network fairness prediction method and related device

Abstract

The invention provides a network fairness prediction method and a related device, and belongs to the technical field of network fairness prediction. According to the method, in a user satisfaction model, a space of service level agreement parameters is scanned to obtain a scanning result; based on a scanning result, obtaining an unbalance degree and an average satisfaction degree, and based on the unbalance degree and the average satisfaction degree, generating a global phase diagram; in the global phase diagram, calculating a curvature field by using a matrix formed by second-order partial derivatives, and judging whether the region is a stable region or not according to the curvature field; if the region is the stable region, calculating an unbalance degree gradient, an average satisfaction degree gradient and an included angle between the unbalance degree gradient and the average satisfaction degree gradient; and predicting the network fairness based on the unbalance degree gradient, the average satisfaction degree gradient and the included angle between the unbalance degree gradient and the average satisfaction degree gradient to obtain a network fairness prediction result. According to the invention, the problem of low network fairness prediction efficiency is solved.

Description

Technical Field

[0001] This invention belongs to the field of network fairness prediction technology, specifically relating to a network fairness prediction method and related apparatus. Background Technology

[0002] In modern network architecture design, meeting strict Service Level Objectives (SLOs) (such as latency limits and hop count limits) has become a core requirement.

[0003] However, a major challenge in network engineering is that even slight tightening of SLA (Service Level Agreement) constraints or minor fluctuations in performance thresholds can cause network traffic to suddenly and unpredictably concentrate on a few shortest paths. This traffic polarization not only leads to severe network QoE (Quality of Experience) inequality (IoE) but also significantly exacerbates the vulnerability of the system (the entire network transmission system, or simply the network), making it highly susceptible to cascading failures.

[0004] Existing technologies mainly focus on static fairness optimization (such as max-min fairness and proportional fairness) or black-box anomaly detection based on machine learning. Static optimization only addresses fixed network states and cannot perceive the dynamic risks brought about by parameter changes. Although machine learning methods can predict failures, they lack interpretability, failing to reveal the underlying topological causes of failures and providing engineers with clear guidance on SLA parameter adjustments, resulting in low efficiency in predicting network fairness. Summary of the Invention

[0005] The purpose of this invention is to provide a method and related apparatus for predicting network fairness, in order to solve the problem of low efficiency in network fairness prediction in the prior art.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a method for predicting network fairness, comprising the following steps: In the user satisfaction model, the space of service level agreement parameters is scanned to obtain the scan results; The method for constructing the user satisfaction model includes: In the network topology model, a user satisfaction model is constructed based on the service level agreement parameters; Based on the scan results, the imbalance degree and average satisfaction are obtained, and a global phase diagram is generated based on the imbalance degree and average satisfaction. In the global phase diagram, the curvature field is calculated using a matrix composed of second-order partial derivatives, and the curvature field is used to determine whether it is a stable region. If it is a stable region, calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient. Network fairness is predicted based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, resulting in a network fairness prediction.

[0007] A further improvement of the present invention is that the service level agreement parameters include evaluation strictness and path cost performance threshold.

[0008] A further improvement of this invention is that it optimizes the evaluation strictness and path cost performance thresholds by adopting a threshold-first principle.

[0009] A further improvement of the present invention is that, in the network topology model, the user satisfaction model is constructed based on the service level agreement, specifically by using the Sigmoid function to construct the user satisfaction model based on the service level agreement parameters in the network topology model.

[0010] A further improvement of this invention is that the formula for calculating the imbalance is:

[0011] in, For the degree of imbalance, For Shannon entropy, The number of node pairs; Shannon entropy The calculation formula is:

[0012] in, Standardized satisfaction share The calculation formula is:

[0013] in, The satisfaction score. For node pairs.

[0014] A further improvement of this invention is that the formula for calculating the average satisfaction level is:

[0015] in, The average satisfaction level. The QoE satisfaction level for each path in the network under any Service Level Agreement (SLA) parameters. The number of nodes; QoE satisfaction for each path in the network under any Service Level Agreement parameters The calculation formula is:

[0016] in, As an objective path cost, This represents the path cost performance threshold. To evaluate the rigor.

[0017] A further improvement of this invention is that the step of determining whether a region is stable based on the curvature field specifically involves: Based on the curvature field, determine the high curvature region and the low curvature region; Regions with low curvature are classified as stable regions.

[0018] In a second aspect, the present invention provides a network fairness prediction system, comprising: The scanning module is used to scan the space of service level agreement parameters in the user satisfaction model and obtain the scanning results. The method for constructing the user satisfaction model includes: In the network topology model, a user satisfaction model is constructed based on the service level agreement parameters; The global phase diagram generation module is used to obtain the imbalance degree and average satisfaction based on the scan results, and to generate a global phase diagram based on the imbalance degree and average satisfaction. The stable region determination module is used to calculate the curvature field in the global phase diagram using a matrix composed of second-order partial derivatives, and to determine whether it is a stable region based on the curvature field. The calculation module is used to calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient in the case of a stable region. The prediction module is used to predict network fairness based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, and obtain the network fairness prediction result.

[0019] Thirdly, the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the network fairness prediction method described above.

[0020] Fourthly, the present invention provides a storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the network fairness prediction method described above.

