CN113590335B - Task load balancing method based on grouping and delay estimation in tree edge network - Google Patents
Task load balancing method based on grouping and delay estimation in tree edge network Download PDFInfo
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Abstract
The invention discloses a task load balancing method based on grouping and delay estimation in a tree-shaped edge network, which is a hierarchical balancing strategy for executing efficient balancing on task loads of a multi-edge server. The method comprises the following steps: considering the constraint of two resources, namely calculation and bandwidth, and forming the load balancing problem of the edge network into a nonlinear programming problem with linear constraint; based on the characteristics of the tree network, specific limitation is applied to unloading decision and transmission bandwidth allocation, an original load balancing problem is decomposed into a plurality of sub-problems, and a delay estimation function is designed to solve the sub-problems; and (5) combining the solutions of all the sub-problems, and analyzing the solution of the original load balancing problem.
Description
Technical Field
The invention belongs to the field of edge calculation, and particularly relates to a hierarchical balancing method for efficiently balancing task loads of a polygonal edge server in a tree-shaped edge network.
Background
With the rapid popularization of the emerging technologies such as the internet of things, artificial intelligence, virtual reality and the like in daily life, terminal equipment at the edge of a network is dramatically increased compared with the terminal equipment which is not seen before being experienced in the past, and according to the estimation of cisco, the terminal equipment which is connected into the internet globally by 2023 can reach 293 billions, which is 3.6 times of the population at that time, the terminal equipment in 2018 has 184 billions, and the terminal equipment in the five-year period is increased by more than 100 billions. The new technology brings higher convenience and also has the cost, such as application of automatic driving, intelligent transportation, AR game and the like, is highly dependent on analysis of high-density data such as video, pictures, sound and the like, and compared with the application which mainly depends on data such as texts, tables and the like, the emerging application has obviously increased requirements on data quantity and calculation quantity and stricter requirements on delay. Thus, massive terminals, massive data, and low latency are important features that service providers need to consider when providing computing services in new era. In the past, cloud computing was the primary way to provide computing services for applications. In the traditional cloud computing, data from a terminal need to be concentrated to a remote cloud server for processing, and in the mode, on one hand, because the data needs to be transmitted to the cloud server from the terminal through a long distance in a new computing age, intolerable long transmission delay is brought to emerging applications, and application response is slow; on the other hand, due to the rising number of network edge terminal devices and the increasing data demand of emerging applications, the bandwidth of the core network is far increased and cannot keep pace with the increasing speed of the data volume of the edge terminal devices, so that the current internet cannot realize a centralized computing mode of transmitting all terminal data to a cloud server for processing. To solve this problem, edge computation is emerging. Because the edge calculation configures the server to be closer to the network edge of the terminal, on one hand, the data transmission distance between the terminal and the server can be shortened, so that low-delay calculation service can be provided for the terminal; on one hand, the data transmission between the terminal and the edge server can finish the task unloading of the application without occupying the bandwidth of the core network, thereby greatly reducing the occupation of the bandwidth of the core network and overcoming the defect of cloud computing in a new application scene.
Therefore, in this new internet era, various computing-intensive and data-intensive terminal applications are gradually created and promoted and popularized, so that the computing devices are promoted to be widely covered at the network edge, and a wide edge computing environment is formed. In the future, perhaps every primary network access point will be provided with an edge server to provide low-latency computing services for nearby end users. The edge network is formed by combining various access networks, and when the access points gather traffic from the terminal to the core network in various access networks such as the current mainstream 4G, 5G and home broadband, the interconnection among the devices is mainly completed by adopting tree topology, so that the edge servers densely deployed at the access points and all levels of switches connected with the edge servers form a tree network. Tasks generated by a wide variety of end applications in the future will be offloaded and computation services will be obtained in such a tree network. Therefore, the problem of edge load balancing under the special network form is researched, a unique balancing strategy is designed for the problem, and the method has important practical significance for reducing task delay and improving resource utilization rate.
In the prior related research aiming at the problem of edge load balancing, most of the work assumes that the edge servers are interconnected through a network with star topology or mesh topology, and no related work has been conducted in-depth theoretical analysis and experimental exploration on the problem of load balancing in a tree network. From the perspective of applicable scenes, the star topology can reasonably describe the interconnection among the edge clouds built in a centralized way or multiple servers in a single access network, and the mesh topology is suitable for the conditions that the edge server deployment is sparse and the distribution range is wide. Both scenarios are in the current edge environment and do not essentially fully describe such tree join features present in future edge networks.
