Multi-target transmission control method realized through self-evolution method

Abstract

The invention provides a multi-target transmission control method realized through a self-evolution method, the fairness is generally defined as whether resource allocation of competitive traffic in a network is equal or not, but the previous transmission control method only considers bandwidth equalization and ignores the same precious transmission resources such as stability and responsiveness when multiple streams coexist, so that the transmission efficiency is greatly improved. According to the method, the transmission performance can be balanced, and the fairness between the traffic is maintained; secondly, on the basis of system analysis and theoretical reasoning on the network, the multi-target performance influence of the congestion control algorithm on the system level is evaluated, and comprehensive mathematical representation is provided; finally, the invention introduces an online evolution congestion control solution generation algorithm based on a first-order derivative, effectively navigates the Pareto frontier of the performance of the congestion control algorithm, and realizes the tradeoff between multi-dimensional performance targets.

Description

Technical Field

[0001] The present invention belongs to the technical field of network communication and data transmission, and in particular relates to a multi-objective transmission control method realized by a self-evolution method. Background Art

[0002] As the cornerstone of Internet infrastructure, transmission control algorithms have been widely studied for decades to improve performance (such as achieving higher throughput, responsiveness, and lower latency). Today, classic transmission control methods such as Cubic and BBR assume the function of congestion control (CC) in today's network transmission processes, and there are also emerging methods that introduce machine learning algorithms into them. What they have in common is that the driving force behind them is to meet the different network performance requirements of new network applications. However, although performance factors are carefully considered in the design of transmission control methods to optimize specific goals, it is still a challenge to achieve a balance and efficiency between different requirements.

[0003] After decades of development, TCP congestion control (CC) algorithms (or their variants) can be roughly divided into two categories: pre-defined policy-based methods and empirical learning-based methods. Pre-defined policy-based methods usually follow pre-designed fixed policies, such as Reno and Cubic (the default transmission control method in the Linux kernel). Most of these methods work with the design idea of ​​filling the buffer. After theoretical design and practical verification, these methods have been proven to achieve satisfactory stability and convergence while achieving good throughput. However, with the rise of real-time applications and the expansion of link capacity, latency has become a more important factor affecting user quality of experience (QoE). This trend has prompted the development of some new pre-defined policy-based transmission control methods, most of which follow the design idea of ​​emptying the buffer queue to reduce latency while sacrificing throughput as little as possible, such as BBR, Copa, and Sprout. Unfortunately, this shift to the design idea of ​​emptying the buffer policy leads to a decrease in responsiveness and convergence. In addition, they show excessive aggression towards other network traffic. The reason for these unexpected performance degradations is that the optimization objectives in algorithm design are often interrelated or even conflicting. Therefore, the design of new congestion control protocols must be comprehensively evaluated, balancing multiple performance objectives rather than addressing any one objective in isolation.

[0004] The transmission control methods based on predetermined policies mentioned above provide a concise way to interact with the network. However, fixed policies are increasingly considered unsuitable for the rapidly evolving network environment. With the advancement of artificial intelligence, experience-based transmission control algorithms have become an active research area. In this approach, the sender treats the network as a black box, observes the feedback from the network environment, uses this feedback to learn a numerical model, and adjusts its strategy based on experience and the objective function. For example, Remy optimizes throughput and delay through offline trained decision trees, while PCC achieves satisfactory throughput and packet loss performance through online learning. Both algorithms attempt to use a learnable model to guide the transmission performance of the sender. However, in a shared network environment, the behavior of these intelligent senders is often selfish. Their experience-based behavior can be regarded as a black box that only seeks higher transmission performance tips for a single user, while ignoring the trade-offs and adjustments between the global network and different performances.

[0005] In summary, although existing transmission control methods may consider various performance factors during the design phase, these algorithms are usually difficult to adapt to the ever-changing transmission requirements of the application layer. Summary of the invention

[0006] To solve the above problems, the present invention provides a multi-objective transmission control method implemented by a self-evolution method, which enables multiple competing sources to find the most suitable performance in a shared limited network resource environment and achieves a trade-off between multi-dimensional performance objectives by exploring the Pareto front.

[0007] A multi-objective transmission control method implemented by a self-evolution method comprises the following steps:

[0008] S1: In addition to normal transmission behavior, each competing source s in the network maintains its own state variable (x s (t),w s (t),q s (t)), each router with limited capacity that makes up the network maintains its own state variables (c l ,p l (t),y l (t));

[0009] Among them, x s (t) is the transmission rate corresponding to the competing source s at the current time t, w s (t) is the congestion window corresponding to the competing source s at the current time t, q s (t) is the end-to-end congestion measurement value corresponding to the competing source s at the current time t; the network consists of L routers with limited capacity, cl is the capacity of the lth router, p l(t) is the congestion metric corresponding to the lth router at the current time t, y l (t) is the aggregate transmission rate of the lth router at the current time t, and y l (t) = ∑ s A ls x s (t),∑ s It represents the weighted sum of the transmission rates of all competing sources using the lth router at the current time t;

[0010] Among them, A ls is the routing matrix A of each competing source s in the network s The elements in A ls ∈{0,1} |L|×|S| , S is the total number of competing sources, and the set of routers used by each competing source s is recorded as L s , element A ls represents the usage status of the contention source s for the lth router. If the lth router belongs to the set L s , then A ls =1, otherwise A ls =0;

[0011] S2: Construct the QoS fairness objective function U corresponding to each contention source s according to the state variables corresponding to each contention source s and router l fair (x s (t)):

[0012]

[0013] Among them, D s (t) is the congestion window reduction of the competing source s at the current time t, I s (t) is the congestion window increment of the competing source s at the current time t, and a is the set weight used to balance efficiency and fairness;

[0014] S3: Solve the QoS fairness objective function U corresponding to each competing source s through the dual gradient descent method s-fair , and obtain the initial solution on the Pareto front in, To make the QoS fairness objective function U s-fair The theoretical value of the transmission rate corresponding to the competing source s that meets the set requirements at the current time t, γ l The positive gain of competing sources in the process of active queue management using random early detection algorithm to achieve transmission control;

