Method, system and device for capacity expansion optimization based on network performance marginal gain

Abstract

The application relates to a capacity expansion optimization method and system based on network performance marginal gain and equipment, and belongs to the technical field of network communication. The method comprises the following steps: constructing an undirected graph of a communication network topology; defining service requirements for each pair of nodes in the undirected graph, and assigning a capacity value to each edge to construct an MCFP model; based on the Lagrange dual theory, a dual model of the MCFP model is constructed, and a column generation algorithm is used to synchronously solve the dual models to obtain a maximum concurrency factor, an optimal path flow and a capacity-constrained optimal dual variable; network key bottlenecks are identified according to the capacity-constrained optimal dual variable, and a plurality of capacity expansion candidate schemes are generated; the capacity expansion candidate schemes are comprehensively evaluated in combination with the network performance marginal gain, the influence degree of link capacity change and the implementation cost, and the optimal capacity expansion scheme is selected for implementation. The application can realize accurate evaluation of communication network load, quantitative identification of bottlenecks and efficient optimization of capacity expansion.

Description

Technical Field

[0001] This application relates to the field of network communication technology, and in particular to a method, system and device for capacity expansion optimization based on the marginal gain of network performance. Background Technology

[0002] In modern communication networks such as industrial automation bus networks, cloud computing data center networks, and IoT communication networks, with the surge in the number of connected devices and the explosive growth of service data, network performance bottlenecks have become a core issue restricting data transmission efficiency and affecting service stability. Existing technologies have significant shortcomings in three key areas: network load assessment, bottleneck identification, and capacity expansion optimization, as detailed below:

[0003] Firstly, there is a lack of scientific quantitative models for assessing network load capacity: existing technologies rely heavily on single-link traffic statistics or empirical judgments to assess network load capacity, without considering the global impact of network topology, link capacity correlation, and business demand distribution. This may lead to excessive resource reservation during network planning, resulting in waste, or performance bottlenecks due to insufficient resource allocation, making it difficult to achieve accurate matching between network resources and business needs.

[0004] Secondly, bottleneck link identification suffers from low accuracy and lacks quantitative basis: existing bottleneck identification technologies, primarily based on traffic threshold triggering or post-fault retrospective analysis, suffer from high false positive rates, strong lag, and an inability to quantify the impact of bottlenecks. On the one hand, some links may have high traffic but are not key constraints on network performance; overemphasizing such links can lead to resource misallocation. On the other hand, some links may have traffic below the threshold but are "structural bottlenecks" (such as the sole link connecting two core areas); ignoring such links can lead to long-term bottleneck risks. Furthermore, existing technologies cannot quantify the impact of each link on overall network performance, nor can they distinguish between critical bottlenecks and general congestion, resulting in a lack of targeted optimization solutions.

[0005] Thirdly, network expansion schemes are often blind and have low resource utilization: existing expansion schemes often adopt uniform expansion by increasing the capacity of all links by the same proportion or random expansion by selecting links based on operation and maintenance experience, without considering the differences in the marginal contribution of different links to network performance.

[0006] The core reason for the aforementioned shortcomings lies in the fact that existing technologies lack the ability to mathematically model the global relationship between "topology-capacity-demand" in communication networks, and cannot quantify the load ceiling, bottleneck impact, and expansion effectiveness from a holistic network perspective. Therefore, there is an urgent need for a technical solution based on a scientific mathematical model to achieve accurate network load assessment, bottleneck quantitative identification, and efficient expansion optimization. Summary of the Invention

[0007] Therefore, it is necessary to provide a capacity expansion optimization method, system, and device based on the marginal gain of network performance to address the above-mentioned technical problems.

[0008] A scaling optimization method based on network performance marginal gain, the method comprising:

[0009] By abstracting the physical devices in the communication network as a set of nodes and the physical links between devices as a set of edges, an undirected graph of the network topology is constructed.

[0010] The MCFP model is constructed by defining business requirements for each pair of nodes in an undirected graph and assigning a capacity value to each edge. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, in order to maximize the concurrency factor, which is defined as the network load carrying capacity coefficient.

[0011] Based on Lagrange duality theory, a dual model of the MCFP model is constructed, and a column generation algorithm is used to solve the two models simultaneously to obtain the maximum concurrency factor, optimal path flow, and optimal dual variables of capacity constraints.

[0012] Based on the optimal dual variables of capacity constraints, the key bottleneck links in the network are quantitatively identified, classified, and prioritized for expansion in sequence. By adjusting the capacity of multiple key bottleneck links after prioritization, multiple expansion candidate schemes with different capacity adjustment amounts are generated.

[0013] The adjusted link capacity of each expansion candidate scheme is resubmitted into the MCFP model for solution, and the updated maximum concurrency factor is obtained and compared with the original maximum concurrency factor to obtain the marginal gain of network performance. The expansion candidate schemes are comprehensively evaluated by combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, and the optimal expansion scheme is selected for implementation.

[0014] In one embodiment, the method further includes, before constructing the MCFP model:

[0015] In an undirected graph of a communication network topology In the definition, the capacity function and the business requirement function are defined; among them, For a set of nodes, Let be the set of edges. The total number of nodes. For the first Link, , This represents the total number of links.

[0016] The capacity function is defined as The capacity function Link The capacity is defined as , The value is determined based on the physical characteristics of the link, protocol standards, or actual test data; among which, It is the set of nonnegative real numbers;

[0017] Business requirement function is defined as ,satisfy and ;in, Represents a node With nodes Average service transmission requirements The value is determined by historical traffic statistics, business forecasts, or business specification requirements;

[0018] Collect the capacity from the capacity function and the business requirements from the business requirements function, and perform preprocessing.

