A multi-objective transmission control method realized by a self-evolution method

Abstract

The application provides a multi-objective transmission control method realized by a self-evolution method, fairness is generally defined as whether resource allocation of competitive traffic in a network is equal, but previous transmission control methods only consider equal distribution of bandwidth when multiple flows coexist, and ignore other valuable transmission resources such as stability and responsiveness, the application can make trade-off between transmission performances and maintain fairness between flows; secondly, the application evaluates multi-objective performance influence of a congestion control algorithm at a system level based on system analysis and theoretical reasoning of the network, and proposes a comprehensive mathematical expression; finally, the application introduces an online evolution congestion control solution generation algorithm based on a first-order derivative, effectively navigates a Pareto front of performance of the congestion control algorithm, and realizes trade-off between multi-dimensional performance objectives.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of network communication and data transmission, and particularly relates to a multi-target transmission control method realized through a self-evolution method. BACKGROUND

[0002] As the cornerstone of the Internet infrastructure, transmission control algorithms have been extensively studied for decades to improve performance (e.g., achieve higher throughput, responsiveness, and lower latency). Today, classic transmission control methods such as Cubic and BBR take on the role of congestion control (CC) in today's network transmission process, while emerging methods introduce machine learning algorithms into them. Their common point is that the driving force behind them is to meet the different network performance needs 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 needs.

[0003] After decades of development, TCP congestion control (CC) algorithms (or their variants) can be roughly divided into two categories: pre-determined strategy-based methods and experience learning-based methods. Pre-determined strategy-based methods usually follow a pre-designed fixed strategy, such as Reno and Cubic (the default transmission control method in the Linux kernel). Most of these methods work using 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 the quality of user experience (QoE). This trend has prompted the development of some new pre-determined strategy-based transmission control methods, which mostly 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 in design philosophy to the empty buffer strategy has led to a decline in responsiveness and convergence. In addition, they show excessive aggressiveness to other network traffic. The reason for these unexpected aspects of performance decline is that the optimization goals in algorithm design are often related to each other and even conflicting. Therefore, the design of new congestion control protocols must be comprehensively evaluated and trade-offs must be made between multiple performance goals, rather than addressing a single goal in isolation.

[0004] The transmission control method based on the predetermined strategy mentioned above provides a simple way of interacting with the network. However, the fixed strategy is increasingly considered unsuitable for the rapidly developing network environment. With the progress of artificial intelligence, the experience-based transmission control algorithm has become an active research field. In this method, the sender regards the network as a black box, observes the feedback of the network environment, uses these feedbacks to learn a numerical model, and adjusts its strategy according to the experience and the objective function. For example, Remy optimizes the throughput and delay by offline training of the decision tree, and PCC achieves satisfactory throughput and packet loss performance by online learning. Both algorithms try 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, which only seeks to improve the transmission performance of a single user, while ignoring the global network and the trade-off and adjustment between different performance.

[0005] In summary, although the existing transmission control methods may consider various performance factors in the design stage, these algorithms are usually difficult to adapt to the changing transmission needs of the application layer. SUMMARY

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

[0007] A multi-objective transmission control method realized by a self-evolution method, comprising the following steps:

[0008] S1: In addition to normal transmission behavior, each competing source s in the network maintains its own state variables (x s (t), w s (t), q s (t)) and each router l consisting of the network maintains its own state variables (c l , p l (t), y l (t));

[0009] wherein 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 value of the lth router corresponding to the current time t, y l (t) is the aggregate transmission rate of the lth router corresponding to the current time t, and y l (t) =∑ s A ls x s (t),∑ s represents a weighted sum of the transmission rates of all competing sources using the lth router at the current time t;

[0010] wherein A ls is an element in the routing matrix A s of each competing source s in the network, and 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 denoted as L s , and the element A ls represents the use state of the lth router by the competing source s, and if the lth router belongs to the set L s , then A ls =1, otherwise A ls =0;

