CN113590335A - 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 PDF

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CN113590335A
CN113590335A CN202110916431.2A CN202110916431A CN113590335A CN 113590335 A CN113590335 A CN 113590335A CN 202110916431 A CN202110916431 A CN 202110916431A CN 113590335 A CN113590335 A CN 113590335A
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储诚贵
叶保留
陆桑璐
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Nanjing University
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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 layered balancing strategy for executing efficient balancing on task loads of multi-edge servers. The method comprises the following steps: considering the constraints of two resources of calculation and bandwidth jointly, and formalizing the load balancing problem of the edge network into a nonlinear programming problem with linear constraint; based on the characteristics of a tree network, specific limits are applied to unloading decision and transmission bandwidth allocation, the original load balancing problem is decomposed into a plurality of subproblems, and a delay estimation function is designed to solve the subproblems; and (4) integrating the solutions of all the subproblems and analyzing the solution of the original load balancing problem.

Description

Task load balancing method based on grouping and delay estimation in tree edge network
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 multi-edge server in a tree-shaped edge network.
Background
With the rapid popularization of emerging technologies such as internet of things, artificial intelligence and virtual reality in daily life, terminal devices at the edge of a network are rapidly increasing compared with the terminal devices in the past, and according to the reckoning, various terminal devices which are globally connected to the internet by 2023 will reach 293 million, which is 3.6 times of the current population, while the number of terminals in 2018 is only 184 million, and the number of terminals in five years is increased by over 100 million. The cost of the new technology is also the higher convenience brought by the new technology, applications such as automatic driving, intelligent transportation, AR games and the like are highly dependent on analysis of high-density data such as videos, pictures, sounds and the like, and compared with the past applications which mainly depend on data such as texts, tables and the like, the requirements of emerging applications on data volume and calculation amount are remarkably increased, and the requirement on delay is stricter. Thus, the massive amount of terminals, massive amounts of data, and low latency are important features that service providers need to consider when providing computing services in a 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 needs to be processed by a remote cloud server in a centralized mode, and in the new computing era, on one hand, as the data needs to be transmitted to the cloud server from the terminal in a long distance, intolerable long transmission delay is brought to emerging applications, and application response is slow; on the other hand, due to the explosion of the number of network edge terminal devices and the increase of data requirements of emerging applications, the bandwidth increase of a core network is far from keeping up with the increase 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 calculation is followed. Because the server is configured at the network edge closer to the terminal by the edge calculation, on one hand, the data transmission distance between the terminal and the server can be shortened, and thus, the low-delay calculation service can be provided for the terminal; on one hand, data transmission between the terminal and the edge server can complete task unloading of application without occupying core network bandwidth, so that the occupation of the core network bandwidth is greatly reduced, and the defects of cloud computing in a new application scene are overcome.
Therefore, in this new internet era, various computing-intensive and data-intensive terminal applications will be gradually created, popularized and popularized, thereby promoting the wide coverage of computing devices at the network edge and forming a wide edge computing environment. In the future, edge servers will be deployed, perhaps at each primary network access point, to provide low-latency computing services to end users in the vicinity. The edge network is formed by combining various access networks, and when the access points gather the flow from the terminal to the core network in various access networks such as 4G, 5G and family broadband, etc. which are mainstream at present, the interconnection among the devices is completed mainly by adopting a tree topology, so that edge servers which are densely arranged at the access points and all levels of switches which are connected with the edge servers form a tree network. In the future, tasks generated by various terminal applications will be offloaded and computing services obtained in such a tree network. Therefore, the research on the edge load balancing problem in the special network form and the design of a unique balancing strategy for the edge load balancing problem have important practical significance for reducing task delay and improving resource utilization rate.
In the existing related research aiming at the problem of edge load balancing, most of the work assumes that edge servers are interconnected through a network with a star topology or a mesh topology, and no related work is deeply researched by theoretical analysis and experiments for the problem of load balancing in a tree network. From the perspective of an application scenario, the star topology can reasonably describe the edge cloud constructed in a centralized manner or the interconnection among multiple servers in a single access network, and the mesh topology is suitable for the situations that the edge servers are sparsely deployed and have a wide distribution range. Both scenarios are for the current edge environment and do not substantially fully describe the tree join features that exist in future edge networks.