[0021] Compared with the prior art, the present invention has the following beneficial effects: The network fairness prediction method proposed in this invention, on the one hand, obtains the imbalance degree based on the scanning results. The imbalance degree can uniquely capture the structural imbalance in network resource allocation, overcoming the shortcomings of traditional statistical indicators in decomposability, and can also ensure the theoretical rigor and physical interpretability of the subsequent network fairness prediction results. On the other hand, based on the imbalance degree and average satisfaction, a global phase diagram is generated. The global phase diagram can intuitively reveal the dynamic changes in network fairness with service level agreement parameters, thereby enabling proactive prediction of potential risks and improving the efficiency of network fairness prediction.

[0022] Furthermore, this invention discloses an optimization of evaluation strictness and path cost performance thresholds using a threshold-first principle. This operation can effectively avoid the risk of network cascading congestion that may be triggered by blindly adjusting parameters. Attached Figure Description

[0023] Figure 1 This is a flowchart of the network fairness prediction method of the present invention; Figure 2 This is a schematic diagram of the network fairness prediction system of the present invention; Figure 3 This is a flowchart of the network fairness prediction method in Embodiment 4 of the present invention; Figure 4 In embodiment 4 of the present invention, the small The results of the imbalance analysis; Figure 5 In Embodiment 4 of the present invention, the large The results of the imbalance analysis; Figure 6 In Embodiment 4 of the present invention, the large Supplementary verification results for the limit; Figure 7 These are the simulation results for each step in Embodiment 4 of the present invention; Figure 8 This is the fairness phase diagram of the star diagram in Embodiment 4 of the present invention; Figure 9 This is a diagram showing the experimental verification results of the mesh curvature asymmetry in Embodiment 4 of the present invention; Figure 10 This is a fairness variation feature diagram of the BA diagram in Embodiment 4 of the present invention; Figure 11 This is a fairness change analysis diagram of the AS topology graph in Embodiment 4 of the present invention; Figure 12 This is a schematic diagram of the structure of the electronic device of the present invention. Detailed Implementation

[0024] To further understand the content of this invention, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0025] Example 1: The flowchart of the network fairness prediction method of this invention is as follows: Figure 1 As shown, the network fairness prediction method of the present invention includes the following steps: S1. In the user satisfaction model, the space of service level agreement parameters is scanned to obtain the scan results; The method for constructing the user satisfaction model includes: In the network topology model, a user satisfaction model is constructed based on the service level agreement parameters; S2. Based on the scan results, obtain the imbalance degree and average satisfaction, and generate a global phase diagram based on the imbalance degree and average satisfaction. S3. In the global phase diagram, the curvature field is calculated using a matrix formed by second-order partial derivatives, and the curvature field is used to determine whether it is a stable region. S4. If it is a stable region, calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient. S5. Based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, network fairness is predicted, and the network fairness prediction results are obtained.

[0026] Example 2: A schematic diagram of the network fairness prediction system of this invention is shown below. Figure 2 As shown, the network fairness prediction system of the present invention includes: The scanning module is used to scan the space of service level agreement parameters in the user satisfaction model and obtain the scanning results. The method for constructing the user satisfaction model includes: In the network topology model, a user satisfaction model is constructed based on the service level agreement parameters; The global phase diagram generation module is used to obtain the imbalance degree and average satisfaction based on the scan results, and to generate a global phase diagram based on the imbalance degree and average satisfaction. The stable region determination module is used to calculate the curvature field in the global phase diagram using a matrix composed of second-order partial derivatives, and to determine whether it is a stable region based on the curvature field. The calculation module is used to calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient in the case of a stable region. The prediction module is used to predict network fairness based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, and obtain the network fairness prediction result.

[0027] Example 3: The network fairness prediction method of this invention includes the following steps: S1. In the user satisfaction model, the space of service level agreement parameters is scanned to obtain the scan results.

[0028] The method for constructing the user satisfaction model in this step includes: In the network topology model, a user satisfaction model is constructed based on Service Level Agreement (SLA) parameters.

[0029] Service level agreement parameters include evaluation strictness and path cost performance thresholds.

[0030] In the network topology model, a user satisfaction model is constructed based on the service level agreement (SLA). Specifically, the user satisfaction model is constructed using the Sigmoid function based on the SLA parameters in the network topology model.

[0031] S2. Based on the scan results, obtain the imbalance degree and average satisfaction, and generate a global phase diagram based on the imbalance degree and average satisfaction.

[0032] The formula for calculating the degree of imbalance is:

[0033] in, For the degree of imbalance, For Shannon entropy, This represents the number of node pairs.

[0034] Shannon entropy The calculation formula is:

[0035] in, Standardized satisfaction share The calculation formula is:

[0036] in, The satisfaction score. For node pairs.

[0037] The formula for calculating average satisfaction is:

[0038] in, The average satisfaction level. The QoE satisfaction level for each path in the network under any Service Level Agreement (SLA) parameters. This represents the number of nodes.

[0039] QoE satisfaction for each path in the network under any Service Level Agreement parameters The calculation formula is:

[0040] in, As an objective path cost, This represents the path cost performance threshold. To evaluate the rigor.

[0041] S3. In the global phase diagram, the curvature field is calculated using a matrix formed by the second-order partial derivatives, and the curvature field is used to determine whether it is a stable region.

[0042] In the global phase diagram, the curvature field is calculated using a matrix composed of second-order partial derivatives (such as the Hessian matrix), and the curvature field is used to determine whether it is a stable region.