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

[0012]

[0013] wherein D s (t) is the congestion window decrement 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 a set weight for balancing efficiency and fairness;

[0014] S3: solving the QoS fairness objective function U s-fair corresponding to each competing source s by a dual gradient descent method to obtain an initial solution wherein is the theoretical value of the transmission rate of the competing source s at the current time t so as to make the QoS fairness objective function U s-fair meet the set requirement, and γ l is a positive gain of the competing source in the process of adopting a random early detection algorithm for active queue management to realize transmission control;

[0015] S4: constructing a responsiveness objective function U rsp(x s (t))、throughput objective function U thp (x s (t))、window fluctuation objective function U wfl (x s (t)) as follows:

[0016]

[0017] wherein the first auxiliary variable τ s is the round-trip time corresponding to the competing source s, and the second auxiliary variable

[0018] S5: search in the set neighborhood of the initial solution corresponding to each competing source s, to obtain a plurality of backup solutions each corresponding to a direction and each located on the Pareto front, based on the first-order derivative restriction theory;

[0019] S6: respectively substitute each backup solution into the responsiveness objective function U rsp (x s (t))、the throughput objective function U thp (x s (t))、the window fluctuation objective function U wfl (x s (t)) corresponding to each competing source s, to obtain the response value, the throughput value, and the window fluctuation value of each competing source s under the corresponding backup solution;

[0020] S7: each competing source s sets different weights for the responsiveness performance, the throughput performance, and the window fluctuation performance according to the preference of the competing source s for the transmission performance, and then each competing source s performs weighted summation on the response value, the throughput value, and the window fluctuation value under the corresponding backup solution according to the different weights, to obtain the score of each corresponding backup solution of each competing source s;

[0021] S8: each competing source s takes the transmission rate, the congestion window decrement, and the congestion window increment contained in the backup solution with the highest score as the transmission control amount at the next time.

[0022] Further, the initial solution located on the Pareto front is obtained by solving the QoS fairness objective function U s-fair corresponding to each competing source s by using the dual gradient descent method. The specific process is as follows:

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

[0024]

[0025] wherein g s represents the step size corresponding to the contention source s, (·) + represents that if the result of the expression in the parentheses is negative, x s (t+1) is maintained; if the result of the expression in the parentheses is positive, the content of the expression in the parentheses is maintained; represents the gradient on the side of the contention source s, and the specific calculation method is:

[0026]

[0027] wherein U′ fair (x s (t)) represents the first derivative of U fair (x s (t));

[0028] S32: taking the transmission rate x s (t+1) of the next time slot as the initial target rate of each contention source, the initial target rate of the contention source is obtained, and at the same time, the positive gain γ l (t+1) of each router at the t+1 time slot is adjusted on the network side:

[0029]

[0030] wherein γ l (t) represents the positive gain at the t time slot, g l represents the step size corresponding to the router l, represents the gradient on the side of the router, and the specific calculation method is:

[0031]

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

[0033] S33: changing the step size g s corresponding to each contention source s and the step size g l corresponding to the router l, each contention source and the router on its path are iterated in a distributed manner to ensure that each contention source and the router on its path complete the convergence of the QoS fairness objective function, wherein the convergence means that the gradient corresponding to the contention source s and the gradient of the router are negative or the change amount of the adjacent two iterations is less than a set threshold; the transmission rate, the positive gain, the congestion window decrement and the congestion window increment corresponding to the convergence of the QoS fairness objective function are taken as the initial solution on the Pareto frontier.