The problem of edge load balancing in tree networks is significantly different from the problem of load balancing in star networks or mesh networks. On the one hand, compared with a star network with only two layers, the extra layers of the tree network not only increase the complexity of unloading decision and path bandwidth allocation among servers, but also bring about the problem of load balancing among a plurality of star networks (i.e. access networks), namely the problem of cross-domain unloading. Because of the coupling between the star networks in the transmission bandwidth allocation, the load balancing problem in the tree network cannot be converted into the load balancing problem in a plurality of star networks by a simple method to solve, and the related research method cannot be applied. On the other hand, although mesh networks are the most widely used, the load balancing problem defined based on the most general network structure is difficult to design and quickly solve by using an effective algorithm because of lack of sufficient characteristics.
Disclosure of Invention
The invention aims to: based on the defects, the task load balancing method based on grouping and delay estimation in the tree-shaped edge network can effectively process the cross-domain unloading problem in the tree-shaped edge network, reduce the complexity of the overall load balancing problem of the network, compress the solution space of the problem and remarkably improve the solution speed.
The technical scheme is as follows: in order to achieve the above object, the present invention adopts the following technical scheme:
step S1, jointly considering the constraint of two resources, namely calculation and bandwidth, and forming a load balancing problem of an edge network into a nonlinear programming problem with linear constraint, wherein the aim of the problem is to minimize calculation delay and transmission delay in the edge network, and the solution of the problem is unloading decision and transmission bandwidth allocation among edge servers;
s2, applying specific limitation to unloading decision and transmission bandwidth allocation based on the characteristics of the tree network, decomposing an original load balancing problem into a plurality of sub-problems, and designing a delay estimation function to solve the sub-problems;
and step S3, combining solutions of all the sub-problems, and analyzing the solutions of the original load balancing problem.
The step S2 includes:
s21, regrouping sub-nodes owned by nodes with the degree larger than 2 in the tree-shaped edge network according to the resource non-uniformity minimum principle, and converting the original tree-shaped network into a binary tree;
and S22, starting from the root nodes of the binary tree, sequentially constructing and solving the load balancing sub-problem corresponding to each node according to the traversing sequence of the first root.
The step S21 includes:
step S21a, sequentially selecting nodes with the degree larger than 2 in the tree network, grouping the owned sub-nodes according to a resource non-uniformity minimization principle, wherein the number of the owned sub-nodes in each group is not more than 2, creating a new Node for each group, and connecting the corresponding sub-nodes in the group to the newly created Node;
step S21b, if the newly built nodes are equal to 2, the newly built nodes are directly connected to the father Node, if the newly built nodes are more than 2, the newly built nodes are continuously grouped, and new nodes are built for the new group until the newly built nodes are equal to 2 in the last grouping, and the two nodes are connected to the father Node.
The step S22 includes:
step S22a, generating resource constraint of the sub-problem corresponding to the node according to the resource information owned by the sub-node of the current node and the solution of the load balancing sub-problem corresponding to the father node;
step S22b, constructing an objective function based on delay estimation by using the delay estimation function;
step S22c, solving a feasible solution for enabling the objective function value to be minimum under the condition of resource constraint by utilizing a sequence least square planning algorithm;
step S22d, finding the next non-leaf node according to the traversing sequence of the prior root, returning to step S22a if the next non-leaf node is found, and ending step S22 if the next non-leaf node is not found.
The step S3 includes:
step S31, for each sub-problem, constructing a linear equation set taking part of the solution of the original problem as a variable and the solution of the sub-problem as a parameter according to the quantity relation between the solution of the sub-problem and the solution of the original problem;
and step S32, solving the linear equation set, and filling the obtained solution into the solution of the original problem.
The beneficial effects are that: according to the invention, on one hand, the special property of the tree network is utilized to carry out layering and grouping on the edge tree, and the original problem is decomposed into a plurality of small-scale sub-problems, so that the size of a solution space of the edge load balancing problem in the tree network is obviously compressed, and the complexity of problem solving is reduced; on the other hand, the delay estimation method is used, so that the dependence of upper-layer sub-problems on lower-layer sub-problems in the edge tree is avoided, and the complexity of solving the sub-problems is further reduced. The method effectively solves the problem that the layering equalization strategy effect is not obvious when the degree of the tree-shaped network is overlarge, and has positive application significance for cross-domain unloading in the tree-shaped edge network.