The problem of edge load balancing in a tree network is significantly different from the problem of load balancing in a star network or a mesh network. On one hand, compared with a star network with only two layers, the additional layers of the tree network not only increase the complexity of the offloading 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 cross-domain offloading problem. Due to the fact that coupling exists between the star networks in transmission bandwidth distribution, the load balancing problem in the tree network cannot be converted into the load balancing problem in the star networks to be solved through a simple method, and the related research method cannot be applied to the method. On the other hand, although the mesh network is the most widely applicable, the load balancing problem defined based on the most general network structure is difficult to design an effective algorithm to solve quickly because of the lack of sufficient features.
Disclosure of Invention
The purpose of the invention is as follows: based on the defects, the invention provides a task load balancing method based on grouping and delay estimation in a tree-shaped edge network, which 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 obviously improve the solving speed.
The technical scheme is as follows: in order to achieve the above purpose, the invention adopts the following technical scheme:
step S1, considering the constraint of two resources of calculation and bandwidth, formalizing the load balance problem of the edge network into a nonlinear programming problem with linear constraint, the objective of the problem is to minimize the calculation delay and the transmission delay in the edge network, and the solution of the problem is the unloading decision and the transmission bandwidth allocation between the edge servers;
step S2, based on the characteristics of the tree network, applying specific limits to the unloading decision and the transmission bandwidth allocation, decomposing the original load balancing problem into a plurality of subproblems, and designing a delay estimation function to solve the subproblems;
and step S3, the solutions of all the subproblems are integrated to analyze the solution of the original load balancing problem.
The step S2 includes:
step S21, according to the minimum principle of resource nonuniformity, sub-nodes owned by nodes with the degree greater than 2 in the tree edge network are regrouped, and the original tree network is converted into a binary tree;
and step S22, starting from the root node of the binary tree, sequentially constructing and solving the load balancing subproblems corresponding to each node according to the sequence of first root traversal.
The step S21 includes:
step S21a, selecting nodes with degree greater than 2 in the tree network in sequence, grouping the subnodes owned by the nodes according to the principle of minimizing the unevenness of resources, wherein the number of the subnodes owned by each group is not more than 2, creating a new Node for each group, and connecting the corresponding subnodes in the group to the new Node;
step S21b, if the new Node number is equal to 2, the newly created Node is directly connected to the father Node, if the new Node number is greater than 2, the newly created Node is continuously grouped and a new Node is created for the new group, and until the new Node number in the last grouping is equal to 2, the two nodes are connected to the father Node.
The step S22 includes:
step S22a, according to the resource information owned by the child node of the current node and the solution of the load balancing child problem corresponding to the parent node, generating the resource constraint of the child problem corresponding to the node;
step S22b, constructing an objective function based on delay estimation by using a delay estimation function;
s22c, solving a feasible solution with the minimum objective function value under the resource constraint condition by using a sequence least square planning algorithm;
and S22d, finding the next non-leaf node according to the sequence of the first root traversal, if so, returning to S22a, and if not, ending the step S22.
The step S3 includes:
step S31, for each subproblem, according to the quantitative relation between the solution of the subproblem and the solution of the original problem, constructing a linear equation set which takes partial solution of the original problem as variable and the solution of the subproblem as parameter;
and step S32, solving the linear equation system, and filling the obtained solution into the solution of the original problem.
Has the advantages that: on one hand, the invention utilizes the special property of the tree network to layer and group the edge tree and decomposes the original problem into a plurality of small-scale sub-problems, thereby obviously compressing the size of the solution space of the edge load balancing problem in the tree network and reducing the complexity of the problem solution; on the other hand, the method of delay estimation is used, so that the dependence of the upper-layer subproblem in the edge tree on the lower-layer subproblem is avoided, and the complexity of subproblem solving is further reduced. The invention effectively solves the problem that the layering balancing strategy effect is not obvious when the degree of the tree network is too large, and has positive application significance for cross-domain unloading of the tree edge network.