[0034] Further, in step S5, based on the first derivative limit theory, search is performed in multiple directions within the set neighborhood of the initial solution corresponding to each competitive source s, to obtain multiple solutions corresponding to each competitive source s and located on the Pareto front in multiple directions respectively, and the specific process is as follows:

[0035] S51: based on the Pareto stationarity representation theory, construct the following model:

[0036]

[0037] Wherein, 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, σ * is the first derivative of the oth objective function at the solution σ m , and o = 1, 2, …, objectives, objectives is the total number of all objective functions;

[0038] S52: construct the Krylov subspace as follows:

[0039]

[0040] Wherein, m represents the dimension of the Krylov subspace, g represents β is a constant vector; is the first derivative of any objective function at 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: obtain b′ that satisfies m by MINRES iteration, wherein b′ m is the first derivative of the direction b m of the mth Pareto front;

[0042] S54: define the offset curve u(θ) between multiple slopes and b m , wherein θ represents the slope; let obtain β corresponding to different offset curves;

[0043] S55: substitute β obtained in step S54 into to obtain b′ m under different β;

[0044] S56: For all different b' m , according to obtain the pareto backup solution on the pareto front in different directions where g e represents the experience step.

[0045] Further, each competitive source vector multiplies its preference weight with each backup solution in the backup solution set, ranks the results by numerical value, and selects the backup solution corresponding to the highest numerical value to update the congestion control of the competitive source.

[0046] Further, after the router receives the AQM parameter γ l contained in the ACK data packet header of the competitive source, the AQM parameter γ l is used to adjust the data flow from the corresponding competitive source.

[0047] Advantages:

[0048] 1. The application provides a multi-objective transmission control method realized by a self-evolution method, fairness is generally defined as whether the resource allocation of competitive traffic in the network is equal, but previous transmission control methods only consider the equal division of bandwidth when multiple flows coexist, ignoring other valuable transmission resources such as stability and responsiveness. The application can make a trade-off between transmission performance and maintain fairness between flows; secondly, based on system analysis and theoretical reasoning of the network, the application evaluates the multi-objective performance influence of the congestion control algorithm at the system level and proposes a comprehensive mathematical representation; finally, the application introduces an online evolution congestion control solution generation algorithm based on first-order derivative, which effectively navigates the pareto front of the congestion control algorithm performance and realizes the trade-off between multi-dimensional performance objectives.

[0049] 2. The application provides a multi-objective transmission control method realized by a self-evolution method, traditional methods pay too much attention to the experience of a single user, resulting in more aggressive design logic of the method, which may be selfish in actual use, thereby damaging the experience of other users in the network; the application uses an algorithm cooperating with the switch to realize collaborative transmission in the entire network. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The pareto front diagram in network transmission provided by the application;

[0051] Figure 2 The network model and HydraCC two-stage algorithm diagram provided by the application;

[0052] Figure 3 The visualization result diagram of HydraCC exploring pareto solution provided by the application. 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 traffic convergence within the network, the present invention proposes HydraCC, 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 impact 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 competitive relationships between these objectives. Based on this insight, the design idea of ​​HydraCC is to balance 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—the Pareto front—that enables senders to evaluate and select the most appropriate solution based on their specific needs from a set of beneficial options (the Pareto front). In this trade-off, some performance attributes are intentionally sacrificed and returned to the network (by adjusting the AQM parameters), enabling each user in the network to achieve the desired functionality. Generating an optimal solution based on network feedback is typically a costly process, requiring the use of complex optimization techniques such as reinforcement learning. To overcome this shortcoming, the HydraCC design employs the classic dual gradient descent method to obtain an initial solution on the Pareto front. It then utilizes the Krylov subspace iteration method (an iterative linear solver that does not require the computation of the Hessian matrix) to explore the solution space of the transmission control problem, enabling the online evolution of the congestion control solution. This framework skillfully balances throughput, window fluctuation, and responsiveness while ensuring stable convergence.

[0056] In this hyper-connected era, a wide variety of applications coexist, each with its unique demands and performance expectations. These applications include big data transfers that prioritize high throughput, real-time video streaming and gaming applications that require low latency, and Internet of Things 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, the present invention introduces the concept of Pareto frontiers in congestion control performance. Furthermore, we propose an innovative mechanism that is based on the Additive Increase / Multiplicative Decrease (AIMD) policy and incorporates a Krylov subspace iteration method.