[0019] In one embodiment, the capacity in the capacity function and the business requirements in the business requirement function are collected and preprocessed, including:

[0020] Outlier handling: using The criteria identify outliers in link capacity and replace them with the average capacity of links of the same type or remove them.

[0021] Demand smoothing: The sliding window averaging method is used to eliminate the impact of short-term traffic pulses on the business demand function. The size of the sliding window is set according to the business cycle.

[0022] Unit unification: The units for link capacity and service requirements are uniformly converted to Mbps.

[0023] In one embodiment, an MCFP model is constructed by defining business requirements for each pair of nodes in the undirected graph and assigning a capacity value to each edge, expressed as:

[0024] ;

[0025] in, Concurrency factor; Path in the network Traffic allocation on the platform; As a constraint of business requirements, it represents the condition for a set of nodes. Any pair of nodes in The sum of traffic on all paths equals the average service transmission demand. The product of the concurrency factor, For nodes With nodes The set of all paths between; Link capacity constraint, meaning that for a set of edges any link in All passing through the link The sum of path traffic does not exceed the link capacity , For included links The set of all paths; and The non-negativity constraint indicates that both path flow and concurrency factor are non-negative.

[0026] In one embodiment, based on Lagrange duality theory, the dual model of the MCFP model is constructed, as follows:

[0027] ;

[0028] in, For link Capacity-constrained dual variables; For node pairs with communication needs The dual variables of the demand constraints between them; This is a function for business requirements.

[0029] In one embodiment, a column generation algorithm is used to solve the dual models simultaneously, obtaining the maximum concurrency factor, optimal path flow, and optimal dual variables for capacity constraints, including:

[0030] Constructing the Restricted Master Problem (RMP): For each pair of average traffic transmission requirements node pairs Generate initial paths to form an initial path set. ;based on Construct an RMP, at which point the RMP variables only contain Path flow and concurrency factor The constraints of RMP are consistent with those of the MCFP model.

[0031] Solving RMP: The interior-point method is used to solve RMP and obtain the initial path flow. Initial concurrency factor Demand constraint dual variables and capacity-constrained dual variables ;

[0032] Pricing sub-problems and finding improvement paths: Defining link weights For each pair node pairs Solve Shortest path with weight The path weight is the sum of the weights of the links contained in the path.

[0033] Calculate the shortest path The test number is When the test number is less than 0, This will improve the concurrency factor. The value, and Added to the path set as an improved path If the test count for all paths is greater than or equal to 0, then the solution process is terminated.

[0034] Iterative update: Adding improvement paths Update the RMP and solve it again. Repeat the RMP solution steps and the steps of pricing the subproblem and finding an improved path until there are no paths with a test number less than 0. Stop the calculation and obtain the optimal solution of the MCFP model and the optimal solution of the dual model. Among them, the optimal solution of the MCFP model includes the maximum concurrency factor. Optimal path traffic and optimal link traffic The optimal solution of the dual model includes the optimal dual variables of the demand constraint. and capacity-constrained optimal dual variables ;in, For included links The set of all paths.

[0035] In one embodiment, the key bottleneck links in the network are quantitatively identified, classified, and prioritized for expansion according to the optimal dual variable of the capacity constraint, including:

[0036] When link of At that time, the link The link was identified as a critical bottleneck; among them, when the link of and At that time, critical bottleneck links are classified as strong bottleneck links; when the link of and At that time, critical bottleneck links are classified into potential bottleneck links; among them, and They represent the capacity-constrained optimal dual variables respectively. The upper and lower bounds; when the optimal solution obtained by the model is unique. ;

[0037] when At that time, the link The link is determined to be non-critical; the non-critical link is classified as one that is fully loaded in some optimal solutions but not fully loaded in other optimal solutions, or one that is not fully loaded in all optimal solutions.

[0038] For all identified The key bottleneck link, based on Sort the values ​​in descending order; The higher the value, the greater the marginal contribution of increasing link capacity to the overall network performance, and the higher the priority for expansion when resources are limited.

[0039] In one embodiment, the impact of link capacity changes includes:

[0040] When link Capacity change When the discrete influence factor is defined, its expression is:

[0041] ;

[0042] in, For link Capacity change The maximum concurrency factor was then obtained by resolving the MCFP model. This represents the original maximum concurrency factor;

[0043] Based on discrete impact factor The upper and lower bounds are used to predict the impact of changes in link capacity. The upper and lower bounds are represented as:

[0044] ;

[0045] in, This indicates the optimal traffic flow for the link. For optimal path traffic, Indicates any path, For included links The set of all paths This is the upper bound of the optimal dual variable for capacity constraints.

[0046] A scaling optimization system based on marginal gain of network performance, the system comprising:

[0047] The network parameter modeling module is used to construct an undirected graph of the network topology by abstracting physical devices in the communication network as a set of nodes and physical links between devices as a set of edges.

[0048] The MCFP model building module is used to construct an MCFP model by defining business requirements for each pair of nodes in an undirected graph and assigning a capacity value to each edge. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, in order to maximize the concurrency factor, where the concurrency factor is defined as the network load carrying capacity coefficient.

[0049] The model solving module is used to construct the dual model of the MCFP model based on Lagrange duality theory, and to solve the dual model simultaneously using a column generation algorithm to obtain the maximum concurrency factor, optimal path flow, and optimal dual variables of capacity constraints.

[0050] The bottleneck identification module is used to quantitatively identify, classify, and prioritize the expansion of key bottleneck links in the network according to the optimal dual variable of capacity constraints. It also generates multiple expansion candidate schemes with different capacity adjustment amounts by adjusting the capacity of multiple key bottleneck links after prioritizing expansion.

[0051] The capacity expansion optimization module is used to re-substitute the adjusted link capacity of each expansion candidate scheme into the MCFP model for solution, obtain the updated maximum concurrency factor and compare it with the original maximum concurrency factor to obtain the marginal gain of network performance. By combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, the expansion candidate schemes are comprehensively evaluated, and the optimal expansion scheme is selected for implementation.