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FIG. 1 is an exemplary diagram of a tree edge network in an embodiment of the present invention;
FIG. 2 is a flow chart of a task load balancing method based on packet and delay estimation according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the relationship between domains and their subdomains in an embodiment of the present invention;
FIG. 4 is an exemplary diagram of sub-domain regrouping for a domain in an embodiment of the present invention;
FIG. 5 is a graph comparing the optimization results of the present method with other numerical methods;
FIG. 6 is a comparison between the time taken to solve the problem of the present method and other numerical methods.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
The tree edge network is a network composed of at least three layers of switching equipment, computing equipment and connection, and is marked as GtreeThe method is called as an edge tree for short, wherein leaf nodes of the tree are all computing devices and are called as edge servers; the non-leaf nodes are all switching devices; the connections between nodes represent round-trip links between devices. An example of a tree edge network is shown in fig. 1. For the convenience of representation, the edge server or switching device is denoted si(i ═ 1, …, m), m is the number of edge servers and switching devices, and the amount of computing resources owned by each device is denoted ci. When s isiWhen it is a switching device, c i0. Device siAnd sjThe connection between is denoted by ei,jThe bandwidth it has is denoted bi,j。
Since each edge server is deployed at a network access point, the tasks uploaded by the user to the network access point will pass through the edge server. Invention falseSet end user transmission to edge server siThe task amount compliance parameter is alphaiPoisson distribution, whereiniThe physical meaning of (c) is the upload rate of the task. The calculation amount of the uploading task of the user and the data amount are random, the random variable has the expectation and the standard deviation or the variance, the calculation amount is expressed by the random variable h, and the expectation is betahStandard deviation is σh(ii) a The data volume of a task is represented by a random variable d whose expectation is betadStandard deviation is σd。
GtreeThe task load balancing problem in (1) is a nonlinear programming problem with linear constraint, and when a general nonlinear programming algorithm is adopted for solving, the time complexity of the problem is at least O (n) theoretically6) And the test shows an exponential grade.
The invention provides a hierarchical load balancing method based on grouping and delay estimation by utilizing the characteristics of a tree network, which is realized by combining GtreeThe whole load balancing problem in (1) is converted into a load balancing sub-problem 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 following steps:
step S1, considering the constraint of two resources of calculation and bandwidth, formalizing the load balance problem of the edge network into a nonlinear programming problem with linear constraint, the objective of the problem is to minimize the calculation delay and the transmission delay in the edge network, and the solution of the problem is the unloading decision and the transmission bandwidth allocation between the edge servers;
step S2, based on the characteristics of the tree network, applying specific limits to the unloading decision and the transmission bandwidth allocation, decomposing the original load balancing problem into a plurality of subproblems, and designing a delay estimation function to solve the subproblems;
and step S3, the solutions of all the subproblems are integrated to analyze the solution of the original load balancing problem.
The following describes a specific implementation of the steps of the method.
Firstly, toGtreeThe domains and the relationships between the domains are defined as follows.
Definition 1: gtreeOne field g inkIs GtreeA sub-tree corresponding to one of the nodes.
This definition also means that G is the root node when the node corresponding to the domain is the root nodetreeWhich may be referred to as a domain, GtreeThe edge servers in as leaf nodes are also referred to as domains.
In addition, a subdomain of the domain needs to be defined.
Definition 2: field gkAt GtreeThe sub-tree of the tree corresponding to (1) is called gkIs determined. gvIs gkIs denoted as gv∈gk。
It should be noted that, in the case of no ambiguity, the present invention expresses an edge server sjBelong to gkWhen it comes to sj∈gkThe expression means sjIs gkThe leaf nodes of the corresponding subtrees.
GtreeEach domain or node in the set corresponds to a load balancing sub-problem, but the sub-problems corresponding to leaf nodes are trivial and do not need to be solved. So the number of sub-problems that need to be solved is GtreeNumber of non-leaf nodes in the leaf. The solution between sub-problems is now coupled. When g isvIs gkWhen the sub-field of (g)kNeed to know gvMinimum delay expectation; gvIs required to be dependent on gkAs a parameter. This coupling can lead to a complex solution. The present invention uses a method of delay estimation that eliminates the dependency of the solution of a domain on the solution of its subdomain. When field gkNeeds to know its subfield gvUsing the formula
Figure BDA0003205738670000061
Direct calculation without the need for recursive solution of individual nonlinear programming problems. The parameters in the formula are explained below.
