An Online Shunting Scheduling Method for Network Application Traffic Based on Nonsmooth Technology

Abstract

The present invention discloses an online split scheduling method for network application traffic based on non-smooth technology. First, an online dynamic split model for network application traffic scheduling is given; secondly, the original problem is transformed into a convex optimization problem through variable substitution; then, based on convex optimization theory, an augmented Lagrangian function is constructed considering both bandwidth constraints and split ratio constraints; finally, an algorithm is designed based on non-smooth technology and the gradient descent method to iteratively update the split ratio and the Lagrange multiplier, and solve the split ratio of each link that minimizes the network-wide bandwidth leasing cost. The present invention has a simple form and strong practicability, can quickly solve the optimal split ratio that minimizes the network-wide bandwidth leasing cost, and has a very broad application prospect.

Description

Technical Field

[0001] The present invention belongs to the technical field of network application traffic scheduling, and in particular relates to an online shunt scheduling method for network application traffic based on non-smooth technology. Background Art

[0002] Enterprise offices in various places lease wide-area bandwidth such as Internet links and MPLS dedicated lines from local operators. Among them, the dedicated line is more expensive than the Internet, but its tariff packages are diverse, making the wide-area network bandwidth leasing cost closely related to the traffic scheduling effect. Its tariff package models are mainly divided into three categories: pay-per-use, fixed bandwidth, and elastic bandwidth. Pay-per-use means charging based on the unit price according to the amount of traffic used; the fixed bandwidth package is to purchase a fixed bandwidth at a fixed amount, and the used traffic is not allowed to exceed this fixed bandwidth; elastic bandwidth is to purchase a fixed bandwidth at a fixed amount, but the used traffic is allowed to exceed this fixed bandwidth, and the excess part is charged additionally according to the amount of traffic. At present, the commonly used bandwidth statistical method is the P95 bandwidth statistical method, that is, the traffic is counted every 5 minutes, and the 95th percentile of the traffic counted in a month is used as the billing bandwidth. On this basis, combined with flexible tariff packages such as elastic bandwidth, the network application traffic is scheduled online, and the traffic of each service is allocated to each network link to minimize the whole network bandwidth leasing cost. This research cross-integrates the frontier theoretical knowledge of multiple disciplines including computer science, communication technology, and engineering optimization.

[0003] The literature (Wang Xuerong, Tang Zhengzhi, Li Yinchuan, Qi Meiyu, Zhu Jianbo, Zhang Liang. Intelligent perception scheduling of delay-sensitive flows based on optimized decision trees. Telecommunications Science, 2023, 39(04): 120-132.) proposed a network traffic performance-sensitive intelligent perception method based on reinforcement learning; the literature (Zhang Huyin, Wang Sisi, Qian Long, Zhou Tianying. Research on energy-saving mechanism for path resource management in SDN data center networks. Journal of Chinese Computer Systems, 2017, 38(04): 755-760.) proposed a Fat-tree dynamic topology scheme based on OpenFlow, using the central controller to determine all links that meet the SLA performance and evenly distributing the traffic to each available link; the literature (Zhang Y, Cui L, and Zhang Y. A stable matching based elephant flow scheduling algorithm in data center networks. Computer Networks, 2017, 120: 186-197.) proposed a traffic scheduling scheme for elephant flows that can avoid network congestion and achieve performance optimization.

[0004] The present invention converts the non - linear programming problem into a convex optimization problem, eliminates the inequality constraints according to the convex optimization theory, reconstructs the traffic scheduling problem by using the augmented Lagrangian multiplier method, and combines the non - smooth technology and the gradient descent method to solve the traffic splitting ratio of each link that minimizes the network bandwidth leasing cost. On the one hand, this method significantly shortens the solving process; on the other hand, the algorithm is simple and easy to understand, has strong scalability, and a wide range of applications. Summary of the Invention

[0005] Object of the Invention: Aiming at the online scheduling problem of network application traffic with time - varying traffic, time - varying link SLA quality, diverse network tariff packages and high requirements for solving time, a method for online splitting and scheduling of network application traffic based on non - smooth technology is proposed.

[0006] Technical Solution: To achieve the object of the present invention, the technical solution adopted by the present invention is: A method for online splitting and scheduling of network application traffic based on non - smooth technology, the steps include:

[0007] Step 1: Give a mathematical model for online scheduling of network application traffic, and appropriately simplify it to form a non - linear programming problem, making it more convenient for analysis and algorithm design while meeting the actual application requirements.

[0008] Step 2: Introduce logarithmic transformation, perform variable substitution on the simplified non - linear programming problem to obtain a convex optimization problem that is convenient to use analysis tools such as convex optimization theory.