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FIG. 1 is an exemplary schematic diagram of a tree edge network in an embodiment of the invention;
FIG. 2 is a flow chart of a method of task load balancing based on packet and delay estimation in an embodiment of the invention;
FIG. 3 is a diagram illustrating the relationship between a domain and its subdomains in an embodiment of the present invention;
FIG. 4 is an exemplary diagram of a sub-domain regrouping of a domain in an embodiment of the present invention;
FIG. 5 is a schematic diagram showing the comparison of the optimization effect of the present method with other numerical methods;
FIG. 6 is a comparison of the solution time consumption of the present method with other numerical methods.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
The tree edge network is a network with at least three layers of switching equipment, computing equipment and connection, and is marked as G tree For short, edge trees, wherein leaf nodes of the tree are all computing devices, called edge servers; the non-leaf nodes are all switching devices; the connections between nodes represent round-trip links between devices. Fig. 1 shows an example of a tree-like edge network. For ease of representation, either the edge server or the switching device is denoted s i (i=1, …, m), m being the number of edge servers and switching devices, each device having an amount of computing resources denoted c i . When s is i In the case of a switching device c i =0. Device s i Sum s j The connection between them is noted as e i,j It is congested withWith bandwidth noted b i,j 。
Since each edge server is deployed at a network access point, the task of a user uploading to the network access point may go through the edge server. The invention assumes that the end user transmits to the edge server s i The task quantity compliance parameter is alpha i Poisson distribution, where alpha i Is the upload rate of the task. The calculation amount and the data amount of the user uploading task are random, and the random variable has the expectation and the standard deviation or variance, wherein the calculation amount is expressed by using the random variable h, and the expectation is beta h Standard deviation is sigma h The method comprises the steps of carrying out a first treatment on the surface of the The data quantity of a task is represented by a random variable d, the expectation of which is beta d Standard deviation is sigma d 。
G tree The task load balancing problem is a nonlinear programming problem with linear constraint, and when a general nonlinear programming algorithm is adopted for solving, the time complexity is at least O (n 6 ) The experiment is shown as an index grade.
The invention provides a hierarchical load balancing method based on grouping and delay estimation by utilizing tree network characteristics, which comprises the following steps of tree The overall load balancing problem in the (a) is converted into load balancing sub-problems in a plurality of domains, so that the load balancing efficiency is improved.
Referring to fig. 2, a hierarchical load balancing method based on packet and delay estimation in a tree edge network includes the steps of:
step S1, jointly considering the constraint of two resources, namely calculation and bandwidth, and forming a load balancing problem of an edge network into a nonlinear programming problem with linear constraint, wherein the aim of the problem is to minimize calculation delay and transmission delay in the edge network, and the solution of the problem is unloading decision and transmission bandwidth allocation among edge servers;
s2, applying specific limitation to unloading decision and transmission bandwidth allocation based on the characteristics of the tree network, decomposing an original load balancing problem into a plurality of sub-problems, and designing a delay estimation function to solve the sub-problems;
and step S3, combining solutions of all the sub-problems, and analyzing the solutions of the original load balancing problem.
The specific implementation of this method step is described below.
First to G tree The relationship between domains is defined as follows.
Definition 1: g tree One domain g of (2) k Is G tree A subtree corresponding to a node in the tree.
This definition also means that when the node to which the domain corresponds is the root node, G tree May be referred to as a domain, G tree The edge servers that act as leaf nodes are also referred to as domains.
In addition, subfields defining a domain are also required.
Definition 2: domain g k At G tree Subtrees of the corresponding tree in (a), called g k Is a sub-domain of (c). g v G is g k The subdomain of (1) is denoted as g v ∈g k 。
It should be noted that, without ambiguity, the present invention describes an edge server s j Belongs to g k Also recorded as s j ∈g k This expression means s j G is g k Leaf nodes of the corresponding subtrees.