[0057] The Pareto frontiers of transmission control defined by the present invention are introduced below: the network serves multiple flows simultaneously. For an individual flow, its competition with other flows at the link bottleneck defines its "performance frontier", which is also the root cause of the differentiation of user experience. The advantage of the present invention comes from the expansion of the competition target from single to multiple. However, the multi-dimensional competition target also raises a question: is there a trade-off between different targets, for example, improving one aspect (such as window jitter) may come at the cost of the decline in the performance of another aspect (such as throughput). These potential solutions that represent the balance between various targets are the Pareto frontiers in congestion control defined by the present invention. The Pareto frontiers include a set of Pareto solutions. Figure 1 The Pareto frontiers in a two-dimensional performance target case are shown, which represent a set of high-quality solutions that users can choose from. However, before the introduction of HydraCC, these solutions were not obvious to users. In addition, it is not easy to identify the Pareto frontiers in a dynamic network environment.

[0058] Specifically, a multi-objective transmission control method realized by a self-evolution method, 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 variables (x s (t), w s (t), q s (t)) and each router l that constitutes the network maintains its own state variables (c l , p l (t), y l (t));

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

[0061] wherein A ls is an element in the routing matrix A s of each competition source s in the network, and A ls ∈{0,1} L×S , S is the total number of competition sources, and the set composed of the routers used by each competition source s is denoted as L s , the element A ls indicates the use state of the lth router by the competition source s, if the lth router belongs to the set L s , then A ls =1, otherwise A ls =0;

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

[0063]

[0064] wherein D s (t) is the congestion window decrement of the competition source s at the current time t, I s (t) is the congestion window increment of the competition source s at the current time t, and a is a set weight for balancing efficiency and fairness;

[0065] S3: solving the QoS fairness objective function U s-fair corresponding to each competition source s by the dual gradient descent method to obtain the initial solution on the Pareto frontier wherein x is the theoretical value of the transmission rate of the competition source s at the current time t to make the QoS fairness objective function U s-fair meet the set requirements, and γ l is a positive gain of the competition source in the process of adopting the random early detection algorithm for active queue management to realize transmission control.

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

[0067] S31: The transmission rate x s (t+1) of each competing source in the t+1 time slot is recursively solved by using the following formula:

[0068]

[0069] where g s s represents the step length corresponding to the competing source s, and (·) + represents that if the result of the expression in the parentheses is negative, the rate x s (t+1) of the competing source s is maintained unchanged as the rate in the last time slot; if the result of the expression in the parentheses is positive, the content in the parentheses is maintained unchanged; represents the gradient on the side of the competing source s, and the specific calculation method is as follows:

[0070]

[0071] where U′ fair (x s (t)) represents the first-order derivative of U fair (x s (t));

[0072] S32: The transmission rate x s (t+1) of the next time slot is taken as the initial target rate of each competing source, so that the initial target rate of the competing source is obtained while the positive gain γ l (t+1) of each router in the t+1 time slot is adjusted on the network side:

[0073]

[0074] where γ l (t) represents the positive gain in the t time slot, g l represents the step length corresponding to the router l, represents the gradient on the side of the router, and the specific calculation method is as follows:

[0075]

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

[0077] S33: The step length gs 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 router's gradient is a negative number or the change in two adjacent iterations is less than the set threshold; the transmission rate, positive gain, congestion window decrement, 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 alternative 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 representation 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 the solution σ * The first 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] Among them, m represents the dimension of 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; let 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 experience step size.

[0093] S6: Substitute all 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)), obtain the response value, throughput, and window fluctuation value of the competing source s under the corresponding backup solution;

[0094] S7: Each of the competing sources s sets different weights for the responsive performance, throughput performance and window fluctuation performance according to the preference of the transmission performance of the source s, and then each of the competing sources s performs weighted summation on the responsive value, throughput and window fluctuation value under the corresponding backup solution according to the different weights and the corresponding backup solution, and each of the competing sources s obtains the score of each of the corresponding backup solutions;

[0095] S8: Each of the competing sources s takes the transmission rate, congestion window decrement and congestion window increment contained in the backup solution with the highest score as the transmission control quantity at the next moment.