[0052] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0053] By abstracting the physical devices in the communication network as a set of nodes and the physical links between devices as a set of edges, an undirected graph of the network topology is constructed.

[0054] The MCFP model is constructed by defining business requirements for each pair of nodes in an undirected graph and assigning a capacity value to each edge. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, in order to maximize the concurrency factor, which is defined as the network load carrying capacity coefficient.

[0055] Based on Lagrange duality theory, a dual model of the MCFP model is constructed, and a column generation algorithm is used to solve the two models simultaneously to obtain the maximum concurrency factor, optimal path flow, and optimal dual variables of capacity constraints.

[0056] Based on the optimal dual variables of capacity constraints, the key bottleneck links in the network are quantitatively identified, classified, and prioritized for expansion in sequence. By adjusting the capacity of multiple key bottleneck links after prioritization, multiple expansion candidate schemes with different capacity adjustment amounts are generated.

[0057] The adjusted link capacity of each expansion candidate scheme is resubmitted into the MCFP model for solution, and the updated maximum concurrency factor is obtained and compared with the original maximum concurrency factor to obtain the marginal gain of network performance. The expansion candidate schemes are comprehensively evaluated by combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, and the optimal expansion scheme is selected for implementation.

[0058] The above-mentioned capacity expansion optimization method, system, and device based on the marginal gain of network performance have the following advantages compared with existing technologies:

[0059] 1. By establishing and solving the Maximum Concurrent Flow Problem (MCFP) model, a theoretical network load limit—the maximum concurrency factor—is directly output. This indicator deeply integrates the global coupling relationship between network topology, link capacity matrix, and service demand matrix, providing a precise and repeatable network performance metric that transcends local observation, thus providing a solid theoretical foundation for network planning, capacity pre-assessment, and performance bottleneck early warning.

[0060] 2. This approach innovatively applies the duality theory of linear programming, transforming bottleneck identification into an adjunct output of an optimization problem. The optimal dual variable for capacity constraints, physically representing the shadow price of link capacity, becomes an objective and rigorous mathematical criterion for judging critical bottlenecks, completely eliminating subjective arbitrariness. More importantly, the calculated values ​​of the optimal dual variable for capacity constraints directly and quantitatively characterize the "marginal value" of each link to global performance, achieving precise quantitative ranking of the importance of bottleneck links and providing guidance for resource allocation.

[0061] 3. This application does not provide a single indicator, but rather constructs a complete closed-loop decision support system. This system uses the maximum concurrent flow model as its computational engine, shadow price as its core decision indicator, and accurate simulation and rapid prediction as evaluation tools, forming a complete closed loop from global performance evaluation to bottleneck quantitative identification, and then to multi-dimensional quantitative simulation and verification of expansion solutions. This system completely upgrades network expansion decisions from the traditional model relying on fragmented experience and passive responses to a scientific decision-making model based on global models, proactive optimization, and data simulation. This ensures that limited network construction and optimization resources are precisely invested in the most effective aspects for improving overall network performance, greatly improving investment efficiency, network robustness, and overall performance. Attached Figure Description

[0062] Figure 1 This is a flowchart illustrating a capacity expansion optimization method based on marginal gain of network performance in one embodiment.

[0063] Figure 2 This is a block diagram of a scaling optimization system based on the marginal gain of network performance in one embodiment;

[0064] Figure 3 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0066] In one embodiment, such as Figure 1 As shown, a scaling optimization method based on the marginal gain of network performance is provided, including the following steps:

[0067] Step 1: By abstracting the physical devices in the communication network into a set of nodes and the physical links between devices into a set of edges, an undirected graph of the network topology is constructed.

[0068] Step 2: By defining business requirements for each pair of nodes in the undirected graph and assigning a capacity value to each edge, the MCFP model is constructed. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, in order to achieve the goal of maximizing the concurrency factor, where the concurrency factor is defined as the network load carrying capacity coefficient.

[0069] Step 3: Based on Lagrange duality theory, construct the dual model of the MCFP model, and use the column generation algorithm to solve the dual model simultaneously to obtain the maximum concurrency factor, optimal path flow, and optimal dual variables of capacity constraints.

[0070] Step 4: Based on the optimal dual variable of the capacity constraint, the key bottleneck links in the network are quantitatively identified, classified, and prioritized for expansion in sequence. Then, by adjusting the capacity of multiple key bottleneck links after prioritization, multiple expansion candidate schemes with different capacity adjustment amounts are generated.

[0071] Step 5: Substitute the adjusted link capacity of each expansion candidate scheme back into the MCFP model for solution, obtain the updated maximum concurrency factor and compare it with the original maximum concurrency factor to obtain the marginal gain of network performance. Then, by combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, a comprehensive evaluation of the expansion candidate schemes is carried out, and the optimal expansion scheme is selected for implementation.

[0072] The aforementioned expansion optimization method based on the marginal gain of network performance, based on the maximum concurrent flow theory, duality theory and marginal utility analysis, constructs a closed-loop, data-driven intelligent expansion decision system of "evaluation-identification-simulation-decision". It can quantify the load limit, bottleneck impact and expansion utility from the perspective of the overall network, and realize accurate network load evaluation, bottleneck quantitative identification and efficient expansion optimization.