G tree Each domain or node in (a) corresponds to a load balancing sub-problem, but the sub-problem corresponding to a leaf node is trivial and does not require solution. The number of sub-problems that need to be solved is G tree The number of non-leaf nodes in the tree. The solutions between the sub-problems are coupled at this point. When g v G is g k G at sub-domain of (2) k Is to know g v Is a minimum delay expectation of (1); g v Is dependent on g for solving k As a parameter. This coupling can lead to complex solutions. The invention uses a delay estimation method to eliminate the dependence of domain solving on the domain solving. Domain g k It is necessary to know its subdomain g v Where minimum delay is desired, the formula is used
Direct calculation without the need to recursively solve individual nonlinear programming problems. The parameters in the formulas are explained below.
Edge tree G tree One domain g of (2) k If it is not a leaf node, it is set to have its external input task quantity as Γ k The output task quantity is theta k Bandwidth occupied by external communicationThe objective function of the delay-optimized edge load balancing sub-problem in this domain can be expressed as:
the sum on the left side in the expression is the calculation delay expectation, the sum on the right side is the transmission delay expectation, and the calculation modes of all symbols are respectively as follows
Wherein gamma is v G is g v Accepted external input task quantity, θ v G is g v The amount of tasks that are output out,and->G is respectively k Is a sub-domain offloading decision and transmission bandwidth allocation. FIG. 3 shows a domain g 0 An example of a numerical relationship with its parent domain, subdomain. g 0 Input task amount and input bandwidth Γ 0 ,/>Output task amount and output bandwidth Θ 0 ,/>Are determined by the resolution of their parent domain, while their child domains g 3 Input task amount and input bandwidth Γ 3 ,/>Output task amount and output bandwidth Θ 3 ,/>Are all g of 0 Is to solve the problem of subdomain g 1 And g is equal to 2 The task transmission delay between them is expected to be also determined by g 0 Is determined by the solution of (2).
In addition, the optimization problem satisfies some necessary constraints, as long as g k Not leaf nodes of the edge tree, then for all g u ,g v ∈g k The following constraints hold:
representing external tasks received by all subfields within a domain and a total input task equal to the domain;
representing output tasks of all subfields in a domain and a total output task equal to the domain;
representing the total amount of tasks to be offloaded for each sub-domain, which is equal to the total amount of tasks generated by the sub-domain;
indicating the total amount of tasks accepted by each sub-domain, and not exceeding the amount of tasks which can be processed per unit time;
the bandwidth of each path representing inter-domain offloading cannot be lower than the task offloading rate multiplied by the data amount of a unit task;
indicating that the sum of the path bandwidths carried on each connection in the domain cannot exceed the amount of bandwidth of that path.
γ v ≥0
θ v ≥0
Indicating that all offloading decisions cannot be negative. Wherein the method comprises the steps of
The objective function in the above optimization problem is in an abstract form, which needs to be based on the domain g k Which is materialized by its identity. If field g k There are grandchild nodes, that is, when its subdomain is not an edge server, there are
Wherein the method comprises the steps ofAnd->Are delay estimation functions defined by the present invention, where they represent respectively
Wherein the method comprises the steps of
m v G is g v Number of middle edge servers, sigma h Is the standard deviation of the task calculation amount h.
α j Is an edge server s j Generating the number of tasks in the unit time;
is domain g k The total load of the task, namely the sum of the task amount received by all edge servers in a unit time domain:
wherein lambda is j Is an edge server s j The sum of the task quantity which is received in unit time and needs to be processed;
e is domain g k Connection of b) e Is the amount of bandwidth that connection e has.
And if the intermediate node g k Without grandchild nodes, then
At this point, its subdomains are leaf nodes, representing edge servers.
The original problem can be decomposed into a plurality of sub-problems of smaller scale, thereby reducing the complexity of solving the problem. However, it is also noted in the study that the size of each sub-problem is determined by the degree of its corresponding non-leaf node. When there are large degrees of non-leaf nodes in an edge tree, hierarchical load balancing does not reduce the complexity of problem solving well. To solve this disadvantage, it is necessary to decompose the non-leaf nodes having a large degree into a plurality of non-leaf nodes having a smaller degree, such as nodes having a degree of 2, so as to further decompose the problem such that the scale of each sub-problem of the edge tree converted after decomposing the nodes thereof does not exceed 2, regardless of the structure of the edge tree.