[0096] Finally, each of the competing sources performs vector multiplication on the preference weight of the source and each of the backup solutions in the backup solution set, ranks the results according to the numerical value, and selects the backup solution corresponding to the highest numerical value to update the parameters of the congestion control of the source. Meanwhile, the router receives the AQM parameter γ l in the ACK data packet header from the competing source, and then adjusts the data flow from the corresponding competing source according to the AQM parameter γ l .

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

[0098] The present application firstly proposes a mathematical model of a TCP / AQM network system, and then models and analyzes the same by using a network utility maximization framework. Then, the present application introduces various performance objectives in the congestion control, and discusses how specific parameters affect these objectives. This discussion constitutes the basis of the HydraCC framework.

[0099] It is assumed that there is a general TCP / AQM network, which is composed of a set of links with limited capacity, denoted as L={1,…l,…}, and the capacity is denoted as c=(c l ,l∈L). These links are shared by a set of competing sources, denoted as S={1,…s,…}. Each of the competing sources s uses a subset of the links L 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 left side shows the network model. Each of the competing sources s maintains a congestion window w s (t) and a round-trip time (RTT) τ s . Let x s (t) = w s / τ s represent the transmission rate of each of the competing sources s at time t, expressed in the number of data packets per second. Associated with each of the links l is a "congestion metric" (here representing the data packet loss rate) pl (t). Since one link can be shared by multiple competing sources, we let y l (t) =∑ s A ls x s (t) be the aggregate transmission rate of link / . Let q s (t) =∑ l p l A ls (t) be the approximate end-to-end congestion measure of source s. In vector notation, we have

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

[0101] where y(t) := (y l (t), / e L) and p(t) := (p l (t), / e L) are located in x(t) := (x s (t), s e S) and q(t) := (q s (t), s e S) are located in For link / , only the local congestion measure p l (t) and the aggregate transmission rate y l (t) are visible. Similarly, a competing source can only observe its own transmission rate x s (t) and the end-to-end congestion measure q s (t). Therefore, we take (x s (t), w s (t), q s (t)) as the corresponding state variables for each competing source s and (c l , p l (t), y l (t)) as the state variables for each link / .

[0102] Transmission control is a distributed algorithm that forms a closed loop between the competing source side and the link side active queue management (AQM). In packet loss based congestion control algorithms, sources control their transmission rates by obtaining the packet loss rate feedback from the links. In terms of the notation defined above, we formulate a fluid dynamic equation (DE) model for the competing source algorithm,

[0103]

[0104] where if x s > 0, and max{0, f} if x s < 0. We define k s (x s) is the decay factor, ψ s (x s ) is the balance factor, time t is omitted to simplify the representation. RED is an AQM algorithm that assumes the packet loss probability is proportional to the backlog, and is a commonly used AQM algorithm, widely used in switches.

[0105] We use a dynamic equation to express the RED

[0106]

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

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

[0109] We use a dynamic equation about the window change to express this.

[0110]

[0111] In the equation, I s and D s represent the increment and decrement respectively. By substituting the relationship between the window and the transmission rate, i.e. x s = w s τ s into equation (4) and omitting the relatively small q s term, we get the following results:

[0112]

[0113] Comparing this with the fluid dynamic equation model in equation (2), we draw the following conclusions:

[0114]

[0115] Generally, the network utility maximization (NUM) problem is considered 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 must be considered for other performance aspects. In this section, we will explore the existence and uniqueness of the equilibrium point within the system. Our analysis is based on the following conditions:

[0116] 1. The matrix A ls is full rank, i.e., rank(A ls ) = l, representing the number of competing sources exceeding the number of links, which is satisfied in most cases of real networks.