[0009] Step 3: Based on the convex optimization theory, according to the idea of the interior - point method and penalty function, eliminate the inequality constraints in the transformed convex optimization problem and construct the corresponding augmented Lagrangian function.

[0010] Step 4: Design a corresponding iterative algorithm based on non - smooth technology and the gradient descent method, iteratively update the splitting ratio and Lagrangian multiplier, so that the gradient quickly drops to a smaller range, that is, solve the traffic splitting ratio of each link that minimizes the network bandwidth leasing cost.

[0011] Furthermore, in the above - mentioned Step 1, the specific mathematical model for online scheduling of network application traffic is as follows:

[0012]

[0013] where, E k is the set of alternative links for service k, K is the set of all services k, is the bandwidth cost function on link e, specifically the sum of the fixed cost f e of all alternative links and the floating cost (the product of the floating cost unit price v e and the billed bandwidth), is the traffic splitting ratio of service k on link e at time t. is the traffic allocated to service k in the selected link set. is the traffic demand of service k at time t. is the upper limit of the physical port capacity of the device on link e. is the P95 billing bandwidth of link e, which is determined by taking the 95% quantile of the traffic points at the current time and previous times. The specific statistical method is as follows: within one month, calculate the average used bandwidth of the link every 5 minutes, and arrange them from largest to smallest. The top 5% of the bandwidth is not charged, and the 95% quantile is used as the monthly billing bandwidth. SLA e refers to the quality of service index on link e, which generally reflects the delay, jitter, packet loss rate, etc. of the link. is the fixed bandwidth.

[0014] Further, in step two, a logarithmic transformation is introduced. Let Then the above non-linear programming problem can be transformed into the following convex optimization problem:

[0015]

[0016] Further, in step three, according to the idea of the interior point method, the bandwidth inequality constraint after the transformation in step two is The transformed cost function is introduced In this case, the convex optimization problem in step two can be transformed into the following model:

[0017]

[0018] In addition, in step three, according to the idea of the penalty function and the augmented Lagrangian multiplier method, the following augmented Lagrangian function is constructed:

[0019]

[0020] where v is the Lagrangian multiplier, and r and ζ are the penalty factors for the inequality constraint and the equality constraint respectively.

[0021] Further, in step four, based on non-smooth technology and the gradient descent method, the iterative algorithm designed for the traffic splitting ratio and the Lagrangian multiplier is as follows:

[0022]

[0023] where sig β (x) = sgn(x)|x| βis a non-smooth function, β ∈ (0, 1) is the non-smooth exponent, sgn(x) is the sign function with respect to x, sgn(x) = 1 when x > 0, and sgn(x) = -1 when x < 0; n is the number of iteration steps, and r, the penalty factor for inequality constraints (n) is a decreasing positive sequence, and ζ, the penalty factor for equality constraints (n) can be taken as 1, or as an increasing positive sequence.

[0024] Select appropriate initial values v (0) , and appropriate β, and perform iterative calculations on the above algorithm. When the gradient drops to a small range, that is

[0025]

[0026] it is considered that the shunt ratios of each link that minimize the network bandwidth leasing cost are solved, where ε is a small positive number.

[0027] Beneficial effects: Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0028] (1) The online shunt scheduling method for network application traffic based on non-smooth technology proposed by the present invention simplifies the scheduling model and converts it into a convex optimization problem that is easy to analyze. It has a simple form and conforms to the actual application conditions, with strong universality, flexibility, and scalability, and can be widely applied to different types of network traffic scheduling;

[0029] (2) The iterative algorithm based on non-smooth technology proposed by the invention has a simple structure, is easy to implement, and can accelerate the solution speed of the optimal shunt ratio, and can achieve high-quality scheduling of network traffic faster;

[0030] (3) The scheduling method proposed by the present invention considers the P95 bandwidth statistics method and tariff packages such as elastic bandwidth on the basis of meeting the requirements of link SLA performance indicators, and shunts different application traffic on the link, significantly reducing the network bandwidth leasing cost and improving the performance of traffic scheduling. Description of the Drawings

[0031] Figure 1 is a topological structure represented by the hub-spoke networking mode;

[0032] Figure 2 is the flowchart of the method of the present invention;

[0033] Figure 3This is the iterative simulation curve graph of the bandwidth lease cost of the method of the present invention, which includes a total of 6 topological networks. Among them, (a), (b), (c), (d), (e), and (f) respectively correspond to Network 0-13, Network 1-11, Network1-13, Network 2-13, Network 3-13, Network 3-23;

[0034] Figure 4 The optimal traffic splitting ratio, solution time, and minimum bandwidth lease cost of each link under the method of the present invention, which includes a total of 6 topological networks. Among them, (a), (b), (c), (d), (e), and (f) respectively correspond to Network 0-13, Network 1-11, Network 1-13, Network 2-13, Network 3-13, Network 3-23. Detailed implementation manners

[0035] The present invention will be further described below in conjunction with the accompanying drawings and detailed implementation manners.