[0043] This step involves determining whether the region is stable based on the curvature field, specifically: Based on the curvature field, determine the high curvature region and the low curvature region; Regions with low curvature are classified as stable regions.

[0044] S4. If it is a stable region, calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient.

[0045] S5. Based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, network fairness is predicted, and the network fairness prediction results are obtained.

[0046] This embodiment uses a threshold-first principle to optimize the evaluation strictness and path cost performance thresholds.

[0047] Example 4: The flowchart of the network fairness prediction method of this invention is as follows: Figure 3 As shown below, the method of the present invention will be described in detail. The network fairness prediction method of the present invention includes the following steps: S1. In the user satisfaction model, the space of service level agreement parameters is scanned to obtain the scan results.

[0048] The method for constructing the user satisfaction model in this step includes: In the network topology model, a user satisfaction model is constructed based on Service Level Agreement (SLA) parameters (to simulate the nonlinear perception characteristics of user QoE near a threshold).

[0049] Service Level Agreement parameters include evaluation rigor. and path cost performance threshold .

[0050] In the network topology model, a user satisfaction model is constructed based on the service level agreement (SLA). Specifically, the user satisfaction model is constructed using the Sigmoid function based on the SLA parameters in the network topology model.

[0051] S2. Based on the scan results, obtain the imbalance degree and average satisfaction, and generate a global phase diagram based on the imbalance degree and average satisfaction.

[0052] In this step, the imbalance can uniquely capture the structural imbalance in network resource allocation, and can overcome the shortcomings of traditional statistical indicators in terms of decomposability.

[0053] The formula for calculating the degree of imbalance is:

[0054] in, For the degree of imbalance, For Shannon entropy, This represents the number of node pairs.

[0055] Shannon entropy The calculation formula is:

[0056] in, Standardized satisfaction share The calculation formula is:

[0057] in, The satisfaction score. For node pairs.

[0058] The formula for calculating average satisfaction is:

[0059] in, The average satisfaction level. The QoE satisfaction level for each path in the network under any Service Level Agreement (SLA) parameters. This represents the number of nodes.

[0060] QoE satisfaction for each path in the network under any Service Level Agreement parameters The calculation formula is:

[0061] in, As an objective path cost, This represents the path cost performance threshold. To evaluate the rigor.

[0062] To understand the global structure (global phase diagram) of the fairness change view, this embodiment analyzes the role of the global phase diagram in evaluating strictness. The behavior under extreme conditions is explained in the analysis process below: A. small Imbalance analysis set up Let be the variance of the shortest path length for all nodes. When QoE Imbalance Having the following threshold The irrelevant second-order approximation is calculated using the following formula:

[0063] QoE Imbalance Having the following threshold The detailed derivation process of the irrelevant second-order approximation is explained below: set up , , , These are the moments of the jump distribution. When When sufficient, the unbalanced measure It can be expanded as follows:

[0064] Among them, the remaining items Controlled by higher-order moments of the path distribution, its dominant term and Irrelevant.

[0065] QoE Imbalance Having the following threshold The irrelevant second-order approximation requires the satisfaction score. and normalized probability Perform a refined Taylor expansion. Specifically, by expanding the logarithmic term in the entropy expression to the third order, the remainder term can be proven. The third and fourth central moments of the path distribution ( and ) control, corresponding and Order of magnitude. The complete derivation process is quite simple and will be omitted here.

[0066] make ,when At that time, the satisfaction score with the Sigmoid function was ,exist Performing Taylor expansion at this point yields:

[0067] For all Sum the results of the nodes to obtain the total weight. After normalization, the probability It can be approximated as:

[0068] This indicates It is in a uniform distribution A small perturbation nearby. For this distribution, the Shannon entropy has a standard second-order expansion, calculated by the sum of squares of the perturbations (which, along with...). (Proportional), we can obtain:

[0069] Substituting it into the definition of imbalance You can then obtain the small details in the main text. Second-order law form.

[0070] It is important to note that when When the probability vector approaches the simplex boundary, the gradient is no longer strictly defined. Therefore, all gradient-based conclusions in this embodiment are within a finite range. This is true in the following circumstances, but in extreme cases, this embodiment relies on... The piecewise constant structure is analyzed, and the analysis includes: For any finite SLA parameters If the satisfaction scores for all paths are strictly positive ( The resulting probability vector Located in the probabilistic simplex Inside this, the unbalanced function... It is continuously differentiable. ).

[0071] Boundary behavior and subgradient: On the boundary of the simplex (at least one Shannon entropy It is no longer differentiable, but remains continuous and convex. Correspondingly, the unbalanced function... It is well defined and has a subgradient.

[0072] when When, probability vector Approaching the boundary of the simplex, the aforementioned non-differentiability phenomenon occurs. All gradient-based conclusions in the main text (such as the covariance law) are valid in the finite... This holds true. In the limiting case, the analysis depends on... The piecewise constant structure has a derivative of 0 on the step plane but no derivative on the step, which can be rigorously described by subdifferentials.

[0073] These properties can be understood as a chain of function composites. The result is jointly guaranteed by the continuity and differentiability at each stage.

[0074] (1) Proof of continuity measure and For parameters and It is a continuous function.

[0075] Next, we will prove the continuity of each link in the complex chain.

[0076] and The continuity of the weighting function. It is composed of a series of elementary continuous functions, and therefore is continuous itself. Average satisfaction rate It is a finite sum of these continuous functions, and therefore continuous.