The decomposition operation (alternatively referred to as a sub-domain grouping operation) of the nodes is actually quite simple. When the scale of each sub-problem after decomposition is required to be not more than r, all nodes, i.e. domains, with degrees greater than r are decomposed. When for a domain g k When decomposing, dividing the subdomain set according to r groups (the number of the last group is possibly less than r), creating a virtual domain in each group, and connecting the domains in the group under the virtual domain; if the number of virtual domains is still greater than r, then the grouping of virtual domains continues, the creation of virtual domains for the group of virtual domains is recreated, and the virtual domains within the group are placed under the newly created virtual domains. Repeating the above steps until the number of the top virtual domains does not exceed r, and connecting the top virtual domains to g k Below as its subdomain. Thus, the original edge tree is changed into a tree with more layers and smaller degrees. At this time, the complexity of the problem can be further reduced by using a hierarchical equalization method for the transformed edge tree. Referring to the example of FIG. 4, by combining g 1 The 4 sub-domains owned are divided into two groups and two virtual sub-domains g are created for them 6 、g 7 Finally make g 1 The number of layers increases by 1 and the number of degrees decreases from 4The low is 2.
Grouping is required to follow the resource non-uniformity minimization principle, where the resource non-uniformity of edge servers in a domain is defined as
Wherein m is k Is domain g k Number of edge servers.
The cross-domain offloading decision and the transmission bandwidth allocation obtained at this time are domain-level, and the solution of the original problem is offloading decision and transmission bandwidth allocation between edge servers. The solution of the sub-problem needs to be converted correspondingly to become the solution of the original problem. Since the solution space of the sub-problem is smaller than that of the original problem, one solution of the sub-problem generally corresponds to a plurality of solutions of the original problem, and if the solution of the original problem is to be obtained, it is necessary to perform a corresponding conversion on the obtained solution. A viable way of conversion is presented here, which implementation requires solving a system of linear equations.
If an offload decision between edge servers in two domains is specified, uniformly from an edge server in the originating domain, and uniformly to an edge server in the target domain, then the offload decision between edge servers satisfies the set of equations:
a i,j refers to a unit time slave edge server s i Offloading to edge server s j Is a mean of task amounts of (a). Solving the linear equation system to obtain g u ,g v And unloading decision among the middle edge servers.
For any two different domains g u ,g v For any s i ∈g u 、s j ∈g v The following constraints are imposed:
the corresponding transmission bandwidth allocation can be obtained.
In an edge network, the delay experienced between the task being sent from the terminal to the receipt of the execution result from the edge server is mainly composed of its computational delay on the edge server and the transmission delay in the edge network. The present invention focuses on the desire to minimize the overall delay of all tasks in an edge network. Since the computational delay expectations of tasks on one edge server are only related to the task load of that server, there is no relation to the transmission bandwidth allocation and the offloading decisions on other edge servers. Whereas in a domain (access network) composed of a plurality of edge servers, the desire for the total computational delay of a task is only related to the task load of the plurality of edge servers therein. This means that when the total load of a task in one domain is determined, the optimal offloading decision in that domain is already fully determined, solely from the point of view of computational delay optimization. Therefore, the optimization of the computation delay in different domains, i.e. different subtrees, in the tree network is irrelevant, so that the optimal offloading decision of the computation delay optimization of the whole tree network can be composed of the optimal offloading decisions of the computation delay optimization in each domain. Therefore, from the viewpoint of algorithm design, the optimization problem of computation delay in the tree network is considered to have an "optimal substructure".
On the other hand, while optimization for computation delay has an optimal substructure, optimization for transmission delay does not have such good properties. This is because the impact of the allocation of transmission bandwidth is cross-domain. When a path is allocated a certain bandwidth, this means that all connections on the path allocate this bandwidth to the path. When optimizing the transmission delay of a task in one domain, the transmission bandwidth of a path connected in this domain needs to be adjusted, so that the influence of transmission bandwidth allocation propagates to another domain through a cross-domain path, and the available bandwidth of the connection in the other domain changes, so that the optimization of the transmission delay does not have the optimal substructure for calculating the delay optimization. However, since in a tree network the total communication bandwidth between any two domains is equal to the communication bandwidth between the switching nodes in the two domains, this means that as long as the communication bandwidth on the path between the switching nodes in the two domains is fixed, the total communication bandwidth between the two domains is fixed; and then the cross-domain path between the two domains can be further defined to bisect the total communication bandwidth by the amount of data of the tasks they carry. At this time, the bandwidth on the path of cross-domain offload is fixed, and the optimization of the transmission delay in different domains is independent of each other. Under the condition, the original problem can be decomposed into sub-problems, corresponding delay estimation functions are designed, and the complexity of solving the load balancing problem is reduced.