[0073] In one embodiment, the purpose of step 1 is to transform the physical characteristics of the actual communication network into standardized parameters required by the MCFP model, providing an input basis for subsequent solutions. The core is to define the mathematical expression of network topology, link capacity, and service requirements, which specifically includes the following steps:

[0074] Step 1.1, Network Topology and Parameter Definition: Abstract the physical devices (routers, switches, terminal nodes, servers) in the communication network into a set of nodes. , Given the total number of nodes, the physical links between devices (fiber optic, wireless, bus links) are abstracted as a set of edges. , For the first Link, , Construct an undirected graph of the network topology to represent the total number of links. For example, in an industrial automation bus network, the master controller and slave devices are nodes, and the bus between the master and slave devices is an edge; in a cloud computing data center network, the core switch and server are nodes, and the optical fiber between the switches is an edge.

[0075] In an undirected graph of a communication network topology In this context, capacity functions and business requirement functions are defined.

[0076] The capacity function is defined as The capacity function Link The capacity is defined as (Unit: Mbps / Gbps) The value is determined based on the physical characteristics of the link (such as fiber bandwidth and wireless channel capacity), protocol standards (such as Ethernet IEEE 802.3 and industrial bus PROFINET), or actual test data; among which, It is the set of non-negative real numbers.

[0077] Business requirement function is defined as ,satisfy (Two-way communication services) and (Nodes have no self-requirements); among them, Represents a node With nodes The average service transmission demand (unit: Mbps) can be obtained in three ways: ① Historical traffic statistics (collecting average values ​​for 1-3 months); ② Service forecasting (ARIMA (Autoregressive Integral Moving Average) / LSTM (Long Short-Term Memory Neural Network) to predict growth trends); ③ Service specification requirements (such as the explicit bandwidth requirements of industrial control instructions and medical imaging).

[0078] Step 1.2: To ensure the accuracy of the input to the MCFP model, the capacity in the capacity function and the business requirements in the business requirements function are further collected and preprocessed.

[0079] In one embodiment, step 1.2 specifically includes:

[0080] Outlier handling: using The criteria identify outliers in link capacity (such as exceeding physical limits due to testing errors), replacing them with the average capacity of similar links or removing them entirely. Demand smoothing: A sliding window averaging method is used to eliminate the impact of short-term traffic spikes on the service demand function; the sliding window size is set according to the service cycle. Unit standardization: The units for link capacity and service demand are standardized to Mbps (bits per second) to avoid calculation errors caused by unit differences.

[0081] In one embodiment, step 2 is the core mathematical support of this application, specifically including: the goal of the MCFP model is to maximize the network's concurrency factor Z (quantifying the network's maximum load-bearing capacity) while satisfying service demand constraints and link capacity constraints. The model form is as follows:

[0082] Decision variables:

[0083] (1) Path flow : ( (a set of all paths in the network), representing a path. Traffic allocation (unit: Mbps).

[0084] (2) Concurrency factor Dimensionless, representing the network load capacity coefficient. The larger the network size, the higher the load it can handle while still meeting demand.

[0085] Objective function: Maximize the concurrency factor ,Right now: .

[0086] Constraints:

[0087] (1) Business requirement constraints: For the node set Any pair of nodes in The sum of traffic on all paths equals the average service transmission demand. The product of this and the concurrency factor ensures that business requirements are met. ,in For nodes With nodes The set of all paths between.

[0088] (2) Link capacity constraint: For the edge set any link in All passing through the link The sum of path traffic does not exceed the link Capacity to avoid link overload: ,in For included links The set of all paths.

[0089] (3) Non-negativity constraint: Both path flow and concurrency factor are non-negative, which is consistent with the physical meaning: .

[0090] Based on the above modeling, the MCFP model is constructed, and its mathematical form is as follows:

[0091] .

[0092] In one embodiment, step 3 specifically includes:

[0093] Step 3.1, Construction of the dual model and its theoretical basis.

[0094] (1) The original problem is transformed into a standard minimization linear programming problem.

[0095] To adapt to the solution of Lagrange duality theory, the MCFP edge-path maximization problem is transformed ( This can be transformed into a standard minimum linear programming problem:

[0096] Decision variable vector: ,in For the initial path set The number of paths in the data.

[0097] Objective function: , corresponding to the target coefficient vector (All path traffic) The coefficient is 0. The coefficient is -1).

[0098] Constraint matrix form:

[0099] Business requirement constraints: ,in For the demand association matrix (if path Belongs to node pairs If the value is 1, then the element at the corresponding position is 1; otherwise, it is 0. The corresponding element is ), (Zero vector).

[0100] Link capacity constraints: ,in For the capacity incidence matrix (if path Includes links If the value is 1, then the element at the corresponding position is 1; otherwise, it is 0. The corresponding column element is 0). Link capacity vector (elements are...) ).

[0101] Lagrange duality theory, also known as Lagrange duality theory, is based on the idea of ​​introducing Lagrange multipliers (dual variables) to integrate the constraints of the original problem into the objective function, forming a Lagrange function. The dual problem is then constructed through minimization and maximization operations on this function.

[0102] (2) Definition and theoretical basis of dual variables.

[0103] Based on the duality theory of linear programming, dual variables are introduced for each of the two types of constraints:

[0104] Demand constraint dual variables : Corresponding demand equality constraint Unsigned (the dual variable of the equality constraint can be positive or negative), representing the implicit contribution of unit business demand to the network's "virtual cost".

[0105] Capacity-constrained dual variables : Corresponding capacity inequality constraint ,satisfy (The dual variable of the inequality constraint “≤” is non-negative), and its physical meaning is the “shadow price” of the link capacity, that is, the degree of influence of each unit increase in capacity on the objective function.

[0106] (3) Construction of dual model.

[0107] Based on the objective function and constraints of the original problem, construct the dual problem:

[0108] Dual objective function: (Minimize the “total virtual capacity cost”, which is the sum of the products of the dual variables of the original problem’s capacity constraint and the capacity.)

[0109] Duality constraint: For node pairs with communication requirements All paths ,satisfy and .

[0110] Dual variable constraints: , No sign restriction.