[0077] Continuity. Total weight. It is a continuous function. For any nontrivial graph, we have: Normalized probability It is the ratio of two continuous functions, and the denominator is not zero, therefore it is continuous.

[0078] Continuity. Shannon entropy. It is a probability vector A continuous function. By the chain rule for continuity of composite functions, Also A continuous function. Because Yes A linear transformation, therefore It is also continuous.

[0079] (2) Proof of differentiability measure and For parameters and It is a differentiable function.

[0080] The proof logic is similar to that of continuity, gradually demonstrating the differentiability of each step.

[0081] and Differentiability. The Sigmoid function itself is infinitely differentiable ( ),therefore right Differentiable, its finite sum That is also true.

[0082] Continuity. Due to and Both can be infinitesimal, then their quotient It is also differentiable.

[0083] Continuity. Shannon entropy. It is differentiable. According to the multivariate chain rule, the composite function... Differentiable. Due to imbalance. yes A linear transformation, therefore It can also be slight.

[0084] Small The main value of second-order imbalance analysis lies in providing a powerful prior design that reveals a profound simplification: in relaxed SLA (small Under these conditions, complex QoE imbalance It is directly governed by a single, static, and easily computed topological property—the variance of all pairs of shortest path distributions. .

[0085] This provides a practical tool for network architecture design. No complex simulations or dynamic analyses are required; only the candidate network topology needs to be calculated. This allows for a comparison of their inherent robustness and fairness in relaxed traffic transmission. If the goal is to design an inherently robust and fair network to support a wide range of fault-tolerant services (such as bulk data transmission), the topology with the smallest path length variance should be prioritized. This transforms a complex topology design problem into an optimization of basic graph metrics. The results of the imbalance analysis are shown in the figure below. Figure 4 As shown, Figure 4 The QoE imbalance for four different topologies is shown as a function of the strictness square. Simulated data points and their corresponding linear fits confirm the quadratic dependence of both. The theoretical slope is... ).

[0086] Table 1 further compares the slopes of the simulation fit. Compared with the theoretically predicted slope For mesh topologies with highly regular structures (such as mesh diagrams), the ratio reaches 0.978, indicating a high degree of agreement between theory and simulation. For more extreme or irregular topologies such as star diagrams, ER diagrams, and path diagrams, Slightly smaller This is to be expected, as in these topologies, higher-order structural moments (such as skewness and kurtosis) play a more significant role than variance, and their influence extends into the extended higher-order terms (…). This is reflected in the fact that the initial secondary growth is weakened. The near-perfect verification on the grid diagram and the predictable deviation from the complex graph structure provide strong evidence for the prediction accuracy of the method of this invention.

[0087] Table 1. Comparison of direct verification of the slope coefficient of Little a's law.

[0088] B. Big Imbalance analysis set up To meet The number of node pairs. When At this point, the QoE imbalance converges to a piecewise constant function, as shown in the following equation:

[0089] convergence to large The limiting velocity is exponentially related to the distance to the nearest threshold, which means the width of the transition region is... .

[0090] The derivation process for the convergence of QoE imbalance to a piecewise constant function is as follows: big Imbalance analysis relies on the Sigmoid function in The point-state limit. Let Indicates that the path cost is satisfied. The number of node pairs.

[0091] (1) If Then the index Therefore ; (2) If Then the index Therefore .

[0092] Total weight Converging to count Therefore, the limiting probability distribution Become in this There is a uniform distribution on a path that satisfies the threshold, and the probability of other paths is 0. Its entropy is... Substitute The limit form can be obtained by defining it.

[0093] This proof is achieved by restricting the potential probability distribution. and The L1 norm distance between them establishes the actual imbalance. Its limit The boundary of the difference between them. Let... It represents the minimum distance from the threshold to any path cost.

[0094] (1) Single path weight error Individual satisfaction score Relative to its limit value The error can be expressed as an exponential upper bound.

[0095]

[0096] (2) Total variation bound of probability probability vector and The L1 norm distance between them can be controlled using the point state error described above, and the standard results provide boundary expressions.

[0097]

[0098] in yes The number of paths, the above exponential error bound is expressed as For a constant that depends on the topology .

[0099] (3) Fannes–Audenaert bound of entropy difference The Fannes-Audenaert inequality provides a tight bound on the entropy difference between two probability distributions based on the L1 norm distance between them. The simplified form is: For ,

[0100] in It is a binary entropy function. For small... The world gave Apply it to and This yields the error in the unbalance measurement.

[0101]

[0102] in, Follow The convergence rate exhibits exponential decay, thus proving its exponential nature. From this, it can also be deduced that for the imbalance value to transition between different steps, the threshold value must be... The cost of traversing a certain path is on the order of magnitude of the width of the transition region. .

[0103] big Imbalance analysis provides a risk planning tool for networks designed to support strict SLAs. In this "all or nothing" extreme case, the entire complex fairness change phase diagram simplifies to a distribution of cumulative hop counts. The determined step function. Engineers only need to draw... By understanding the basic distribution of the topology, a complete risk map of all potential performance cliffs can be obtained. This allows identification of which Service Losses (SLOs) are inherently risky because they lie on steep steps, and which are relatively safe because they lie on a broad plane. The above analysis is entirely based on the topology itself, thus providing crucial strategic insights before service deployment. The results of the imbalance analysis are shown in the figure below. Figure 5 As shown, Figure 5 Fixed in the middle (Solid line) and the theoretical piecewise constant limit function The imbalance in the numerical simulation is plotted between the dashed lines. Near-perfect consistency verifies the large... Imbalance analysis predicts network size N=50 (M=2450).