The performance of the process according to the invention is verified by experiments. The hierarchical load balancing algorithm of the present invention is denoted as the HIER algorithm. The two histograms of fig. 5 are the comparison of the effects of the HIER algorithm with the numerical algorithms SLSQP, PVI and SEP, wherein the mean and minimum values of the solutions of the respective algorithms are obtained statistically after 20 repeated solutions to the problem. The SLSQP algorithm is a sequence least squares programming method; the PVI algorithm is a partial variable iterative algorithm that optimizes the overall delay expectations of the task by updating the offload decisions first, then updating the transmission bandwidth allocation, then continuing to update the offload decisions, … so repeatedly updated; the SEP algorithm is a separate iterative algorithm, which is an algorithm that optimizes the desire for the overall transmission delay of a task separately from the desire for the computation delay. As can be seen from the comparison result of the minimum values of the solutions, the HIER algorithm has poorer solving effects compared with SLSQP and PVI when the problem scale is 4, but the optimal solving effect of the HIER algorithm is not different from the effects of SLSQP and PVI on a larger scale. From the mean value comparison result of the solutions, the SLSQP algorithm has the best average effect when the problem scale is smaller, and as the problem scale becomes larger, the mean value of the solutions is obviously higher than that of PVI and HIER due to unstable solution, and the mean values of the solutions of PVI and HIER are very close in various scales, so that the solutions have the same stability and average solution effect.
FIG. 6 illustrates a comparison of the solution time consumption of HIER, PVI and SLSQP algorithms. Wherein the abscissa of the coordinate system is the number of servers, i.e. the problem size; each point in the graph is the time consuming solution of the corresponding algorithm at the specified problem scale, and the lines are regression approximations made to show their increasing trend. As can be seen from the figure, the time consumption of the SLSQP and PVI algorithms increases exponentially with the problem size, while the time consumption of the HIER increases linearly. At a problem size of 2, the solution time of the three algorithms is in the range of tens to hundreds of milliseconds, while when the problem size is increased to 13, the solution time of the SLSQP and PVI algorithms already reaches the level of about one thousand seconds, and the time of the HIER solution once is still between 1 and 10 seconds. The HIER shows a very significant efficiency advantage. The method has the advantages of obvious speed, on one hand, the original problem can be decomposed into a plurality of small-scale sub-problems by layering and grouping the edge tree by utilizing the special property of the tree network, so that the size of the known space is obviously compressed, and the complexity of problem solving is reduced; on the other hand, because a delay estimation method is used, the dependence of the upper-layer sub-problem on the lower-layer sub-problem in the edge tree is avoided, and therefore the complexity of solving the sub-problem is further reduced.
Claims (2)
1. A method for task load balancing based on packet and delay estimation in a tree-shaped edge network, comprising the steps of:
step S1, jointly considering the constraint of two resources, namely calculation and bandwidth, forming a load balancing problem of an edge network into a nonlinear programming problem with linear constraint, wherein the aim of the problem is to minimize calculation delay and transmission delay in the edge network, and the solution of the problem is unloading decision and transmission bandwidth allocation among nodes in the edge network;
step S2, based on the characteristics of the tree network, applying specific limits to unloading decision and transmission bandwidth allocation, decomposing an original load balancing problem into a plurality of sub-problems, and designing a delay estimation function to solve the sub-problems, wherein the step comprises the following steps:
s21, regrouping sub-nodes owned by nodes with the degree larger than 2 in the tree-shaped edge network according to the resource non-uniformity minimum principle, and converting the original tree-shaped network into a binary tree;
s22, starting from the root node of the binary tree, sequentially constructing and solving a load balancing sub-problem corresponding to each node according to the traversing sequence of the first root;
step S3, the solutions of all the sub-problems are combined, and the solutions of the original load balancing problem are resolved, wherein the step includes:
step S31, for each sub-problem, constructing a linear equation set taking part of the solution of the original problem as a variable and the solution of the sub-problem as a parameter according to the quantity relation between the solution of the sub-problem and the solution of the original problem;
step S32, solving the linear equation set, and filling the obtained solution into the solution of the original problem;