[0015] S4: Construct the responsiveness objective function U corresponding to each competing source s according to the state variables corresponding to each competing source s and router l rsp(x s (t)), throughput objective function U thp (x s (t)), window fluctuation objective function U wfl (x s (t)) are as follows:

[0016]

[0017] Among them, the first auxiliary variable τ s is the round trip time corresponding to the competing source s, the second auxiliary variable

[0018] S5: Initial solution corresponding to each competing source s based on the first-order derivative restriction theory Search in multiple directions within the set neighborhood of , and obtain backup solutions in multiple directions corresponding to each competing source s and all located on the Pareto front;

[0019] S6: Substitute all the alternative solutions into the responsiveness objective function U corresponding to each competing source s one by one rsp (x s (t)), throughput objective function U thp (x s (t)), window fluctuation objective function U wfl (x s (t)), the response value, throughput, and window fluctuation value of the competing source s under their respective corresponding backup solutions are obtained;

[0020] S7: Each competing source s sets different weights for responsiveness, throughput, and window fluctuation according to its own preference for transmission performance. Then, each competing source s performs weighted summation with the response value, throughput, and window fluctuation value under its corresponding backup solution according to the different weights. Each competing source s obtains the score of each corresponding backup solution.

[0021] S8: Each competing source s uses the transmission rate, congestion window reduction, and congestion window increase contained in the backup solution with the highest score as the transmission control amount at the next moment.

[0022] Furthermore, the QoS fairness objective function U corresponding to each competing source s is solved by the dual gradient descent method: s-fair , and obtain the initial solution on the Pareto front The specific process is as follows:

[0023] S31: Recursively solve the transmission rate x of each competing source in the t+1 time slot by the following formula: s (t+1):

[0024]

[0025] Among them, g s represents the step size corresponding to the competing source s, (·) + If the result of the expression in the brackets is negative, x is maintained. s (t+1) The rate of the previous time slot remains unchanged; if the result of the expression in the brackets is a positive value, the content of the expression in the brackets remains unchanged; It represents the gradient on one side of the competition source s, and the specific calculation method is:

[0026]

[0027] Among them, U′ fair (x s (t)) represents U fair (x s The first derivative of (t));

[0028] S32: Set the transmission rate of the next time slot to x s (t+1) are used as the initial target rate of each contention source. Then, while obtaining the initial target rate of the contention source, the positive gain γ of each router in the t+1 time slot is adjusted on the network side. l (t+1):

[0029]

[0030] Among them, γ l (t) represents the positive gain at time slot t, g l represents the step size corresponding to router l, Indicates the gradient on the router side. The specific calculation method is:

[0031]

[0032] Among them, x(p t ) represents the transmission rate target value calculated according to the packet loss rate pt of time slot t, and c represents the capacity of the current router;

[0033] S33: Change the step length g corresponding to each competing source s s The step length g corresponding to router l l , each competing source and the routers on its path are iterated in a distributed manner to ensure that each competing source and the routers on its path complete the convergence of the QoS fairness objective function, where convergence refers to the gradient corresponding to the competing source s and the gradient of the router is a negative number or the change in two consecutive iterations is less than the set threshold; the transmission rate, positive gain, congestion window reduction, and congestion window increment corresponding to the convergence of the QoS fairness objective function are taken as the initial solution on the Pareto front.

[0034] Furthermore, in step S5, based on the first-order derivative restriction theory, the initial solution corresponding to each competing source s is Search in multiple directions within the set neighborhood of , and obtain alternative solutions in multiple directions corresponding to each competing source s and all located on the Pareto front. The specific process is as follows:

[0035] S51: Based on the Pareto stationary characterization theory, the following model is constructed:

[0036]

[0037] Among them, α is a weight vector, α o is an element in the weight vector α, and α o is the weight of the oth objective function, σ * is a solution on the Pareto plane, For the oth objective function in solving σ * The first-order derivative under , and o = 1, 2, ..., objectives, objectives is the total number of all objective functions;

[0038] S52: Constructing Krylov subspaces as follows:

[0039]

[0040] Where m represents the dimension of the Krylov subspace and g is expressed as β is a constant vector; is the first-order derivative of any objective function under any solution σ, span{·} represents the linear space generated by the elements in the brackets, that is, the set of linear combinations of all these elements, and H represents the Hessian matrix;

[0041] S53: Obtaining satisfaction through MINRES iteration b′ m , where b′ m is the direction b of the mth Pareto front m The first derivative of

[0042] S54: Define multiple slopes and b m The difference between is less than the set value of the offset curve u(θ), where θ represents the slope; Get the β corresponding to different offset curves;

[0043] S55: Substitute the β obtained in step S54 into Get b′ under different β m ;

[0044] S56: For all different b′ m ,according to Obtain Pareto alternative solutions on the Pareto front in different directions Among them, g e Represents the empirical step length.

[0045] Furthermore, each competing source vector-multiplies its own preference weight with each backup solution in the backup solution set, sorts the results by numerical value, and selects the parameter corresponding to the backup solution with the highest value to update its own congestion control.

[0046] Furthermore, the router includes the AQM parameter γ in the ACK packet header received from the competing source. l Then, the AQM parameter γ l Used to adjust the data flow from the corresponding competing source.

[0047] Beneficial effects:

[0048] 1. The present invention provides a multi-objective transmission control method implemented by a self-evolution method. Fairness is usually defined as whether the resource allocation of competing flows in the network is equal. However, previous transmission control methods only considered the equal distribution of bandwidth when multiple flows coexist, but ignored equally valuable transmission resources such as stability and responsiveness. The present invention can make a trade-off between transmission performance and maintain fairness between flows; secondly, based on the system analysis and theoretical reasoning of the network, the present invention evaluates the multi-objective performance impact of the congestion control algorithm at the system level and proposes a comprehensive mathematical representation; finally, the present invention introduces an online evolutionary congestion control solution generation algorithm based on a first-order derivative, which effectively navigates the Pareto frontier of the congestion control algorithm performance and achieves a trade-off between multi-dimensional performance objectives.