[0104] Figure 5 The strictness of the grid diagram was compared. (blue solid line) and the theoretically derived limit function The imbalance in the numerical simulation is shown on the orange dashed line. The results show that the simulation curve closely matches the theoretical step function, with the equilibrium and descent of each step occurring at the precisely predicted values ​​and locations. The width of the smooth transition region of the step also corresponds to the transition width predicted in Proposition 1. Consistent. This result demonstrates that for networks operating under stringent SLA service requirements, the framework can accurately predict the location of all major performance cliffs.

[0105] To verify the selection in this embodiment This embodiment does not present experimental results by simply selecting parameters; rather, it provides examples of a series of large... Supplementary verification under different values. Its theoretical basis is based on convergence to the largest value. The process at its limit has an exponentially fast speed.

[0106] Figure 6 For the great Supplementary verification results for the limit are shown in the figure. Figure 6The range of strictness parameters was compared. Under these conditions, the theoretical step function (Black dashed line) and simulated curve. With... As the value increases, the simulated curve gradually becomes sharper, approaching the theoretical step more closely. This indicates that... The constraint is not a product of a single parameter choice, but rather the robustness of the proposed framework, which approaches exponentially as the SLA becomes more stringent. The good consistency indicates that even with finite strictness, the theoretical limit provides highly accurate predictions of the behavior of the system (the entire network transmission system, or simply the network).

[0107] Therefore, this embodiment selects As a representative value to showcase large The numerical verification of the limit is reasonable and robust. The value of will not change the qualitative conclusion.

[0108] The two asymptotic laws mentioned above (small) Imbalance analysis and large Imbalance analysis provides boundary conditions for the entire equity landscape and has strong predictive capabilities at both ends of business needs.

[0109] S3. In the global phase diagram, the curvature field is calculated using a matrix formed by the second-order partial derivatives, and the curvature field is used to determine whether it is a stable region.

[0110] In the global phase diagram, the curvature field is calculated using a matrix composed of second-order partial derivatives (such as the Hessian matrix), and the curvature field is used to determine whether it is a stable region.

[0111] The formula for the Hessian matrix is:

[0112] According to Clairaut's theorem, the mixed second-order partial derivatives are equal, making Hessian symmetric. Specifically, It is a powerful, quantitative "performance cliff detector".

[0113] For most nontrivial topologies, the global phase diagram exhibits fundamental asymmetry in curvature.

[0114]

[0115] The physical reason behind this asymmetry lies in the completely different mechanisms of action of the two types of SLA parameters. (Adjusting the threshold) This is equivalent to sliding a dividing line on a discrete distribution of hop counts. When this threshold line crosses a certain integer number of hops, a large number of path satisfaction levels on both sides of the threshold may experience a sudden change, causing the unbalanced gradient to change and forming a high-curvature ridge. In contrast, adjusting the evaluation strictness... This is a globally smoothing transformation. It changes the steepness of the QoE evaluation curve as a whole, and usually does not introduce new abrupt changes; it only lengthens or tightens existing performance bottlenecks. The curvature of the axis will be much smaller than that along the path. The curvature.

[0116] This step involves determining whether the region is stable based on the curvature field, specifically: Based on the curvature field, we determine the high curvature region (which corresponds to the "performance cliff," i.e., the boundary where a small change in SLA parameters can lead to a catastrophic deterioration in network fairness) and the low curvature region (where the network is naturally robust to parameter fluctuations).

[0117] Regions with low curvature are classified as stable regions.

[0118] To facilitate a direct comparison of the fairness of different topologies (network topology models), this embodiment defines the following two scalars: A. Area of ​​Robustness (AoR) This metric characterizes the network's ability to maintain robustness and adaptability across a wide range of business demands. For ease of normalized comparison, this embodiment defines it as the optimal working area. The percentage occupied in the scanned parameter space is shown in the following formula:

[0119] in, This represents the total area of ​​the scanned SLA parameter space. A higher AoR value indicates a more robust network topology design.

[0120] B. Maximum Curvature Risk (MCR) This metric is used to characterize the sharpness of performance risk at the acceptable performance boundary, and is defined as the level at the optimal region boundary. The maximum value of the curvature in the threshold direction is shown in the following formula:

[0121] The smaller the MCR value, the smoother the performance transition of the network topology design and the lower the risk.

[0122] S4. If it is a stable region, calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient.

[0123] S5. Based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, network fairness is predicted, and the network fairness prediction results are obtained.

[0124] unbalanced gradient The gradient of average satisfaction points in the fastest direction of increasing local unfairness. It points in the direction of the fastest increase in average satisfaction. The gradient is a simple average of the path sensitivity, while The gradient has a more complex structure and contains deeper insights.

[0125] For any SLA parameter The partial derivative of the QoE imbalance metric (imbalance gradient) can be expressed as a weighted covariance, as shown in the following equation.

[0126]

[0127] in, For weighted covariance, The sensitivity term is and The detailed derivation of this formula is explained below: The above formula mainly relies on the chain rule; this embodiment uses subscripts. Represents a node pair .