wherein, the step S21 includes:
step S21a, sequentially selecting nodes with the degree larger than 2 in the tree network, grouping the owned sub-nodes according to a resource non-uniformity minimization principle, wherein the number of the owned sub-nodes in each group is not more than 2, creating a new Node for each group, and connecting the corresponding sub-nodes in the group to the newly created Node;
step S21b, if the number of newly built nodes is equal to 2, directly connecting the newly built nodes to a father Node, if the number of newly built nodes is greater than 2, continuing to group the newly built nodes, and building new nodes for the new group until the number of the newly built nodes in the last grouping is equal to 2, and connecting the two nodes to the father Node;
the step S22 includes:
step S22a, generating resource constraint of the sub-problem corresponding to the node according to the resource information owned by the sub-node of the current node and the solution of the load balancing sub-problem corresponding to the father node;
step S22b, constructing an objective function based on delay estimation by using the delay estimation function;
step S22c, solving a feasible solution for enabling the objective function value to be minimum under the condition of resource constraint by utilizing a sequence least square planning algorithm;
step S22d, finding the next non-leaf node according to the traversing sequence of the prior root, if so, returning to the step S22a, and if not, ending the step S22;
the objective function of the load balancing sub-problem is:
wherein s is j Representing a j-th node in the tree edge network; the edge tree containing nodes and connections between nodes is noted as G tree ，g k Represents G tree The domain is a subtree corresponding to a node in the edge tree; g v G is g k Is a subdomain of domain g k At the edge tree G tree Subtrees of the corresponding tree; s is(s) j ∈g v Representing nodes s j Belonging to subdomain g v ；
Wherein,
c j is node s j Amount of owned computing resources, beta h Representing the expectation of the calculated amount h of the task, beta d Representing the expectations of the data volume d of the task, m v G is g v The number of intermediate nodes is set to be equal to the number of intermediate nodes,and->G is respectively expressed as g v Input bandwidth and output bandwidth of (a);
ψ is a shorthand for the following formula:
wherein sigma h Standard deviation representing the task calculation amount h;
α j is node s j Generating the number of tasks in the unit time;
is domain g k The total load of the task, namely the sum of the task amount received by all nodes in a unit time domain:
wherein lambda is j Is node s j The sum of the task quantity which is received in unit time and needs to be processed;
is domain g v Total load of the middle task;
e is domain g k Connection of b) e Is the amount of bandwidth that connection e has;
the linear equation set in step S31 includes:
unloading decision equation set between nodes:
s j representing a j-th node in the tree edge network; the edge tree containing nodes and connections between nodes is noted as G tree ，g k Represents G tree The domain is a subtree corresponding to a node in the edge tree; g v 、g u G is g k Is a subdomain of domain g k At the edge tree G tree Subtrees of the corresponding tree; s is(s) i ∈g u Representing nodes s i Belonging to subdomain g u ，s j ∈g v Representing nodes s j Belonging to subdomain g v ；a i，j Refers to slave node s per unit time i Unloading to node s j Is the average of the task amounts;
γ j is subdomain g v Accepted external input task amount Γ v Is subdomain g v Is used for inputting the task quantity,representing a slave subfield g u To subdomain g v Is a decision to unload; θ i G is g u The task quantity theta output outwards u Is subdomain g u Output task amount of (2);
a system of transmission bandwidth equations between nodes:
is a slave node s i To node s j Transmission bandwidth of>Is a slave node s j To node s i Transmission bandwidth of>Is a sub-field g v To subdomain g u Is a load decision of->Is subdomain g u To subdomain g v Transmission bandwidth allocation of>Is subdomain g v To subdomain g u Is allocated to the transmission bandwidth of the mobile station.
2. The method for task load balancing based on packet and delay estimation in a tree edge network according to claim 1, wherein the resource non-uniformity is defined as:
wherein s is j Representing a j-th node in the tree edge network; the edge tree containing nodes and connections between nodes is noted as G tree ，g k Represents G tree The domain is a subtree corresponding to a node in the edge tree; s is(s) j ∈g k Representing nodes s j Belongs to domain g k ；
Wherein,
c j is node s j Amount of owned computing resources, beta h Representing the desire for the calculated amount h of the task,
is domain g k The sum of the task amounts which can be processed by all nodes in unit time, m v Is subdomain g v Number of middle nodes g v G is g k Is a subdomain of domain g k At the edge tree G tree Subtrees, m of the corresponding tree in k Representation field g k Number of intermediate nodes.
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