[0049] 2. The present invention provides a multi-objective transmission control method implemented by a self-evolution method. Traditional methods pay too much attention to the experience of a single user, which makes the design logic of the method more radical and may behave selfishly during actual use, thereby destroying the experience of other users in the network. The present invention uses an algorithm that cooperates with the switch to achieve collaborative transmission across the entire network. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A schematic diagram of the Pareto front in network transmission provided by the present invention;

[0051] Figure 2 A schematic diagram of the network model and the HydraCC two-stage algorithm provided by the present invention;

[0052] Figure 3 A schematic diagram of the visualization results of the HydraCC exploration of the Pareto solution provided by the present invention. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0054] In order to achieve harmonious flow convergence within the network, the present invention proposes HydraCC, which is an innovative multi-objective transmission control method. First, the present invention establishes an evaluation model for the TCP / AQM system. Through theoretical derivation, the present invention clarifies the influence of algorithm parameters on multiple performance indicators (such as QoS fairness, responsiveness, throughput and window fluctuation), and provides a concise and intuitive mathematical representation. The analysis of the present invention shows that there are often correlations and competitions between these objectives. Based on this insight, the design idea of ​​HydraCC is to weigh between multiple competing performance objectives and expand a Pareto solution set from the initial solution. Specifically, the present invention uses a carefully constructed algorithm based on Krylov subspace iteration to effectively explore the evolution direction of Pareto solutions. In particular, each explored solution has its own advantages and disadvantages, thereby providing users with a wider decision-making space.

[0055] In this paper, we introduce a core concept - Pareto front, which enables senders to evaluate and select the most appropriate solution from a set of beneficial options (Pareto front) according to their specific needs. In the trade-off process, some performance attributes are intentionally sacrificed and returned to the network (by adjusting the AQM parameters), so that each user in the network can get what they need. Generally speaking, generating the optimal solution based on network feedback is usually a costly process and requires the use of complex optimization techniques such as reinforcement learning. To overcome this shortcoming, the design of HydraCC adopts the classic dual gradient descent method to obtain an initial solution on the Pareto front. Then, the Krylov subspace iteration method (an iterative linear solver that does not require the calculation of the Hessian matrix) is used to explore the solution set space of the transmission control problem and realize the online evolution of the congestion control solution. The framework cleverly balances throughput, window fluctuations and responsiveness while ensuring stable convergence.

[0056] In this hyperconnected era, diverse applications coexist, each with its unique requirements and performance expectations. These applications include big data transmission that prioritizes high throughput, real-time video streaming and gaming applications that require low latency, and IoT devices that focus on network stability. Maintaining fairness and optimizing the performance of these different applications in the face of fluctuating network conditions is a daunting challenge. In this complex context, this paper introduces the concept of Pareto frontier in congestion control performance. In addition, we propose an innovative mechanism based on the additive gain / multiplicative loss (AIMD) strategy combined with a Krylov subspace iteration method.

[0057] The following is an introduction to the Pareto front of transmission control defined in the present invention: the network serves multiple flows simultaneously. For a single flow, its competition with other flows at the link bottleneck defines its "performance boundary", which is also the fundamental reason for the differentiation of user experience. The advantage of the present invention comes from expanding the competition target from single to multiple. However, multi-dimensional competition targets also raise a question: whether there is a trade-off between different targets. For example, improving one aspect (such as window jitter) may come at the expense of performance degradation in another aspect (such as throughput). These potential solutions that represent a balance between various objectives are the Pareto front in congestion control defined in the present invention. The Pareto front includes a set of Pareto solutions. Figure 1 The Pareto front for a two-dimensional performance target case is shown, which represents a set of quality solutions that users can choose from. However, before the introduction of HydraCC, these solutions were not obvious to users. Moreover, identifying the Pareto front in a dynamic network environment is far from easy.

[0058] Specifically, a multi-objective transmission control method implemented by a self-evolution method is characterized by comprising the following steps:

[0059] S1: In addition to normal transmission behavior, each competing source s in the network maintains its own state variable (x s (t),w s (t),q s (t)), each router with limited capacity that makes up the network maintains its own state variables (c l ,p l (t),y l (t));

[0060] Among them, x s (t) is the transmission rate corresponding to the competing source s at the current time t, w s (t) is the congestion window corresponding to the competing source s at the current time t, q s(t) is the end-to-end congestion measurement value corresponding to the competing source s at the current time t; the network consists of L routers with limited capacity, cl is the capacity of the lth router, p l (t) is the congestion metric corresponding to the lth router at the current time t, y l (t) is the aggregate transmission rate of the lth router at the current time t, and y l (t) = ∑ s A ls x s (t),∑ s It represents the weighted sum of the transmission rates of all competing sources using the lth router at the current time t;

[0061] Among them, A ls is the routing matrix A of each competing source s in the network s The elements in A ls ∈{0,1} L×S , S is the total number of competing sources, and the set of routers used by each competing source s is recorded as L s , element A ls represents the usage status of the contention source s for the lth router. If the lth router belongs to the set L s , then A ls =1, otherwise A ls =0;

[0062] S2: Construct the QoS fairness objective function U corresponding to each contention source s according to the state variables corresponding to each contention source s and router l fair (x s (t)):

[0063]

[0064] Among them, D s (t) is the congestion window reduction of the competing source s at the current time t, I s (t) is the congestion window increment of the competing source s at the current time t, and a is the set weight used to balance efficiency and fairness;

[0065] S3: Solve the QoS fairness objective function U corresponding to each competing source s through the dual gradient descent method s-fair , and obtain the initial solution on the Pareto front in, To make the QoS fairness objective function U s-fair The theoretical value of the transmission rate corresponding to the competing source s that meets the set requirements at the current time t, γ l The positive gain of competing sources in the process of active queue management using random early detection algorithm to achieve transmission control;

[0066] Furthermore, the QoS fairness objective function U corresponding to each competing source s is solved by the dual gradient descent method: s-fair , and obtain the initial solution on the Pareto front The specific process is as follows:

[0067] S31: Recursively solve the transmission rate x of each competing source in the t+1 time slot by the following formula: s (t+1):

[0068]