[0111] The mathematical form of the dual model is:

[0112] .

[0113] Step 3.2, Solving for the optimal solution and deriving the core conclusions.

[0114] (1) Synchronous acquisition of optimal solution and application of strong duality theorem.

[0115] When solving the MCFP model and its dual model using the column generation algorithm, the optimal solutions of the MCFP model and the dual model are obtained simultaneously.

[0116] The optimal solution for the MCFP model is: (Maximum Concurrency Factor) (Optimal path traffic) (Optimal traffic for the link).

[0117] Optimal solution of dual model: (Demand-constrained optimal dual variables) (Capacity-constrained optimal dual variable).

[0118] According to the strong duality theorem, if the primal problem has an optimal solution, then the dual problem also has an optimal solution, and the optimal objective function values ​​of the two problems are equal. For the MCFP problem in this application, the optimal objective function value of the primal problem is... The optimal objective value of the dual problem is Therefore:

[0119] ;

[0120] This formula shows that the maximum load-carrying capacity of a network is determined by the sum of the products of the capacity of each link and its "shadow price" (the capacity-constrained optimal dual variable). It directly reflects the weight of link capacity in terms of its contribution to the overall network performance.

[0121] (2) Key applications of complementary relaxation.

[0122] The complementary slackness of linear programming states that at the optimal solution, if a constraint of the original problem is a "loose constraint" (i.e., the inequality constraint is strictly true), then its corresponding dual variable is 0; if the dual variable is not 0, then its corresponding constraint of the original problem is a "tight constraint" (i.e., the equality constraint or inequality constraint is equal).

[0123] Applying complementary relaxation to the MCFP problem, specifically addressing capacity constraints. With dual variables ,have: .

[0124] Based on the three categories of links in MCFP (critical edges, saturated non-critical edges, and unsaturated edges), the derivation is performed for each case. The possible values ​​of:

[0125] Critical edge: defined as "a link that saturates under all maximum concurrent flows", i.e. ( (for the optimal flow set) At this point, the capacity constraint is a "tight constraint". Combined with complementary relaxation, It can be non-zero; further combining the strong duality theorem and the envelope theorem, and considering the possibility of multiple solutions, its upper bound can be derived. ,and The value of is positively correlated with the strength of the link's constraint on network performance.

[0126] Saturated non-critical edges: defined as "there exists a partial maximum concurrent flow such that..." There exists a part that makes "Link". For making The optimal flow has a "loose constraint" on capacity. In conjunction with complementary relaxation, the following must be satisfied: .

[0127] Unsaturated edges: defined as "links that are not saturated under all maximum concurrent flows", that is , At this point, the capacity constraint is a "loose constraint". Combined with complementary relaxation, .

[0128] In summary, the core conclusion can be drawn: the link Capacity-constrained upper bound of optimal dual variables The necessary and sufficient condition is This conclusion, which identifies critical edges, provides a rigorous theoretical basis for critical link identification.

[0129] (3) Deepening the physical meaning of dual variables.

[0130] According to the envelope theorem, if a linear programming problem has a unique solution, then the partial derivative of the optimal value of the objective function with respect to a certain parameter is equal to the value of the coefficient of that parameter in the Lagrange function at the dual optimal solution. For the MCFP problem, ... Considered as link capacity The function, for Find the partial derivative: .

[0131] Since linear programming may have multiple optimal solutions, using and Let these represent the upper and lower bounds of the dual variable, respectively. If the solution is unique, then... The above formula can now be restated using the directional derivative as follows:

[0132] ;

[0133] in, The positive directional derivative, It is the negative directional derivative. The vector corresponding to the right-hand side of the capacity constraint (i.e., all) (A vector formed by splicing together) for Unit vector in the direction, For the optimal dual variable set, Let it be "defined as"; from the above equation, it is clear that for the case of a unique optimal solution... This still holds true. Its physical meaning is: link. For every tiny increase / decrease in capacity, the network's maximum concurrency factor decreases. The increment / decrement directly quantifies the marginal impact of changes in link capacity on network performance.

[0134] Step 3.3, Quantitative identification of critical links.

[0135] based on The core conclusion is the definition of two types of quantitative impact factors to achieve accurate identification and impact assessment of key links:

[0136] (1) Continuous Influence Factor: Marginal Throughput Gain Its definition is to directly take the optimal solution of the dual variable, that is... The calculation method involves directly extracting the optimal solution from the dual problem of the MCFP. No additional calculations are required. The identification rule is: At that time, the link This refers to the critical link. It's important to note that within the critical link, only increasing the capacity of the bottleneck link will improve performance. For potentially bottlenecked links, simply increasing the capacity of that side will not improve performance. The necessary and sufficient condition for a critical link is that reducing the capacity of this edge will inevitably lead to... During the descent, the link... For non-critical links (capacity increase to) No impact).

[0137] Result verification: Referring to MCFP, "after the key edge is deleted..." The property of "inevitable decline" is addressed through "virtual link deletion". Then re-solve MCFP to verify – if deleted ,but As a critical link, with The recognition results are consistent.

[0138] (2) Discrete Influence Factor: Intensity of Fault Influence In real-world networks, link capacity can fluctuate significantly (e.g., a sudden drop in capacity due to a fault). It is necessary to quantify the impact of discrete capacity changes on network performance. Therefore, a threshold is defined for when the link capacity changes... Capacity change When the discrete influence factor is expressed, it is:

[0139] ;

[0140] in, For link Capacity change The maximum concurrency factor was then obtained by resolving the MCFP model. This is the original maximum concurrency factor. The calculation steps are as follows: Adjust the link Capacity: ;by To obtain the new capacity, construct a new MCFP instance and solve for it. Substitute into the formula to calculate. A negative result indicates Decline (e.g., malfunction).