[0036] The network topology structure established with the hub-spoke networking mode as the representative is as Figure 1 shown, including 10 branch sites and 1 data center site. The network is named after the number of upper-layer elastic links - the number of lower-layer elastic links, and a total of 6 network topologies are constructed, which are respectively named six topologies Network 0-13, Network 1-11, Network 1-13, Network 2-13, Network 3-13, Network 3-23.

[0037] The specific flowchart of an online traffic splitting and scheduling method for network applications based on non-smooth technology proposed by the present invention is as Figure 2 shown, and the steps include:

[0038] Step 1: Give a mathematical model for the online scheduling of network application traffic, and appropriately simplify it to form a non-linear programming problem, making it more convenient for analysis and algorithm design on the basis of meeting the actual application requirements;

[0039] Step 2: Introduce logarithmic transformation, perform variable substitution on the simplified non-linear programming problem, and obtain a convex optimization problem that is convenient to use analysis tools such as convex optimization theory;

[0040] Step 3: Based on convex optimization theory, according to the ideas of the interior point method and penalty function, eliminate the inequality constraints in the transformed convex optimization problem, and construct a corresponding augmented Lagrangian function;

[0041] Step 4: Design a corresponding iterative algorithm based on non-smooth technology and the gradient descent method to iteratively update the splitting ratio and Lagrange multiplier, so that the gradient quickly drops to a small range, that is, solve the splitting ratio of each link that minimizes the network bandwidth leasing cost.

[0042] In Step 1, the specific mathematical model of online scheduling of network application traffic is as follows:

[0043]

[0044]

[0045] Among them, E k is the set of optional links for service k, K is the set of all services k, is the bandwidth cost function on link e, specifically the sum of the fixed cost f e of all optional links and the floating cost (the product of the floating cost unit price v e and the billed bandwidth), is the splitting ratio of service k on link e at time t, is the traffic allocated by service k in the selected link set, is the traffic demand of service k at time t, is the upper limit of the physical port capacity of the device on link e, is the P95 billed bandwidth of link e, which is determined by taking the 95% quantile of the sampled traffic at the current time and previous times. The specific statistical method is as follows: within a month, the average used bandwidth of the link during this period is calculated by sampling every 5 minutes, and arranged in descending order. The top 5% of the bandwidth is not charged, and the 95% quantile is used as the billed bandwidth for the current month. SLA e refers to the quality of service index on link e, which generally reflects the delay, jitter, packet loss rate, etc. of the link. is the fixed bandwidth.

[0046] In Step 2, introduce logarithmic transformation, let Then the above non-linear programming problem can be transformed into the following convex optimization problem:

[0047]

[0048] In Step 3, according to the idea of the interior point method, use the logarithmic barrier function to transform the bandwidth inequality constraint obtained in Step 2 Introduce the transformed cost function into it. At this time, the convex optimization problem in Step 2 can be transformed into the following model:

[0049]

[0050] In addition, in the third step, according to the idea of penalty function and augmented Lagrangian multiplier method, the following augmented Lagrangian function is constructed:

[0051]

[0052] where v is the Lagrangian multiplier, and r and ζ are the penalty factors for inequality constraint and equality constraint respectively.

[0053] In the fourth step, based on non-smooth technology and gradient descent method, the iterative algorithm for the split ratio and Lagrangian multiplier is designed as follows:

[0054]

[0055] where sig β (x) = sgn(x)|x| β is a non-smooth function, β ∈ (0, 1) is the non-smooth exponent, sgn(x) is the sign function with respect to x, when x > 0, sgn(x) = 1, when x < 0, sgn(x) = -1; n is the number of iteration steps, the penalty factor r (n) for the inequality constraint is a decreasing positive sequence, and the penalty factor ζ (n) for the equality constraint can be taken as 1, or as an increasing positive sequence.

[0056] Select appropriate initial values v (0) , and appropriate β, and perform iterative calculations on the above algorithm. When the gradient descends to a small range, that is

[0057]

[0058] it is considered that the split ratios of each link that minimize the network bandwidth leasing cost are solved, where ε is a small positive number.

[0059] To verify the effectiveness of the network application traffic scheduling method proposed by the present invention, numerical simulation experiments are carried out on 6 network topologies of 10 branch sites as shown in Figure 1 , which jointly undertake the traffic of 3 network application APPs, namely APP_0, APP_1, and APP_2.