[0069] Among them, g s represents the step size corresponding to the competing source s, (·) + If the result of the expression in the brackets is negative, x is maintained. s (t+1) The rate of the previous time slot remains unchanged; if the result of the expression in the brackets is a positive value, the content of the expression in the brackets remains unchanged; It represents the gradient on one side of the competition source s, and the specific calculation method is:

[0070]

[0071] Among them, U′ fair (x s (t)) represents U fair (x s The first derivative of (t));

[0072] S32: Set the transmission rate of the next time slot to x s (t+1) are used as the initial target rate of each contention source. Then, while obtaining the initial target rate of the contention source, the positive gain γ of each router in the t+1 time slot is adjusted on the network side. l (t+1):

[0073]

[0074] Among them, γ l (t) represents the positive gain at time slot t, g l represents the step size corresponding to router l, Indicates the gradient on the router side. The specific calculation method is:

[0075]

[0076] Among them, x(p t ) represents the transmission rate target value calculated according to the packet loss rate pt of time slot t, and c represents the capacity of the current router;

[0077] S33: Change the step length g corresponding to each competing source ss The step length g corresponding to router l l , each competing source and the routers on its path are iterated in a distributed manner to ensure that each competing source and the routers on its path complete the convergence of the QoS fairness objective function, where convergence refers to the gradient corresponding to the competing source s and the gradient of the router is a negative number or the change in two consecutive iterations is less than the set threshold; the transmission rate, positive gain, congestion window reduction, and congestion window increment corresponding to the convergence of the QoS fairness objective function are taken as the initial solution on the Pareto front.

[0078] S4: Construct the responsiveness objective function U corresponding to each competing source s according to the state variables corresponding to each competing source s and router l rsp (x s (t)), throughput objective function U thp (x s (t)), window fluctuation objective function U wfl (x s (t)) are as follows:

[0079]

[0080] Among them, the first auxiliary variable τ s is the round trip time corresponding to the competing source s, the second auxiliary variable

[0081] S5: Initial solution corresponding to each competing source s based on the first-order derivative restriction theory Search in multiple directions within the set neighborhood of , and obtain backup solutions in multiple directions corresponding to each competing source s and all located on the Pareto front;

[0082] Furthermore, based on the first-order derivative restriction theory, the initial solution corresponding to each competing source s is Search in multiple directions within the set neighborhood of , and obtain alternative solutions in multiple directions corresponding to each competing source s and all located on the Pareto front. The specific process is as follows:

[0083] S51: Based on the Pareto stationary characterization theory, the following model is constructed:

[0084]

[0085] Among them, α is a weight vector, α o is an element in the weight vector α, and α o is the weight of the oth objective function, σ * is a solution on the Pareto plane, For the oth objective function in solving σ * The first-order derivative under , and o = 1, 2, ..., objectives, objectives is the total number of all objective functions;

[0086] S52: Constructing Krylov subspaces as follows:

[0087]

[0088] Where m represents the dimension of the Krylov subspace and g is expressed as β is a constant vector; is the first-order derivative of any objective function under any solution σ, span{·} represents the linear space generated by the elements in the brackets, that is, the set of linear combinations of all these elements, and H represents the Hessian matrix;

[0089] S53: Obtaining satisfaction through MINRES iteration b′ m , where b′ m is the direction b of the mth Pareto front m The first derivative of

[0090] S54: Define multiple slopes and b m The difference between is less than the set value of the offset curve u(θ), where θ represents the slope; Get the β corresponding to different offset curves;

[0091] S55: Substitute the β obtained in step S54 into Get b′ under different β m ;

[0092] S56: For all different b′ m ,according to Obtain Pareto alternative solutions on the Pareto front in different directions Among them, g e Represents the empirical step length.

[0093] S6: Substitute all the alternative solutions into the responsiveness objective function U corresponding to each competing source s one by one rsp (x s (t)), throughput objective function U thp (x s (t)), window fluctuation objective function U wfl (x s (t)), the response value, throughput, and window fluctuation value of the competing source s under their respective corresponding backup solutions are obtained;

[0094] S7: Each competing source s sets different weights for responsiveness, throughput, and window fluctuation according to its own preference for transmission performance. Then, each competing source s performs weighted summation with the response value, throughput, and window fluctuation value under its corresponding backup solution according to the different weights. Each competing source s obtains the score of each corresponding backup solution.

[0095] S8: Each competing source s uses the transmission rate, congestion window reduction, and congestion window increase contained in the backup solution with the highest score as the transmission control amount at the next moment.

[0096] Finally, each competing source multiplies its preference weight by each alternative solution in the alternative solution set, sorts the results by numerical value, and selects the parameters corresponding to the alternative solution with the highest value to update its own congestion control. At the same time, the router receives the AQM parameter γ contained in the ACK packet header from the competing source. l Then, the AQM parameter γ l Used to adjust the data flow from the corresponding competing source.

[0097] The derivation process of the four objective functions is introduced in detail below.

[0098] The present invention first proposes a mathematical model of TCP / AQM network system, and then adopts the network utility maximization framework to model and analyze it. Then, the present invention introduces various performance goals in congestion control and explores how specific parameters affect these goals. This discussion forms the basis of the HydraCC framework.

[0099] Assume that there is a general TCP / AQM network consisting of a set of links with finite capacity, denoted by L = {1,…l,…}, and its capacity is denoted by c = (c l ,l∈L). These links are shared by a set of competing sources, denoted by S = {1,…s,…}. Each competing source s uses a subset of the links We define the routing matrix A ls ∈{0,1} |L|×|S| , if l belongs to L s , then A ls =1, otherwise A ls =0. Figure 2 The network model is shown on the left. Each competing source s maintains a congestion window w s (t) and a round trip time (RTT) τ s Let x s (t) = w s / τ s denotes the transmission rate of each competing source s at time t, expressed in packets per second. Associated with each link l is the “congestion measure” (here representing the packet loss rate) p at time t.l (t). Since a link may be shared by multiple competing sources, we let y l (t) = ∑ s A ls x s (t) is the aggregate transmission rate of link l. Let q s (t) = ∑ l p l A ls (t) is the approximate end-to-end congestion measure for source s. Expressed as a vector, we have

[0100] y(t)=Ax(t),q(t)=A T p(t), (1)

[0101] Where, y(t):=(y l (t),l∈L) and p(t):=(p l (t),l∈L) is located x(t):=(x s (t),s∈S) and q(t):=(q s (t),s∈S) is located For link l, only the local congestion measurement p l (t) and the aggregate transmission rate y l (t) is visible. Similarly, competing sources can only observe their own transmission rate x s (t) and the end-to-end congestion measurement q s (t). Therefore, we will s (t),w s (t),q s (t)) as the corresponding state variable of each competing source s, and (c l ,p l (t),y l (t)) as the state variable of each link l.