[0141] Through mathematical derivation, the upper and lower bounds of the discrete influence factor can be obtained, expressed as:

[0142] ;

[0143] in, This indicates the optimal traffic flow for the link. For optimal path traffic, Indicates any path, For included links The set of all paths This serves as the upper bound for the optimal dual variable of the capacity constraint. These upper and lower bounds can quickly predict the impact of changes in link capacity, such as... , , , , ,but: It can be used to guide emergency response or capacity expansion planning.

[0144] Furthermore, an additivity analysis of MCFP was conducted: First, the necessary and sufficient conditions for the feasibility of MCFP were given: Given an MCFP instance The necessary and sufficient condition for the existence of a feasible solution to the MCFP problem is: for any positive demand... Node pairs Located in the figure Positive capacity subgraph In the same connected component. Among them, the positive capacity subgraph is the subgraph obtained by deleting all edges with zero capacity from the original graph.

[0145] MCFP Additivity Analysis: Consider two MCFP instances and The two instances differ only in their capacity matrices. Assume the maximum concurrency factor for the two instances is... So, for stacked instances... Its maximum concurrency factor .remember , and Let each represent the set of key edges for the two instances above. The equality condition for the above inequality is that there exists a demand pair. This makes the node and exist The upper part is not connected. The symbol "" is used in this context. "" represents the difference operation between sets.

[0146] Based on the additivity of MCFP, consider a certain MCFP instance. and expansion plan The necessary and sufficient condition for the effectiveness of this scheme is that, for any pair of nodes with communication needs, ,node and In the figure Upward connected.

[0147] In one embodiment, since the number of network paths may increase exponentially with the number of nodes, the traditional simplex method is inefficient. Therefore, a column generation algorithm is used to solve the model. Step 3.2 uses the column generation algorithm to solve the dual models simultaneously, obtaining the maximum concurrency factor, optimal path flow, and optimal dual variables for capacity constraints, including:

[0148] (1) Constructing the Restricted Master Problem (RMP): For each pair of average service transmission requirements node pairs Generate initial paths, for example, by using Dijkstra's algorithm to find the shortest path, where "shortest" is defined as having the fewest links, thus forming an initial path set. ;based on Construct an RMP, at which point the RMP variables only contain Path flow and concurrency factor The constraints of RMP are consistent with those of the MCFP model.

[0149] (2) Solving RMP: The interior point method is used to solve RMP to obtain the initial path flow. Initial concurrency factor Demand constraint dual variables and capacity-constrained dual variables .

[0150] (3) Pricing sub-problem and finding improvement paths: Defining link weights For each pair node pairs Solve Shortest path with weight The path weight is the sum of the weights of the links within the path; the shortest path is calculated. The reduced cost is: When the test number is less than 0, This will improve the concurrency factor. The value, and Added to the path set as an improved path If the test number for all paths is greater than or equal to 0, then the solution process is terminated.

[0151] (4) Iterative update: Add the improvement path Update the RMP and solve it again. Repeat the RMP solution steps and the steps of pricing the subproblem and finding an improved path until there are no paths with a test number less than 0. Stop the calculation and obtain the optimal solution of the MCFP model and the optimal solution of the dual model. Among them, the optimal solution of the MCFP model includes the maximum concurrency factor. (Network maximum load capacity limit), optimal path traffic (Optimal network traffic distribution) and optimal link traffic The optimal solution of the dual model includes the optimal dual variables of the demand constraint. and capacity-constrained optimal dual variables ;in, For included links The set of all paths.

[0152] In one embodiment, step 4 involves sequentially quantizing, classifying, and prioritizing the expansion of critical bottleneck links in the network based on the optimal dual variable of the capacity constraint, including:

[0153] When link of At that time, the link It has been identified as a critical bottleneck link; mathematically proven, This is a necessary and sufficient condition for a link to be fully loaded under all optimal traffic distributions (i.e., traffic strictly equals capacity). This means that such links are the absolute bottleneck restricting network performance improvement. Furthermore, when the link... of and At that time, critical bottleneck links are classified as strong bottleneck links; when the link of and In this context, critical bottleneck links are classified as potential bottleneck links. Strong bottleneck links and potential bottleneck links respectively indicate whether increasing the capacity of only that link can effectively improve network performance. and They represent the capacity-constrained optimal dual variables respectively. The upper and lower bounds; when the optimal solution obtained by the model is unique. .

[0154] when At that time, the link Links are classified as non-critical. Non-critical links are further categorized into those that are fully loaded in some optimal solutions but not fully loaded in others (saturated non-critical edges) or those that are not fully loaded in any optimal solution (unsaturated edges). Expanding the network under these two conditions will not directly increase the maximum concurrency factor for links in the current network state. However, the capacity expansion effect can be achieved through certain combination methods.

[0155] For all identified The key bottleneck link, based on Sort the values ​​in descending order; The higher the value, the greater the marginal contribution of increasing link capacity to the overall network performance, and the higher the priority for expansion when resources are limited.

[0156] It's important to note that a necessary condition for the effectiveness of a capacity expansion scheme in step 5 is that the expanded network must still be able to support all original service demands. This is equivalent to verifying that, under the expanded network capacity configuration, all pairs of nodes with service demands are connected in the subgraph composed of positive capacity links. This is achieved by obtaining the updated maximum concurrency factor. By comparing with the original maximum concurrency factor, the marginal gain of network performance is obtained. This condition can be naturally verified (if) (If so, it is effective). Finally, by combining the marginal gain of network performance (ΔZ), the rapid prediction results of the impact of link capacity changes, and implementation costs of each expansion candidate scheme, a multi-objective trade-off is made, and the optimal expansion scheme is selected for implementation.