[0117] 2. The objective function is strictly concave in and continuously twice differentiable.

[0118] 3. For each competing source s ∈ S, the derivative of ψ s (x s ) with respect to x s is negative, which can be represented 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 a congestion control algorithm shares 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 between efficiency and fairness according to specific requirements. Therefore, we define the objective function of QoS fairness as follows:

[0122]

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

[0124] Responsiveness: Responsiveness refers to the system's ability to respond quickly to network dynamic changes. To evaluate this, we consider the behavior of the equilibrium point (x * , p * ) in the linear system formed by equations (2) and (3), represented by the Jacobian matrix:

[0125]

[0126] Applying the stability analysis theory of linear systems, we compute the eigenvalues λ of the system. Then we determine the stability of the system by examining the real part of λ. The procedure is as follows:

[0127]

[0128] By multiplying the conjugate transpose of the eigenvector to both sides of the equation, we can obtain:

[0129]

[0130] If the real part of all the eigenvalues of the linear system defined by equations (2)-(3) is negative, the system exhibits enhanced responsiveness (i.e., converges to equilibrium faster). By examining equation (6), we find that if the constant negative value in the numerator meets the condition C3, the linear system remains stable. Furthermore, larger and k s values result in faster convergence and higher responsiveness. Based on these observations, we propose the following responsiveness objective function:

[0131]

[0132] U rsp represents an evaluation metric of 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 equilibrium that satisfies the KKT condition. By applying equation (10), we derive:

[0134]

[0135] Subsequently, we can further deduce that:

[0136]

[0137] This observation indicates a trade-off between throughput and responsiveness.

[0138] Window fluctuation: The window fluctuation of the CC algorithm affects the stability of the traffic, which is particularly important for applications that require high traffic stability. This performance aspect is related to the decay factor k s (x s ). Larger k s (x s ) values (or smaller D s ) result in a significant reduction in the window upon receiving a congestion signal, thereby increasing window fluctuation.

[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 preference is larger k s This demonstrates the existence of trade-offs between different objectives. Formulas (13, 17, 19, 20) represent the utility functions for the four performance aspects obtained from this analysis. Clearly, these objectives conflict with each other and cannot be simultaneously improved. Therefore, a trade-off is necessary.

[0142] In the past, transmission performance objectives were typically 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 overall network resources. This requires competing sources to compromise performance in other areas while seeking to improve specific performance. This dynamic performance trade-off enables the construction of 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, an approach 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 denoted by σ. We can represent σ as a tuple of variables as follows:

[0145]

[0146] We formulate the transmission control algorithm parameter selection for competing sources as a multi-objective optimization problem, aiming to address 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] The first step of HydraCC involves the traditional dual gradient descent method to obtain an initial solution. For the network utility maximization (NUM) problem, the initial solution is obtained by the collaboration of the 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 is the step size, and according to equations (3) and (8), Each link is iterated in a distributed manner. Subsequently, all sources determine their target rates based on their observations:

[0150]

[0151] where, is derived from the AIMD equilibrium. Figure 2 The first phase of the 1st stage demonstrates the iterative process. In recent years, many studies have used gradient-based methods to solve the transmission control problem, proving that they can converge to the optimal solution. However, these models usually have a single objective function, and the optimal solution obtained is only one point on the Pareto frontier. 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 to the bandwidth fair optimal solution * convergence. After obtaining this fair optimal solution, we introduce three independent objective functions: responsiveness, throughput, and window fluctuation. This encourages sources to explore the Pareto frontier of the network based on the fair optimal solution. The exploration process requires a balance between multiple objectives. A comprehensive explanation of the algorithm will be provided in the subsequent sections of this paper.