[0102] Transmission control is a distributed algorithm that forms a closed loop between the active queue management (AQM) on the contention source side and the link side. In the packet loss-based congestion control algorithm, the source controls the transmission rate by obtaining feedback on the packet loss rate of the link. According to the symbols defined above, we establish a fluid dynamic equation (DE) model for the contention source algorithm.

[0103]

[0104] in, If x s >0, and max{0,f} if x s ≤0. We define k s (x s) is the attenuation factor, ψ s (x s ) is the balancing factor, and time t is omitted for simplicity. RED is an AQM algorithm that assumes that the packet loss probability is proportional to the backlog. It is a commonly used AQM algorithm and is widely used in switches.

[0105] We use the dynamic equation to express RED

[0106]

[0107] in represents the packet loss rate p on each link l l Updates. γ l >0 is the positive gain of the RED algorithm. The above two equations (2) and (3) respectively describe the rate update process of the AIMD algorithm in the competing source and the feedback update process of the link to the source, which together form a closed-loop feedback system.

[0108] The congestion control mechanism in the transmission control method is a window-based algorithm. We first use a general model to describe this window-based behavior. When an ACK is received, the congestion control window will increase, while in some other cases (receiving three duplicate ACKs, RTO timeout, ECN), it will decrease.

[0109] We use a window change This can be expressed using the dynamic equations of .

[0110]

[0111] In this equation, I s and D s Represents increment and decrement respectively. By the relationship between the window and the transmission rate, that is, x s =w s τ s , substitute into equation (4) and omit the relatively small q s Item, we get the following results:

[0112]

[0113] Comparing this to the fluid dynamics model in equation (2), we conclude that:

[0114]

[0115] Typically, the network utility maximization (NUM) problem is viewed as a zero-sum game with limited bandwidth, where each competing source aims to achieve higher throughput. However, we argue that relying solely on throughput as an evaluation criterion is insufficient; additional objective functions for other performance aspects must be considered. In this section, we explore the existence and uniqueness of equilibrium points within the system. Our analysis is based on the following conditions:

[0116] 1. Matrix A ls is full rank, that is, rank(A ls )=1, which means that the number of competing sources exceeds the number of links, which is satisfied in most cases of real networks.

[0117] 2. The objective function is is strictly concave and continuously second-order differentiable.

[0118] 3. For each competing source s∈S, the ψ in its algorithm parameters s (x s ) for x s The derivative of is negative and can be expressed as

[0119] QoS fairness: In a shared network, achieving QoS fairness for multiple flows is a key factor that should be considered. QoS fairness is a concept that describes how congestion control algorithms share network bandwidth with other TCP flows. We introduce the alpha fairness theory here:

[0120]

[0121] Here, a represents the degree of fairness. By considering a as a variable, we can balance efficiency and fairness according to specific needs. Therefore, we define the objective function of QoS fairness as follows:

[0122]

[0123] In our model, a is less than 1, higher $a$ leads to higher efficiency but lower fairness, while lower a increases QoS fairness at the cost of efficiency.

[0124] Responsiveness: Responsiveness refers to the ability of a system to respond quickly to changes in network dynamics. To evaluate this, we consider the equilibrium point (x * ,p * ) is expressed as the Jacobian matrix:

[0125]

[0126] Applying the theory of stability analysis of linear systems, we calculate the eigenvalue λ of the system. Then we determine the stability of the system by checking the real part of λ. The process is as follows:

[0127]

[0128] By taking the feature vector By multiplying both sides of the equation, we can get:

[0129]

[0130] If the real parts of all the eigenvalues ​​of the linear system defined as Equations (2)-(3) are negative, the system exhibits enhanced responsiveness (i.e., converges to equilibrium more quickly). By inspecting Equation (6), we find that if the numerator The negative value of the constant meets condition C3, and the linear system remains stable. In addition, the larger and k s Values ​​of will lead to faster convergence and higher responsiveness. Based on these observations, we propose the following responsiveness objective function:

[0131]

[0132] U rsp An evaluation indicator representing the responsiveness of the CC algorithm.

[0133] Throughput: Each competing source aims to obtain more bandwidth from the network. According to Theorem 1, the network achieves an optimal balance that satisfies the KKT condition. By applying equation (10), we derive:

[0134]

[0135] Then, we can further infer that:

[0136]

[0137] This observation suggests that there is a trade-off between throughput and responsiveness.

[0138] Window Fluctuation: The window fluctuation of the CC algorithm affects the flow stability, which is especially important for applications that require high flow stability. This performance aspect is related to the attenuation factor k s (x s ) is related. The larger k s (x s ) value (or the smaller D s ) can cause the window to decrease significantly when a congestion signal is received, thereby increasing window fluctuations.

[0139] To evaluate this performance, we define an objective function.

[0140]

[0141] It is worth noting that the window fluctuation objective function prefers a smaller k s , while the responsiveness prefers a larger k s This shows that there is a trade-off between different goals. Formulas (13, 17, 19, 20) are the utility functions of the four aspects of performance obtained by analysis. Obviously, these goals conflict with each other and cannot be improved at the same time. Therefore, it is necessary to make a trade-off between them.