[0157] In one embodiment, such as Figure 2 As shown, a scaling optimization system based on the marginal gain of network performance is provided, including:

[0158] The network parameter modeling module 201 is used to construct an undirected graph of the network topology by abstracting the physical devices in the communication network as a set of nodes and the physical links between devices as a set of edges.

[0159] The MCFP model building module 202 is used to construct the MCFP model by defining business requirements for each pair of nodes in the undirected graph and assigning a capacity value to each edge. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, so as to achieve the goal of maximizing the concurrency factor, where the concurrency factor is defined as the network load carrying capacity coefficient.

[0160] The model solving module 203 is used to construct the dual model of the MCFP model based on Lagrange duality theory, and to solve the dual model synchronously using a column generation algorithm to obtain the maximum concurrency factor, optimal path flow and capacity constraint optimal dual variables.

[0161] The bottleneck identification module 204 is used to quantitatively identify, classify and prioritize the expansion of key bottleneck links in the network according to the optimal dual variables of capacity constraints, and generate multiple expansion candidate schemes with different capacity adjustment amounts by adjusting the capacity of multiple key bottleneck links after the expansion priority is ranked.

[0162] The capacity expansion optimization module 205 is used to re-substitute the adjusted link capacity of each capacity expansion candidate scheme into the MCFP model for solution, obtain the updated maximum concurrency factor and compare it with the original maximum concurrency factor to obtain the marginal gain of network performance. By combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, the capacity expansion candidate schemes are comprehensively evaluated, and the optimal capacity expansion scheme is selected for implementation.

[0163] Specific limitations regarding the capacity expansion optimization system based on network performance marginal gain can be found in the limitations of the capacity expansion optimization method based on network performance marginal gain mentioned above, and will not be repeated here. Each module in the aforementioned capacity expansion optimization system based on network performance marginal gain can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independent of the processor in the computer device, or stored in software in the memory of the computer device, so that the processor can call and execute the corresponding operations of each module.

[0164] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 3 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a capacity expansion optimization method based on the marginal gain of network performance. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0165] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0166] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to perform the following steps:

[0167] By abstracting the physical devices in the communication network as a set of nodes and the physical links between devices as a set of edges, an undirected graph of the network topology is constructed.

[0168] The MCFP model is constructed by defining business requirements for each pair of nodes in an undirected graph and assigning a capacity value to each edge. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, in order to maximize the concurrency factor, which is defined as the network load carrying capacity coefficient.

[0169] Based on Lagrange duality theory, a dual model of the MCFP model is constructed, and a column generation algorithm is used to solve the two models simultaneously to obtain the maximum concurrency factor, optimal path flow, and optimal dual variables of capacity constraints.

[0170] Based on the optimal dual variables of capacity constraints, the key bottleneck links in the network are quantitatively identified, classified, and prioritized for expansion in sequence. By adjusting the capacity of multiple key bottleneck links after prioritization, multiple expansion candidate schemes with different capacity adjustment amounts are generated.

[0171] The adjusted link capacity of each expansion candidate scheme is resubmitted into the MCFP model for solution, and the updated maximum concurrency factor is obtained and compared with the original maximum concurrency factor to obtain the marginal gain of network performance. The expansion candidate schemes are comprehensively evaluated by combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, and the optimal expansion scheme is selected for implementation.

[0172] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0173] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application.

Claims

1. A scaling optimization method based on the marginal gain of network performance, characterized in that, The method includes: By abstracting the physical devices in the communication network as a set of nodes and the physical links between devices as a set of edges, an undirected graph of the network topology is constructed. The MCFP model is constructed by defining business requirements for each pair of nodes in an undirected graph and assigning a capacity value to each edge. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, in order to maximize the concurrency factor, which is defined as the network load carrying capacity coefficient. Based on Lagrange duality theory, a dual model of the MCFP model is constructed, and a column generation algorithm is used to solve the two models simultaneously to obtain the maximum concurrency factor, optimal path flow, and optimal dual variables of capacity constraints. Based on the optimal dual variables of capacity constraints, the key bottleneck links in the network are quantitatively identified, classified, and prioritized for expansion in sequence. By adjusting the capacity of multiple key bottleneck links after prioritization, multiple expansion candidate schemes with different capacity adjustment amounts are generated. The adjusted link capacity of each expansion candidate scheme is resubmitted into the MCFP model for solution, and the updated maximum concurrency factor is obtained and compared with the original maximum concurrency factor to obtain the marginal gain of network performance. The expansion candidate schemes are comprehensively evaluated by combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, and the optimal expansion scheme is selected for implementation.

2. The scaling optimization method based on network performance marginal gain according to claim 1, characterized in that, Before constructing the MCFP model, the method also includes: In an undirected graph of a communication network topology In the definition, the capacity function and the business requirement function are defined; among them, For a set of nodes, Let be the set of edges. The total number of nodes. For the first Link, , This represents the total number of links. The capacity function is defined as The capacity function in the first Link The capacity is defined as , The value is determined based on the physical characteristics of the link, protocol standards, or actual test data; among which, It is the set of nonnegative real numbers; The business requirement function is defined as follows: ,satisfy and ;in, Represents a node With nodes Average service transmission requirements The value is determined by historical traffic statistics, business forecasts, or business specification requirements; Collect the capacity from the capacity function and the business requirements from the business requirement function, and perform preprocessing.

3. The scaling optimization method based on network performance marginal gain according to claim 2, characterized in that, Collect the capacity from the capacity function and the business requirements from the business requirement function, and perform preprocessing, including: Outlier handling: using The criteria identify outliers in link capacity and replace them with the average capacity of links of the same type or remove them. Demand smoothing: The sliding window averaging method is used to eliminate the impact of short-term traffic pulses on the business demand function. The size of the sliding window is set according to the business cycle. Unit unification: The units for link capacity and service requirements are uniformly converted to Mbps.