[0152] The dual gradient descent method based on QoS fairness establishes an initial solution for network congestion control. This fairness concept primarily focuses on bandwidth allocation. However, when the objective function expands to multiple dimensions, this initial solution is only one point on the Pareto frontier in the solution space. Our goal is to navigate these Pareto frontiers, thereby providing users with a wider range of congestion control parameter choices.

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

[0154]

[0155] where a i Given by Lemma 1.

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

[0157]

[0158] 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 will solve the process of finding the direction of the Pareto front in two steps. First, we solve the following problem based on the characterization of Pareto stationarity presented in Lemma 1:

[0162]

[0163] This problem is a classic least-norm problem. Given that our model only contains three objective functions, we can utilize 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 constraint and aim to minimize the second-norm value in the problem, rather than 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, as the size of the network grows, its dimension increases, and directly obtaining it and finding its inverse matrix poses significant challenges. Therefore, we employ an evolutionary exploration method to construct a Krylov subspace to approximate the direction of the Pareto front.

[0164]

[0165] where g represents where β is a constant vector. This means that the content of 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 precludes the application of the classic conjugate gradient (CG) algorithm. Therefore, we chose the minimum residual error (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 is expressed as We can construct the Krylov subspace. This process avoids the calculation and inversion of the Hessian matrix of the objective function.

[0168] Scalability: In congestion control scenarios, the dimension of the Hessian matrix increases with L s The convergence rate 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 computation and storage requirements from growing rapidly with iterations.

[0170] The Krylov subspace defined above It 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 enables the method to effectively approximate the direction of the Pareto front. Importantly, this approach promotes evolutionary exploration of the Pareto direction and achieves a balance between accuracy and resource consumption through early stopping.

[0171] The following is a detailed derivation of how to explore 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 that alternates between iteratively validating the direction through the Krylov subspace and generating new solutions based on the confirmed direction.

[0173] The preceding method makes it possible to identify the edge of the Pareto frontier in a single direction. However, when the target dimension exceeds two, the Pareto frontier is no longer a line but a plane. To cope with this complexity and expand the Pareto frontier, this section introduces a method to extend the Pareto frontier in multiple directions.

[0174] Under the premise of Theorem 2, let there exist a curve u(θ) that is offset, where θ ∈ (-ε, ε). Assume that the newly constructed curve d(θ), denoted as u(θ) + b(θ), intersects the optimal point σ * If H(σ * )u' ≈ 0 is satisfied, we deduce that at the point σ * , the curves d and b have similar derivatives. Furthermore, they are coplanar but not parallel.

[0175] Proof: To verify whether the curves d and b have similar properties, we perform derivative calculations on the curve d in the objective function space:

[0176]

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

[0178]

[0179] Considering that H(σ * )u' tends to zero, we can deduce that This indicates that the curves d and b have similar derivatives at σ * , but they are not parallel.

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

[0181]

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

[0183]

[0184] This shows that at θ = 0, the curve d(θ) is orthogonal to the vector a. Similarly, when the offset vector u is zero, the curve b(θ) also becomes orthogonal to a. Therefore, regardless of the choice of u, the curves b(θ) and d(θ) are coplanar at the Pareto optimal point σ *

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

[0186] Having outlined the process of finding the Pareto front, the competing source inputs its own preference into the weighted sum model (WSM) model after obtaining the Pareto front set. WSM is a mature tool in multi-criteria decision analysis that calculates a score by summing the product of the evaluation value of each objective function of each alternative and the corresponding preference weight. Then, the competing source selects the solution with the highest score from the numerous solutions on the Pareto front, adjusts its congestion control algorithm based on this, and returns the AQM parameter γ s of link l e L l back to the network.