[0128] (1) Regarding probability Differentiation Imbalance is defined as For ease of derivation, entropy is expressed in the form of the natural logarithm. For parameter space Differentiating, we get:

[0129] Will Expressed as a weight function Depend on The general derivative form of the weights According to the application merchant rule:

[0130] in, Sensitivity Item In distribution The expectations below.

[0131] (2) Merge and identify covariance structures Will Substitution ,get:

[0132] The above summation term is the weighted covariance. From the definition of covariance, we can derive the formula for calculating covariance.

[0133] The partial derivative of the QoE imbalance metric (imbalance gradient), expressed as a weighted covariance, is a powerful mathematical tool for local judgment. It indicates that the change in the overall imbalance of the network is determined by the covariance between the two key quantities of each path: A. Entropy lever

[0134] This term comes directly from the derivative of entropy and can be considered a weight in the information theory sense. Regarding the percentage of satisfaction... Minimal paths (i.e., those at the edge or with low traffic). Taking a large negative value corresponds to a very large leverage; while for paths with a high percentage of satisfaction (core or good), the leverage is smaller.

[0135] B. Parameter Sensitivity

[0136] This is characterized in SLA parameters. The degree to which the satisfaction score of a path changes drastically when a small change occurs. Typically, performance approaches a threshold. The path is the most sensitive.

[0137] Meanwhile, covariance reveals the properties of the system response: a. Positive definite covariance ( This leads to a deterioration in fairness. This is an extremely serious adverse effect. This occurs when the path most sensitive to SLA is also the path with the highest entropy leverage. From a physical perspective, changes to SLA parameters disproportionately affect marginal paths, widening the gap between them and the critical path, and thus exacerbating the overall imbalance.

[0138] b. Negative definite covariance ( Fairness improvement. When SLA changes primarily affect the dominant path with a high share, weakening its dominance by altering satisfaction levels on the critical path can lead to a more even distribution of overall satisfaction.

[0139] c. Zero covariance ( The system is robust to changes in the current SLA. That is, the impact of the network strategy corresponding to the current SLA parameters on each path is almost unrelated to its existing proportion, remaining in a stable region.

[0140] The above analysis transforms the gradient from a simple vector into a rich, narrative interpretation of network behavior. Furthermore, by analyzing two gradient vectors... and The angle between them is used to reveal the trade-offs and to quantitatively characterize the local "efficiency-fairness" conflict.

[0141] Compared to purely numerical gradients, covariance has a significant advantage in studying changes in network fairness. Assume the engineer slightly increases the threshold... And observed the overall network imbalance. Increase. Numerical gradients are only reported. This proves that it produced negative results, but it cannot provide a causal explanation. Covariance, on the other hand, can not only report... This further illustrates that positive definite covariance is caused by a high-parameter sensitivity term ( ) and high-entropy levers ( The strong correlation between these paths is the driving force. In practice, this suggests that current SLA changes do not affect all paths equally, but rather impose an excessive burden on a set of long paths that have already been marginalized and are on the verge of being overloaded.

[0142] In engineering practice, "coarse tuning first, then fine tuning" is a common rule of thumb. This embodiment provides a rigorous quantitative demonstration of this strategy for the first time in the context of SLA parameter tuning. Furthermore, analysis shows that along the threshold axis... The curvature ratio along The curvature of the axis is several orders of magnitude higher. In summary, this embodiment uses a threshold-first principle to optimize the evaluation strictness and path cost performance thresholds. The specific operation for optimizing the evaluation strictness and path cost performance thresholds is as follows: A. First adjust the path cost performance threshold. , set the path cost performance threshold As a coarse-grained control variable, it seeks a broad, low-curvature stable region in the global phase diagram and prioritizes moving SLA parameter points away from any high-performance risks.

[0143] B. Re-adjusting the evaluation strictness

[0144] After entering the stable region, the evaluation rigor is then assessed. Fine-tuning is required to achieve the desired balance between fairness and business QoE.

[0145] In this embodiment, the threshold-first rule is a direct and operable result of second-order curvature analysis, which realizes the transformation of theoretical insights into practical design guidance tools for network engineering, and can also effectively avoid the risk of network cascading congestion that may be triggered by blindly adjusting parameters.

[0146] The simulation results of each step of the method of the present invention are as follows: Figure 7 As shown, Figure 7 (a) To construct the unbalanced phase map Figure 7 (b) To generate a curvature risk map, revealing high-risk jumps during integer jump number transitions. Figure 7 (c) For a stable region (e.g.) Analyze the gradient field to understand the performance trade-offs. Figure 7 (d) is for superimposed service targets ( ), thus determining the final optimal operating region (highlighted in red).

[0147] To understand the origins of these high-risk ridge areas, this embodiment studies an extreme case—a star-shaped map, such as... Figure 8 As shown Figure 8 (a) The unbalanced phase diagram shows a sharp performance cliff. Figure 8 (b) To accurately identify the cliff in the curvature risk map. High-risk areas Figure 8 (c) reveals the reason for the hop count distribution: the path length of the network exhibits a bimodal distribution at hop 1 and hop 2, making... (This is a key bifurcation point.) The path length distribution in the star graph exhibits a clear bimodal structure, with only two types of paths: 1-hop and 2-hop. Therefore, in... An extremely steep performance cliff will appear nearby. When the threshold is adjusted from greater than 1.5 to less than 1.5, the set of critical paths that meet the threshold will drop sharply from almost all paths to a very small number of paths, resulting in a sharp drop in system entropy and a sharp increase in imbalance, corresponding to a distinct ridge on the curvature graph.