4. The scaling optimization method based on network performance marginal gain according to claim 2 or 3, characterized in that, By defining business requirements for each pair of nodes in an undirected graph and assigning a capacity value to each edge, an MCFP model is constructed, expressed as: ； in, Concurrency factor; Path in the network Traffic allocation on the platform; As a constraint of business requirements, it represents the condition for a set of nodes. Any pair of nodes in The sum of traffic on all paths equals the average service transmission demand. The product of the concurrency factor, For nodes With nodes The set of all paths between; Link capacity constraint, meaning that for a set of edges any link in All passing through the link The sum of path traffic does not exceed the link capacity , For included links The set of all paths; and The non-negativity constraint indicates that both path flow and concurrency factor are non-negative.

5. The scaling optimization method based on network performance marginal gain according to claim 4, characterized in that, Based on Lagrange duality theory, the dual model of the MCFP model is constructed as follows: ； in, For link Capacity-constrained dual variables; For node pairs with communication needs The dual variables of the demand constraints between them; This is a function for business requirements.

6. The scaling optimization method based on network performance marginal gain according to claim 5, characterized in that, A column generation algorithm is used to solve the dual model synchronously, yielding the maximum concurrency factor, optimal path flow, and optimal dual variables for capacity constraints, including: Constructing the Restricted Master Problem (RMP): For each pair of average traffic transmission requirements node pairs Generate initial paths to form an initial path set. ;based on Construct an RMP, at which point the RMP variables only contain Path flow and concurrency factor The constraints of RMP are consistent with those of the MCFP model. Solving RMP: The interior-point method is used to solve RMP and obtain the initial path flow. Initial concurrency factor Demand constraint dual variables and capacity-constrained dual variables ; Pricing sub-problems and finding improvement paths: Defining link weights For each pair node pairs Solve Shortest path with weight The path weight is the sum of the weights of the links contained in the path. Calculate the shortest path The test number is When the test number is less than 0, This will improve the concurrency factor. The value, and Added to the path set as an improved path If the test count for all paths is greater than or equal to 0, then the solution process is terminated. Iterative update: Adding improvement paths Update the RMP and solve it again. Repeat the RMP solution steps and the steps of pricing the subproblem and finding an improved path until there are no paths with a test number less than 0. Stop the calculation and obtain the optimal solution of the MCFP model and the optimal solution of the dual model. Among them, the optimal solution of the MCFP model includes the maximum concurrency factor. Optimal path traffic and optimal link traffic The optimal solution of the dual model includes the optimal dual variables of the demand constraint. and capacity-constrained optimal dual variables ;in, For included links The set of all paths.

7. The scaling optimization method based on network performance marginal gain according to claim 6, characterized in that, Based on the optimal dual variables of capacity constraints, the key bottleneck links in the network are quantitatively identified, classified, and prioritized for expansion in sequence, including: When link of At that time, the link The link was identified as a critical bottleneck; among them, when the link of and At that time, critical bottleneck links are classified as strong bottleneck links; when the link of and At that time, critical bottleneck links are classified into potential bottleneck links; among them, and They represent the capacity-constrained optimal dual variables respectively. The upper and lower bounds; when the optimal solution obtained by the model is unique. ; when At that time, the link The link is determined to be non-critical; the non-critical link is classified as one that is fully loaded in some optimal solutions but not fully loaded in other optimal solutions, or one that is not fully loaded in all optimal solutions. For all identified The key bottleneck link, based on Sort the values ​​in descending order; The higher the value, the greater the marginal contribution of increasing link capacity to the overall network performance, and the higher the priority for expansion when resources are limited.

8. The scaling optimization method based on network performance marginal gain according to claim 1, characterized in that, The impact of the link capacity change includes: When link Capacity change When the discrete influence factor is defined, its expression is: ； in, For link Capacity change The maximum concurrency factor was then obtained by resolving the MCFP model. This represents the original maximum concurrency factor; Based on discrete impact factor The upper and lower bounds are used to predict the impact of changes in link capacity. The upper and lower bounds are represented as: ； in, This indicates the optimal traffic flow for the link. For optimal path traffic, Indicates any path, For included links The set of all paths This is the upper bound of the optimal dual variable for capacity constraints.

9. A capacity expansion optimization system based on the marginal gain of network performance, characterized in that, The system includes: The network parameter modeling module is used to construct an undirected graph of the network topology by abstracting physical devices in the communication network as a set of nodes and physical links between devices as a set of edges. The MCFP model building module is used to construct an MCFP model by defining business requirements for each pair of nodes in an undirected graph and assigning a capacity value to each edge. The MCFP model is configured to search for the optimal path traffic while satisfying business requirement constraints and link capacity constraints, in order to maximize the concurrency factor, where the concurrency factor is defined as the network load carrying capacity coefficient. The model solving module is used to construct the dual model of the MCFP model based on Lagrange duality theory, and to solve the dual model simultaneously using a column generation algorithm to obtain the maximum concurrency factor, optimal path flow, and optimal dual variables of capacity constraints. The bottleneck identification module is used to quantitatively identify, classify, and prioritize the expansion of key bottleneck links in the network according to the optimal dual variable of capacity constraints. It also generates multiple expansion candidate schemes with different capacity adjustment amounts by adjusting the capacity of multiple key bottleneck links after prioritizing expansion. The capacity expansion optimization module is used to re-substitute the adjusted link capacity of each expansion candidate scheme into the MCFP model for solution, obtain the updated maximum concurrency factor and compare it with the original maximum concurrency factor to obtain the marginal gain of network performance. By combining the marginal gain of network performance, the impact of link capacity changes and implementation costs, the expansion candidate schemes are comprehensively evaluated, and the optimal expansion scheme is selected for implementation.

10. A computer 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 method according to any one of claims 1 to 8.

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