[0142] In the past, transport performance objectives have typically been considered separately. The importance of these mathematical analyses lies in their ability to integrate these objectives into a unified framework. Each objective is associated with algorithmic parameters for a multi-competing source TCP / AQM system. HydraCC aims to balance the performance requirements of individual competing sources with the overall network resources. This requires competing sources to compromise performance in other areas while seeking to improve specific performance. This dynamic performance exchange makes it possible to build a performance market in the network, where the "price" of resources is set by all competing sources. Implementing this concept in a distributed CC algorithm involves exploring a balanced global solution, which we will explore in depth in the next section.

[0143] The following is a detailed derivation of the process of defining the Pareto front using the objective function.

[0144] Let the congestion control solution be σ. We can represent σ as a tuple of variables as follows:

[0145]

[0146] We consider the selection of transmission control algorithm parameters for competing sources as a multi-objective optimization problem, aiming to solve various performance criteria and rsp ,U thp ,U fair ,U wfl} to achieve a good balance between the conflicting objectives described. For any solution σ1, If and only if for all targets U o (σ1)≥U o (σ2) and there exists a target U o (σ1)>U o (σ2), then σ1 is said to be better than σ2. If there is no solution better than a solution σ in its solution space neighborhood * , then the solution is considered to be locally Pareto optimal.

[0147] When the initial solution is obtained by dual gradient descent, the first step of HydraCC involves the traditional dual gradient descent method. For the network utility maximization (NUM) problem, the initial solution is obtained by the collaboration of the competitive source side and the link side. The link value in the (k+1)th iteration is calculated as follows:

[0148]

[0149] where g k >0 indicates the step size. According to equation (3) and equation (8), Each link iterates in a distributed manner. All competing sources then determine their target rates based on their observations:

[0150]

[0151] in, is derived from the AIMD equilibrium. Figure 2 The first stage of the HydraCC algorithm shows the iterative process. In recent years, many studies have used gradient-based methods to solve transmission control problems and proved that they can converge to the optimal solution. However, these models usually have a single objective function and the optimal solution obtained is only a point on the Pareto front. In the initial stage of the HydraCC algorithm, we mainly use QoS fairness as the objective function. This approach guides the congestion control and AQM parameters in the network towards the optimal solution σ for bandwidth fairness. * Convergence. After obtaining this fair optimal solution, we introduce three independent objective functions: responsiveness, throughput, and window fluctuation. This encourages competing sources to explore the Pareto frontier of the network based on the fair optimal solution. The exploration process requires finding a balance between multiple objectives. A full explanation of the algorithm will be given in the subsequent part of this paper.

[0152] The dual gradient descent method based on QoS fairness establishes an initial solution for network congestion control. This fairness concept mainly focuses on bandwidth allocation. However, when the objective function is extended to multiple dimensions, this initial solution is just a point on the Pareto front in the solution space. Our goal is to navigate these Pareto fronts to provide users with a wider range of congestion control parameter choices.

[0153] Theorem 2 (First-order derivative restriction theory): If U o It is second-order differentiable. Assume that there exists a smooth curve b(θ), where θ∈(-ε,ε), passing through a Pareto optimal point σ * We have b(0) = σ * There exists a set of weights Make

[0154]

[0155] in α i It is given by Lemma 1.

[0156] To understand the relationship between a Pareto solution and its surrounding Pareto front, we establish the following equation according to Lemma 1.

[0157]

[0158] In order to obtain other solutions on the Pareto front, we need to determine its update direction. By taking the derivative of equation (25):

[0159]

[0160] Substituting θ = 0 into equation (26), we can derive the result stated in Theorem 2.

[0161] At this stage, we observe that the direction of the Pareto front and the spatial transformation of the Hessian matrix can be interpreted as a subspace of the first-order gradient tensor of the objective function. We divide the process of solving the direction of the Pareto front into two steps. First, based on the Pareto stationarity representation proposed in Lemma 1, we solve the following problem:

[0162]

[0163] This problem is a classic minimum norm problem. Given that our model contains only three objective functions, we can use the least squares method to solve α. It is worth mentioning that since the initial Pareto optimal solution is obtained by a gradient-based method, it is difficult to fully converge to a strict Pareto optimal solution. Therefore, we relax the constraints and aim to minimize the second-order norm value in the problem instead of strictly requiring it to be zero. In Theorem 2, b′ is determined as the direction of the Pareto front. Given the complexity of the Hessian matrix, its dimension increases as the network size grows, and directly obtaining it and finding its inverse matrix poses significant challenges. Therefore, we adopt an evolutionary exploration method to construct a Krylov subspace to approximate the direction of the Pareto front.

[0164]

[0165] Among them, g is represented by where β is a constant vector. This means that the content of the equal sign on the right side of equation (26) is equivalent to The generated subspace.

[0166] Given the strict concavity of the objective function specified in the C2 and C3 constraints, the Hessian matrix is ​​rendered as a negative definite matrix. This situation excludes the application of the classical conjugate gradient (CG) algorithm. Therefore, we chose the minimum residual (MINRES) method which is more suitable for our network congestion control scenario. This method brings several advantages:

[0167] There is no need to calculate the Hessian matrix: by using the product of the Hessian matrix and the vector, it can be expressed as We can construct a Krylov subspace. This process avoids the calculation and inversion of the Hessian matrix of the objective function.

[0168] Scalability: In the congestion control scenario, the dimension of the Hessian matrix increases with L s The convergence speed of the MINRES method is relatively less sensitive to the matrix size, thus ensuring the scalability of the algorithm.

[0169] Resource efficiency: The MINRES method exploits the symmetry of the Hessian matrix. By using short recursions, it prevents the computational and storage requirements from growing rapidly as the iterations proceed.

[0170] The Krylov subspace defined above plays a key role in the MINRES method. This iterative process computes an approximation of the solution to the symmetric linear system Hb′=g, aiming to minimize the Euclidean norm of the residual in the Krylov subspace. In each iteration m, MINRES forms a solution To reduce the residual norm |Hb′ m -g2. This approach of gradually expanding the Krylov subspace at each iteration allows the method to effectively approximate the direction of the Pareto front. Importantly, this approach promotes evolutionary exploration of the Pareto direction, achieving a balance between accuracy and resource consumption through early stopping.

[0171] The following is a detailed derivation of the process of exploring the Pareto frontier in multiple directions in a low-cost manner.