[0148] The phenomenon of adjusting h0 as a discrete parameter across the path distribution is the fundamental reason for the basic asymmetry of the global phase diagram curvature. Figure 9 As shown, Figure 9 (a) is the global phase diagram. Figure 9 (b) is The curvature of the axis, with sharp ridges indicating high-risk areas. Figure 9 (c) Logarithmic ratio of curvature The bright red area indicates that curvature ratio A curvature an order of magnitude larger confirms the danger of adjustment along the threshold axis. In contrast, the adjustment evaluation strictness... It is a globally smoothing transformation that simultaneously alters the steepness of the QoE curves for all paths. Therefore, the risk (curvature) along the h0 axis is always several orders of magnitude higher than along the a axis. ).

[0149] The above in-depth analysis directly leads to the most important design principle of this paper: the threshold-first tuning strategy. This strategy first browses the most dangerous dimension in the parameter space, using a threshold as coarse-grained control to locate a safe, low-curvature stable region, and then uses strictness to fine-tune within the pre-verified safe region, effectively reducing the risk of catastrophic performance changes.

[0150] In stark contrast to the high-risk areas, the dark, low-curvature areas in the grid plot correspond to robust, stable regions where the system is almost insensitive to parameter adjustments, providing engineers with greater freedom in parameter tuning.

[0151] The formation of these stable regions is closely related to the concentration of path lengths. Take the BA diagram as an example (…). Figure 10 As shown in the figure, its path length is highly concentrated around 2 hops and 3 hops, accounting for over 90%. This structural homogeneity is precisely its... The fundamental reason for the large stable region is that within this threshold range, almost all paths are considered critical paths with high satisfaction. This also demonstrates a key principle of QoE fairness: topologies with centralized network structure (and low path variance) exhibit strong robustness across a wide range of SLAs. Figure 10 (a) The phase diagram is dominated by a large, low-disequilibrium stable region in the upper left corner and a high-disequilibrium dangerous region. Figure 10 (b) The hop count distribution reveals the reason: the vast majority of paths are highly concentrated in 2- and 3-hop areas, forming a stable region, while the danger zone is the result of selecting only a few 1-hop paths under strict SLA. Under a relaxed SLA, the change in network fairness is proportional to... Therefore, this embodiment proposes a second design principle: path variance serves as a priori surrogate for stable regions. This provides network designers with a low-complexity, early screening tool, requiring only comparison during the candidate topology design phase. By prioritizing the structure that minimizes the path length variance, we can predict its fairness and resilience at the topology level before deploying it in large-scale simulations.

[0152] To demonstrate the applicability of the method to real-world large-scale infrastructure, this embodiment presents a case study of a real-world AS topology. This embodiment uses publicly available data released by CAIDA in August 2025 to extract the largest connected component. To focus on the core network backbone while considering computational feasibility, this embodiment performs 10-core extraction on the graph, a common method in network science for finding the most dense subgraph. The resulting subgraph contains 9068 nodes and over 420,000 edges. Based on this, this embodiment performs a complete four-step fairness analysis process.

[0153] The AS topology diagram shows the fairness changes. Figure 11 As shown. First, through the global phase diagram ( Figure 11 (a) shows that the phase diagram of the AS topology is similar to that of the BA diagram, also having a wide stable region, in which the unbalance... The value remains close to 0, indicating that the AS network core structure maintains a high degree of fairness under a very wide range of SLA requirements. Figure 11 (a) shows the global phase, revealing a large stable region. The optimal operating region is marked by a red outline. ), Figure 11 (b) is a curvature risk plot, indicating that the highest performance cliff is concentrated at a very low threshold. ). from Figure 11 As can be seen, the performance cliff is mainly concentrated in a narrow region with extremely strict thresholds. The highest curvature risk occurs in... Nearby, and towards Further, the maximum curvature risk (MCR) at the optimal region boundary is approximately 0.0117, which is still relatively small, indicating that while these performance changes exist, they are not catastrophic abrupt changes.

[0154] Table 2 compares the AS 10-core model with the BA model of the same size. The path variance of AS is also shown. It is much lower than the BA model, which makes it suitable for small... It exhibits extremely strong stability in this case. Compared to the BA model, the AS topology has a larger robust area AoR and a smaller maximum curvature risk MCR, indicating that it not only has highly compact paths but also smoother performance transitions at the boundaries.

[0155] Table 2 Comparison of performance metrics between AS 10-core and BA network of similar size

[0156] The experimental environment used in the method of this invention is described below: This simulation experiment will generate and analyze two defined metrics for a series of representative network topologies: annotated phase diagrams and quantitative metrics (AoR, MCR). All simulations are implemented in Python, based on the NetworkX, NumPy, and SciPy libraries.

[0157] The selected topologies reflect different and typical structural characteristics, which are described below: (1) Typical diagram. Complete diagram. Path map With star diagram As a benchmark, it is used to explore the response of the proposed framework to extreme cases such as network connectivity, linear structure, and centralization.

[0158] (2) Random graph models. The Erdos-Rényi (ER), Barabási-Albert (BA) and Watts-Strogatz (WS) models were analyzed to study the fairness of network topologies with random connections, scale-free properties and small-world effects.

[0159] (3) Real Topology. The applicability of the framework to real-world large-scale network infrastructure was verified using Internet Autonomous System (AS) topology snapshots provided by the CAIDA project.