[0060] Taking the site site_1 in the topology Network 0-13 as an example, its Internet link delay is 196 ms, jitter is 13 ms, packet loss rate is 8%, the baseline bandwidth (the bandwidth included in the fixed monthly rent in the elastic bandwidth tariff package) is 129 Mbps, and its bandwidth upper limit It is 129 Mbps, the fixed cost is 12,900 yuan, and the unit price of the floating cost is 0. The specific P95 bandwidth statistics method is as follows: within one month, the average used bandwidth of the link during this period is calculated every 5 minutes, totaling 8,640 bandwidths. Arranged from largest to smallest, the top 5% of the bandwidths are free of charge, and the 95th percentile is used as the monthly billed bandwidth. That is, the first 432 bandwidth points are free of charge, and the 433rd bandwidth point is used as the billed bandwidth. Taking the branch site site_1 as an example, among the traffic of application APP_1 it undertakes, the total upstream traffic of the 8,640 billed bandwidths is 141,127.16 Mbps, and the total downstream traffic is 529,454.55 Mbps; among them, the 95th percentile traffic of the upstream traffic is 48.57 Mbps, and the 95th percentile of the downstream traffic is 202.28 Mbps. The data of the remaining branch sites and network applications APP are similar to the above. Due to excessive data, they are omitted here.

[0061] During the simulation process, for the SLA performance constraint, the shunt ratio on the link e that does not meet the SLA performance requirements of service k is set to 0. The specific simulation results are as Figures 3 - 4 shown. Among them, Figure 3 is the curve graph of the total floating cost in the bandwidth rental cost in each topological network changing with the number of iterations, Figure 4 is the optimal shunt ratio of each corresponding link, the solution time, and the optimal floating cost and fixed cost in the bandwidth rental cost.

[0062] The above implementation is only to illustrate the technical idea of the present invention and should not limit the protection scope of the present invention. It should be noted that any improvement made to the technical solution based on the technical idea of the present invention falls within the protection scope of the present invention.

Claims

1. An online shunt scheduling method for network application traffic based on non-smooth technology, characterized in that, The method includes the following steps: Step 1: Give a non-linear programming problem that is convenient for analysis and design and meets the actual application requirements to describe the mathematical model of online traffic splitting of network applications; Step 2: Introduce a logarithmic function to perform variable substitution on the non-linear programming problem in Step 1 to obtain a convex optimization problem that is convenient for using convex optimization theory for analysis; Step 3: Based on convex optimization theory, according to the ideas of the interior point method and penalty function, eliminate the inequality constraints in the convex optimization problem obtained by conversion in Step 2 and construct the corresponding augmented Lagrangian function; Step 4: Design an algorithm based on non-smooth technology and gradient descent method to iteratively update the splitting ratio and Lagrange multiplier, and solve the splitting ratio of each link that minimizes the network bandwidth leasing cost; In the said Step 1, the basic mathematical model of online traffic splitting of network applications is as follows: Among them, E k is the set of optional links for service k, and K is the set of all services k. is the bandwidth cost function on link e. is the traffic splitting ratio of service k on link e at time t. is the traffic allocated by service k in the selected link set. is the traffic demand of service k at time t. is the upper limit of the device physical port capacity of link e. is the P95 metering billing bandwidth of link e, SLA e refers to the quality of service index on link e, which is reflected by the delay, jitter, and packet loss rate of the link, f e is the fixed cost, v e is the floating cost unit price. is the fixed bandwidth.

2. The online shunt scheduling method for network application traffic based on non-smooth technology according to claim 1, characterized in that, In the first step, by using variable substitution, let The above non-linear programming problem is transformed into the following convex optimization problem:

3. The online shunt scheduling method for network application traffic based on non-smooth technology according to claim 2, characterized in that, In the third step, according to the idea of the interior point method, the bandwidth inequality constraint after the transformation in the second step is transformed by using the logarithmic barrier function and the transformed cost function is introduced in which the convex optimization problem in the second step is transformed into the following model: Based on the converted model, construct the following augmented Lagrangian function: where \(v\) is the Lagrange multiplier, and \(r\) and \(\zeta\) are the penalty factors of the inequality constraint and the equality constraint respectively.

4. The online shunt scheduling method for network application traffic based on non-smooth technology according to claim 3, characterized in that, In the said Step 4, the splitting ratio iterative algorithm designed by combining non-smooth technology and gradient descent method is as follows: where sig β (x) = sgn(x)|x| β is a non-smooth function, β ∈ (0, 1), n is the number of iteration steps, r (n) is the penalty factor of the inequality constraint, ζ (n) is the penalty factor of the equality constraint, sgn(x) is the sign function, when x > 0, sgn(x) = 1, when x < 0, sgn(x) = -1.

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