Edge tree GtreeOne field g inkIf it is not a leaf node, the external input task quantity is set to be gammakAnd the outward output task quantity is thetakBandwidth occupied by external communication
Figure BDA0003205738670000062
The objective function of the delay-optimized oriented edge load balancing sub-problem in this domain can be expressed as:
Figure BDA0003205738670000063
in the expression, the summation on the left side is expected to calculate the delay, the summation on the right side is expected to transmit the delay, and the calculation modes of all symbols are respectively
Figure BDA0003205738670000064
Figure BDA0003205738670000065
Figure BDA0003205738670000066
Figure BDA0003205738670000067
Figure BDA0003205738670000068
Wherein gamma isvIs gvAmount of externally input task accepted, θvIs gvThe amount of the task output to the outside,
Figure BDA0003205738670000069
and
Figure BDA00032057386700000610
are respectively gkAnd (3) offloading decisions and transmission bandwidth allocation between sub-domains. FIG. 3 shows a field g0An example of a numerical relationship with its parent and child domains. g0Input task amount and input bandwidth Γ0,
Figure BDA00032057386700000611
And output workload and output bandwidth Θ0,
Figure BDA00032057386700000612
Are all determined by the resolution of its parent domain, while its child domain g3Input task amount and input bandwidth Γ3,
Figure BDA00032057386700000613
And output workload and output bandwidth Θ3,
Figure BDA00032057386700000614
Are all g of it0To solve, sub-field g1And g2The expectation of the task transmission delay between is also g0The solution of (2).
In addition, the optimization problem satisfies some necessary constraints as long as g is satisfiedkNot the leaf node of the edge tree, then for all gu,gv∈gkThe following constraints hold:
Figure BDA0003205738670000071
representing the external tasks received by all sub-domains within the domain and the total input tasks equal to the domain;
Figure BDA0003205738670000072
representing the output tasks of all sub-domains within the domain and the total output task equal to the domain;
Figure BDA0003205738670000073
the total amount of tasks required to be unloaded by each subdomain is equal to the total amount of tasks generated by the subdomain;
Figure BDA0003205738670000074
the total amount of tasks accepted by each subdomain cannot exceed the amount of tasks which can be processed per unit time;
Figure BDA0003205738670000075
the bandwidth of each path representing inter-domain unloading cannot be lower than the data quantity of a unit task multiplied by the task unloading rate;
Figure BDA0003205738670000076
Figure BDA0003205738670000077
indicating that the sum of the bandwidth of the paths carried on each connection in the domain cannot exceed the bandwidth of this path.
Figure BDA0003205738670000078
γv≥0
θv≥0
Indicating that all offload decisions cannot be negative. Wherein
Figure BDA0003205738670000079
Figure BDA00032057386700000710
The objective function in the above optimization problem is an abstract form, and needs to be according to the field gkThe identity of which embodies it. If field gkWhen there is a grandchild node, i.e., its subdomain is not an edge server, there are
Figure BDA0003205738670000081
Wherein
Figure BDA0003205738670000082
And
Figure BDA0003205738670000083
are the delay estimation functions defined in the present invention, and they are herein separately denoted
Figure BDA0003205738670000084
Figure BDA0003205738670000085
Wherein
Figure BDA0003205738670000086
Figure BDA0003205738670000087
Figure BDA0003205738670000088
Figure BDA0003205738670000089
Figure BDA00032057386700000810
Figure BDA00032057386700000811
mvIs gvNumber of middle edge servers, σhIs the standard deviation of the task computation h.
αjIs an edge server sjThe number of tasks generated in the unit time is increased;
Figure BDA00032057386700000812
is field gkThe total load of the medium tasks, that is, the sum of the tasks received by all edge servers in a unit time domain:
Figure BDA00032057386700000813
wherein λjIs an edge server sjThe sum of the task quantities to be processed received per unit time;
e is field gkConnection of (b)eIs the amount of bandwidth owned by connection e.
And if intermediate node gkWithout grandchild node, then
Figure BDA0003205738670000091
At this point, its subdomains are all leaf nodes, representing edge servers.
The original problem can be decomposed into a plurality of sub-problems with smaller scale, thereby reducing the solving complexity of the problem. However, it is also noted during the study that the size of each sub-question is determined by the degree of its corresponding non-leaf node. When non-leaf nodes with large degrees exist in one edge tree, the hierarchical load balancing cannot well reduce the complexity of problem solving. To solve this drawback, it is necessary to decompose the non-leaf node with a large degree into a plurality of non-leaf nodes with a small degree, such as nodes with a degree of 2, so as to further decompose the problem, so that the size of each sub-problem of the edge tree converted after decomposing its nodes does not exceed 2, regardless of the structure of the edge tree.