[0160] To ensure consistent variables, all graphical models in this embodiment are... This is generated under the network scale condition. First, the shortest path distribution (APSP) of all node pairs for each topology is calculated. Then, we systematically scan the SLA parameters. The method of this invention is executed on a high-density grid to obtain the corresponding spectra and indices.

[0161] In summary, the present invention provides strong evidence for its application in the real world. The AS topology creates a highly efficient backbone network with very low path length differences. The present invention demonstrates that this structural efficiency not only benefits performance but is also the fundamental reason why real-world networks possess special functional fairness and robustness under varying service demands.

[0162] Example 5: Please see Figure 12 As shown, the present invention also provides an electronic device 100 for a network fairness prediction method; the electronic device 100 includes a memory 101, at least one processor 102, a computer program 103 stored in the memory 101 and executable on the at least one processor 102, and at least one communication bus 104.

[0163] The memory 101 can be used to store the computer program 103. The processor 102 implements the steps of the network fairness prediction method described in Embodiment 1 by running or executing the computer program stored in the memory 101 and calling the data stored in the memory 101. The memory 101 may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created according to the use of the electronic device 100 (such as audio data), etc. In addition, the memory 101 may include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other non-volatile solid-state storage device.

[0164] The at least one processor 102 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor 102 may be a microprocessor or any conventional processor. The processor 102 is the control center of the electronic device 100, connecting various parts of the electronic device 100 via various interfaces and lines.

[0165] The memory 101 in the electronic device 100 stores multiple instructions to implement a network fairness prediction method, and the processor 102 can execute the multiple instructions to achieve the following: In the user satisfaction model, the space of service level agreement parameters is scanned to obtain the scan results; The method for constructing the user satisfaction model includes: In the network topology model, a user satisfaction model is constructed based on the service level agreement parameters; Based on the scan results, the imbalance degree and average satisfaction are obtained, and a global phase diagram is generated based on the imbalance degree and average satisfaction. In the global phase diagram, the curvature field is calculated using a matrix composed of second-order partial derivatives, and the curvature field is used to determine whether it is a stable region. If it is a stable region, calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient. Network fairness is predicted based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, resulting in a network fairness prediction.

[0166] Example 6: If the modules / units integrated in the electronic device 100 are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, and a read-only memory (ROM).

[0167] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0168] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0169] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0170] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0171] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting network fairness, characterized in that, Includes the following steps: In the user satisfaction model, the space of service level agreement parameters is scanned to obtain the scan results; The method for constructing the user satisfaction model includes: In the network topology model, a user satisfaction model is constructed based on the service level agreement parameters; Based on the scan results, the imbalance degree and average satisfaction are obtained, and a global phase diagram is generated based on the imbalance degree and average satisfaction. In the global phase diagram, the curvature field is calculated using a matrix composed of second-order partial derivatives, and the curvature field is used to determine whether it is a stable region. If it is a stable region, calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient. Network fairness is predicted based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, resulting in a network fairness prediction.

2. The network fairness prediction method according to claim 1, characterized in that, The service level agreement parameters include evaluation strictness and path cost performance threshold.

3. The network fairness prediction method according to claim 2, characterized in that, The threshold priority principle is adopted to optimize the evaluation strictness and path cost performance thresholds.

4. The network fairness prediction method according to claim 1, characterized in that, The process of constructing a user satisfaction model based on the Service Level Agreement (SLA) within the network topology model involves using the Sigmoid function to build the user satisfaction model based on SLA parameters.

5. The network fairness prediction method according to claim 1, characterized in that, The formula for calculating the unbalance is: in, For the degree of imbalance, For Shannon entropy, The number of node pairs; Shannon entropy The calculation formula is: in, Standardized satisfaction share The calculation formula is: in, The satisfaction score. For node pairs.

6. The network fairness prediction method according to claim 1, characterized in that, The formula for calculating the average satisfaction level is: in, The average satisfaction level. The QoE satisfaction level for each path in the network under any Service Level Agreement (SLA) parameters. The number of nodes; QoE satisfaction for each path in the network under any Service Level Agreement parameters The calculation formula is: in, As an objective path cost, This represents the path cost performance threshold. To evaluate the rigor.

7. The network fairness prediction method according to claim 1, characterized in that, The determination of whether a region is stable based on the curvature field is as follows: Based on the curvature field, determine the high curvature region and the low curvature region; Regions with low curvature are classified as stable regions.

8. A network fairness prediction system, characterized in that, include: The scanning module is used to scan the space of service level agreement parameters in the user satisfaction model and obtain the scanning results. The method for constructing the user satisfaction model includes: In the network topology model, a user satisfaction model is constructed based on the service level agreement parameters; The global phase diagram generation module is used to obtain the imbalance degree and average satisfaction based on the scan results, and to generate a global phase diagram based on the imbalance degree and average satisfaction. The stable region determination module is used to calculate the curvature field in the global phase diagram using a matrix composed of second-order partial derivatives, and to determine whether it is a stable region based on the curvature field. The calculation module is used to calculate the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient in the case of a stable region. The prediction module is used to predict network fairness based on the imbalance gradient, the average satisfaction gradient, and the angle between the imbalance gradient and the average satisfaction gradient, and obtain the network fairness prediction result.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the network fairness prediction method according to any one of claims 1 to 7.

10. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the network fairness prediction method according to any one of claims 1 to 7.

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