[0172] Once the direction b′ of the Pareto front is determined m , the next stage involves calculating σ * +g e b′ m To derive the next Pareto solution where g e represents the empirical step size. The evolutionary exploration process of the Pareto front can be conceptualized as a cyclic procedure. It alternates between iteratively verifying the direction through the Krylov subspace and generating new solutions based on the confirmed direction.

[0173] The aforementioned methods make it possible to identify the edge of the Pareto front in a single direction. However, when the target dimension exceeds two, the Pareto front is no longer a line, but a surface. To cope with this complexity and expand the Pareto front, this section introduces methods to expand the Pareto front in multiple directions.

[0174] Under the premise of Theorem 2, suppose there is a shift curve u(θ), where θ∈(-ε,ε). Suppose the constructed new curve d(θ), expressed as u(θ)+b(θ), is similar to the optimal point σ * If H(σ * )u′≈0, then we infer that at point σ * At , curve d and curve b have similar derivatives. Furthermore, they are coplanar but not parallel.

[0175] Proof: To verify whether curve d and curve b have similar properties, we calculate the derivative of curve d in the target function space:

[0176]

[0177] It can be seen that the two curves are * The similarity of the derivatives at depends on the second term on the right side of Eq. (29). Multiplying this term by β and organizing it according to Theorem 2, if H(σ * )u′≈0, we can draw the following conclusions:

[0178]

[0179] Considering H(σ * )u′ approaches zero, it can be inferred that This shows that curves d and b are in σ * have similar derivatives at , but they are not parallel.

[0180] According to the definition of the curve b(θ) = U o (σ * +θb′), further showing that u(θ)+b(θ)=U o (σ * +θ(u′+b′)). By differentiating both sides of this equation and evaluating it at θ=0, we obtain:

[0181]

[0182] By multiplying both sides of Eq. (31) by α in Lemma 1 and recognizing that σ * is Pareto optimal, which means We infer that:

[0183]

[0184] This shows that when θ = 0, the curve d(θ) is orthogonal to the vector α. Similarly, when the offset vector u is zero, the curve b(θ) also becomes orthogonal to α. Therefore, no matter what u is chosen, the curves b(θ) and d(θ) are at the Pareto optimal point σ * They are all coplanar.

[0185] In Theorem 3, we propose a new method for deriving curves that are similar in value, derivative, and coplanarity near the Pareto optimal point σ by introducing offset curves into the exploration directions. This approach provides multiple feasible directions for Eq. (26), thereby fully exploring the Pareto front without compromising its quality. In our HydraCC implementation, we introduce a variable N to determine the number of exploration directions to discover the Pareto front. In addition, we use an empirical threshold to filter the offset curves $u$. This strategy effectively increases the diversity of the set of available Pareto fronts.

[0186] So far, the process of finding the Pareto front has been outlined. After obtaining the Pareto front set, the competing sources input their own preferences into the weighted sum model (WSM) model. WSM is a well-established tool in multi-criteria decision analysis, which calculates the score by summing the product of the evaluation value of each objective function and the corresponding preference weight for each alternative. The competing source then selects the solution with the highest score from the many solutions on the Pareto front, adjusts its congestion control algorithm based on this, and congests the link l∈L s AQM parameter γ l Return to Network.

[0187] Let the preference weight be △, where each △ o represents the weight assigned to each target. The condition can be mathematically expressed as:

[0188] Each △ o are all positive real numbers:

[0189] The sum of all weights is 1:

[0190] For the link side, the AQM parameter γ contained in the ACK packet header received from the competing source l After that, the AQM parameters will be adjusted for the data streams from the corresponding competing sources. Figure 2 The second phase of shows the process of exploring the Pareto frontier. From a practical point of view, the sender s of HydraCC only updates its own algorithm parameters and L s This means that even as the network size increases, HydraCC still focuses mainly on “local” considerations, reflecting a practical distributed design approach.

[0191] When multiple competing sources share a network, it is challenging to simultaneously meet the diverse needs of router AQM parameters. Adjusting AQM parameters for each user flow individually may lead to network unfairness.

[0192] HydraCC addresses this problem by following the principle of fairness in network Quality of Service (QoS). It emphasizes fairness for all users rather than prioritizing the experience of a single user. In our approach, achieving favorable AQM parameters involves adjusting the aggressiveness of each TCP algorithm to achieve a balanced network state. In addition, excessive data exceeding the link-side buffer capacity will cause tail packet loss, which is a side effect of the aggressive strategy.

[0193] The concept of “fairness” is particularly important here. HydraCC considers the network sources and links as a whole. Therefore, algorithms are deployed on both the sources and links to promote comprehensive network convergence that meets multiple user needs and goals. Figure 3 This trade-off is shown in Figure 1. We select two parameter sets with different performance characteristics from the Pareto front determined by HydraCC. The right plot shows the corresponding sending rates as the path capacity varies. The strategy focusing on responsiveness converges faster and more stably, while the strategy focusing on throughput uses bandwidth more efficiently but suffers from larger window fluctuations.