[0187] Let the preference weights be denoted as Δ, where each Δ o represents the weight assigned to each objective. The conditions can be mathematically represented as:

[0188] · Each Δ o is a positive real number:

[0189] · The sum of all weights is 1:

[0190] For the link side, upon receiving the AQM parameter γ l contained in the ACK packet header from the competing source, the AQM parameter will be adjusted for the data flow from the corresponding competing source. Figure 2 The second phase demonstrates the process of exploring the Pareto front. From a practical perspective, the sender s of HydraCC only updates its own algorithm parameters and the parameters of devices in L s . This means that even if the network size expands, HydraCC still focuses on "local" considerations, embodying a practical distributed design approach.​

[0191] When multiple competing sources share a network, simultaneously satisfying the diverse needs of router AQM parameters presents a challenge. Individual adjustment of AQM parameters for each user traffic can lead to network unfairness.

[0192] HydraCC addresses this issue by following the principle of network quality of service (QoS) fairness. It emphasizes fairness for all users, rather than prioritizing the experience of individual users. In our approach, achieving favorable AQM parameters involves adjusting the aggressiveness of each TCP algorithm to achieve a balanced network state. Furthermore, excessive data beyond the link-side buffer capacity can lead to tail packet drops, a side effect of the aggressive strategy.

[0193] The concept of "fairness" is particularly important here. HydraCC views the network source and link as a whole. Therefore, algorithms are deployed on both the source and link sides to facilitate overall network convergence that meets the needs and goals of multiple users. Figure 3 This balance is demonstrated. We selected two parameter sets with different performance characteristics from the Pareto front determined by HydraCC. As the path capacity changes, the right-hand plot demonstrates the corresponding sending rates. The strategy that focuses on responsiveness converges faster and more stably, while the strategy that focuses on throughput more effectively utilizes bandwidth, but with larger window fluctuations.

[0194] Of course, the present application can have other various embodiments, and those skilled in the art can certainly make various corresponding changes and modifications to the present application according to the present application without departing from the spirit and essence of the present application. However, these corresponding changes and modifications shall all belong to the protection scope of the claims attached to the present application.

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 variables (x s (t),w s (t),q s (t)), each router with limited capacity constituting 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 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 Indicates 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 competing source s according to the state variables corresponding to each competing source s and router l fair (x s (t)): Among them, D s (t) is the congestion window decrement 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 alternative solutions in multiple directions corresponding to each competing source s and all located on the Pareto front; S6: Substitute all 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)), obtain the response value, throughput, and window fluctuation value of the competing source s under the corresponding backup solution; S7: Each competing source s sets different weights for responsiveness, throughput, and window fluctuation based on its own transmission performance preferences. Each competing source s then performs a weighted summation of the response value, throughput, and window fluctuation value of its corresponding backup solution based on these weights. Each competing source s then obtains a score for each of its corresponding backup solutions. S8: Each competing source s uses the transmission rate, congestion window decrement, and congestion window increment contained in the backup solution with the highest score as the transmission control variable at the next moment.

2. The multi-objective transmission control method implemented by the self-evolution method according to 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 time slot t+1 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, then x is maintained. s The rate of (t+1) remains unchanged from the previous time slot. If the result of the expression in the brackets is positive, the content of the expression in the brackets remains unchanged. It represents the gradient on the side of the competition source s, and is calculated as follows: Among them, U′ fair (x s (t)) represents U fair (x s (t))'s first derivative; S32: Set the transmission rate of the next time slot to x s (t+1) 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, which is calculated as follows: 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 size 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 router's gradient is a negative number or the change in two adjacent iterations is less than the set threshold; the transmission rate, positive gain, congestion window decrement, 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. The multi-objective transmission control method implemented by the self-evolution method according to claim 1, characterized in that: In step S5, the initial solution corresponding to each competing source s is obtained based on the first-order derivative constraint theory. 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 representation 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 the solution σ * The first derivative under , and o = 1, 2, ..., objectives, objectives is the total number of all objective functions; S52: Constructing Krylov subspaces as follows: Among them, m represents the dimension of 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; let 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 experience step size.

4. The multi-objective transmission control method implemented by the self-evolution method according to claim 1, characterized in that: Each competing source multiplies its preference weight by 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. The multi-objective transmission control method implemented by the self-evolution method according to 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.

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