[0194] Of course, the present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may certainly make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A multi-objective transmission control method implemented by a self-evolution method, characterized in that: The following steps are involved: S1: In addition to normal transmission behavior, each competing source s in the network maintains its own state variable (x s (t),w s (t),q s (t)), each router with limited capacity that makes up the network maintains its own state variables (c l ,p l (t),y l (t)); Among them, x s (t) is the transmission rate corresponding to the competing source s at the current time t, w s (t) is the congestion window corresponding to the competing source s at the current time t, q s (t) is the end-to-end congestion measurement value corresponding to the competing source s at the current time t; the network consists of L routers with limited capacity, c l is the capacity of the lth router, pl(t) is the congestion metric corresponding to the lth router at the current time t, and y l (t) is the aggregate transmission rate of the lth router at the current time t, and y l (t) = ∑ s A ls x s (t),∑ s It represents the weighted sum of the transmission rates of all competing sources using the lth router at the current time t; Among them, A ls is the routing matrix A of each competing source s in the network s The elements in A ls ∈{0,1} L×S , S is the total number of competing sources, and the set of routers used by each competing source s is recorded as L s , element A ls represents the usage status of the contention source s for the lth router. If the lth router belongs to the set L s , then A ls =1, otherwise A ls =0; S2: Construct the QoS fairness objective function U corresponding to each contention source s according to the state variables corresponding to each contention source s and router l fair (x s (t)): Among them, D s (t) is the congestion window reduction of the competing source s at the current time t, I s (t) is the congestion window increment of the competing source s at the current time t, and a is the set weight used to balance efficiency and fairness; S3: Solve the QoS fairness objective function U corresponding to each competing source s through the dual gradient descent method s-fair , and obtain the initial solution on the Pareto front in, To make the QoS fairness objective function U s-fair The theoretical value of the transmission rate corresponding to the competing source s that meets the set requirements at the current time t, γ l The positive gain of competing sources in the process of active queue management using random early detection algorithm to achieve transmission control; S4: Construct the responsiveness objective function U corresponding to each competing source s according to the state variables corresponding to each competing source s and router l rsp (x s (t)), throughput objective function U thp (x s (t)), window fluctuation objective function U wfl (x s (t)) are as follows: Among them, the first auxiliary variable τ s is the round trip time corresponding to the competing source s, the second auxiliary variable S5: Initial solution corresponding to each competing source s based on the first-order derivative restriction theory Search in multiple directions within the set neighborhood of , and obtain backup solutions in multiple directions corresponding to each competing source s and all located on the Pareto front; S6: Substitute all the alternative solutions into the responsiveness objective function U corresponding to each competing source s one by one rsp (x s (t)), throughput objective function U thp (x s (t)), window fluctuation objective function U wfl (x s (t)), the response value, throughput, and window fluctuation value of the competing source s under their respective corresponding backup solutions are obtained; S7: Each competing source s sets different weights for responsiveness, throughput, and window fluctuation according to its own preference for transmission performance. Then, each competing source s performs weighted summation with the response value, throughput, and window fluctuation value under its corresponding backup solution according to the different weights. Each competing source s obtains the score of each corresponding backup solution. S8: Each competing source s uses the transmission rate, congestion window reduction, and congestion window increase contained in the backup solution with the highest score as the transmission control amount at the next moment.

2. A multi-objective transmission control method implemented by a self-evolution method as claimed in claim 1, characterized in that: The QoS fairness objective function U corresponding to each competing source s is solved by the dual gradient descent method s-fair , and obtain the initial solution on the Pareto front The specific process is as follows: S31: Recursively solve the transmission rate x of each competing source in the t+1 time slot by the following formula: s (t+1): Among them, g s represents the step size corresponding to the competing source s, (·) + If the result of the expression in the brackets is negative, x is maintained. s (t+1) The rate of the previous time slot remains unchanged; if the result of the expression in the brackets is a positive value, the content of the expression in the brackets remains unchanged; It represents the gradient on one side of the competition source s, and the specific calculation method is: Among them, U′ fair (x s (t)) represents U fair (x s The first derivative of (t)); S32: Set the transmission rate of the next time slot to x s (t+1) are used as the initial target rate of each contention source. Then, while obtaining the initial target rate of the contention source, the positive gain γ of each router in the t+1 time slot is adjusted on the network side. l (t+1): Among them, γ l (t) represents the positive gain at time slot t, g l represents the step size corresponding to router l, Indicates the gradient on the router side. The specific calculation method is: Among them, x(p t ) represents the packet loss rate p according to time slot t t The calculated transmission rate target value, c represents the capacity of the current router; S33: Change the step length g corresponding to each competing source s s The step length g corresponding to router l l , each competing source and the routers on its path are iterated in a distributed manner to ensure that each competing source and the routers on its path complete the convergence of the QoS fairness objective function, where convergence refers to the gradient corresponding to the competing source s and the gradient of the router is a negative number or the change in two consecutive iterations is less than the set threshold; the transmission rate, positive gain, congestion window reduction, and congestion window increment corresponding to the convergence of the QoS fairness objective function are taken as the initial solution on the Pareto front.

3. A multi-objective transmission control method implemented by a self-evolution method as claimed in claim 1, characterized in that: In step S5, based on the first-order derivative restriction theory, the initial solution corresponding to each competing source s is Search in multiple directions within the set neighborhood of , and obtain alternative solutions in multiple directions corresponding to each competing source s and all located on the Pareto front. The specific process is as follows: S51: Based on the Pareto stationary characterization theory, the following model is constructed: Among them, α is a weight vector, α o is an element in the weight vector α, and α o is the weight of the oth objective function, σ * is a solution on the Pareto plane, For the oth objective function in solving σ * The first-order derivative under , and o = 1, 2, ..., objectives, objectives is the total number of all objective functions; S52: Constructing Krylov subspaces as follows: Where m represents the dimension of the Krylov subspace and g is expressed as β is a constant vector; is the first-order derivative of any objective function under any solution σ, span{·} represents the linear space generated by the elements in the brackets, that is, the set of linear combinations of all these elements, and H represents the Hessian matrix; S53: Obtaining satisfaction through MINRES iteration b′ m , where b′ m is the direction b of the mth Pareto front m The first derivative of S54: Define multiple slopes and b m The difference between is less than the set value of the offset curve u(θ), where θ represents the slope; Get the β corresponding to different offset curves; S55: Substitute the β obtained in step S54 into Get b′ under different β m ; S56: For all different b′ m ,according to Obtain Pareto alternative solutions on the Pareto front in different directions Among them, g e Represents the empirical step length.

4. A multi-objective transmission control method implemented by a self-evolution method as claimed in claim 1, characterized in that: Each competing source vector-multiplies its preference weight with each backup solution in the backup solution set, sorts the results by numerical value, and selects the parameters corresponding to the backup solution with the highest value to update its own congestion control.

5. A multi-objective transmission control method implemented by a self-evolution method as claimed in claim 1, characterized in that: The AQM parameter γ included by the router in the ACK packet header received from the competing source l Then, the AQM parameter γ l Used to adjust the data flow from the corresponding competing source.

Images