The splitting operation of the nodes (otherwise known as a sub-domain grouping operation) is quite simple in nature. When the size of each subproblem after decomposition is required not to exceed r, all nodes with degrees larger than r, namely domains, are decomposed. When aiming at a domain gkWhen decomposing, dividing the subdomain set of the system into r groups (the number of the last group is less than r), creating a virtual domain for each group, and connecting the domains in the group to the virtual domain; and if the number of the virtual domains is still larger than r, continuously grouping the virtual domains, recreating the virtual domains for the group formed by the virtual domains, and placing the virtual domains in the group under the newly-built virtual domain. Repeating the steps until the number of the top-level virtual domains does not exceed r, and connecting the top-level virtual domains to gkBelow as its subdomain. Thus, the original edge tree is changed into a tree with more layers and smaller degrees. At this time, the hierarchical equalization method is used for the transformed edge tree, so that the complexity of the problem can be further reduced. Referring to the example of FIG. 4, by comparing g1The 4 sub-domains owned are divided equally into two groups and two virtual sub-domains g are created for them6、g7Finally result in g1Increases by 1 and decreases from 4 to 2.
The grouping needs to follow the principle of minimizing resource non-uniformity, which is defined as the resource non-uniformity of the edge server in a domain
Figure BDA0003205738670000092
Wherein m iskIs domain gkThe number of medium edge servers.
The cross-domain offload decision and the transmission bandwidth allocation obtained at this time are domain-level, and the original problem is solved by the offload decision and the transmission bandwidth allocation between the edge servers. The solution of the sub-problem needs to be converted into the solution of the original problem. Since the solution space of the subproblem is smaller than that of the original problem, one solution of the subproblem usually corresponds to multiple solutions of the original problem, and if the solution of the original problem is to be obtained, the obtained solution needs to be correspondingly converted. A possible transformation is proposed, which requires solving a linear system of equations.
If an offload decision between edge servers in two domains is specified, uniformly from the edge server in the origin domain, and uniformly offloaded to the edge server in the target domain, then the offload decision between the edge servers satisfies the equation set:
Figure BDA0003205738670000101
Figure BDA0003205738670000102
ai,jrefers to a unit time slave edge server siOffloading to edge servers sjIs measured. Solving the system of linear equations to obtain gu,gvOffload decisions between the middle edge servers.
For any two different domains gu,gvFor any si∈gu、sj∈gvThe following constraints apply:
Figure BDA0003205738670000103
Figure BDA0003205738670000104
the corresponding transmission bandwidth allocation can be obtained.
In the edge network, the delay experienced between the issuance of a task from a terminal to the reception of the execution result from the edge server is mainly composed of its computation delay on the edge server and its transmission delay in the edge network. The present invention is concerned with the desire to minimize the total delay of all tasks in the edge network. Since the computation delay expectation of the task on one edge server is only related to the task load of the server, the method has no relation to the transmission bandwidth allocation and the unloading decision on other edge servers. In a domain (access network) composed of a plurality of edge servers, the expectation of the total task computation delay is only related to the task load of the plurality of edge servers. This means that when the total load of a task in a domain is determined, the optimal offloading decision in the domain has been completely determined from the point of view of computational delay optimization alone. Therefore, in the tree network, the optimization of the computation delay in different domains, i.e. different subtrees, is irrelevant, so that the optimal offloading decision for the computation delay optimization of the whole tree network can be formed by the optimal offloading decision for the computation delay optimization in each domain. Therefore, from the perspective of algorithm design, it is considered that the optimization problem of computation delay in the tree network has an "optimal substructure".
On the other hand, although optimization for computational delay has an optimal substructure, optimization for propagation 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, it means that all connections on the path are allocated this bandwidth to the path. When optimizing the transmission delay of a task in a domain, the transmission bandwidth of a path connected in the domain needs to be adjusted, so that the influence of transmission bandwidth allocation can be propagated to another domain through a path across domains, resulting in a change in available bandwidth of connections in other domains, and thus the optimization of the transmission delay does not have the optimal substructure for calculating the delay optimization. However, since in the 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 halve the total communication bandwidth according to the data volume of the tasks carried by the two domains. At this time, the bandwidth on the cross-domain offload path 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 a subproblem, and a corresponding delay estimation function is designed, so that the complexity of solving the load balancing problem is reduced.
The performance of the process of the invention is verified by tests below. The hierarchical load balancing algorithm of the invention is denoted as the HIER algorithm. The two histograms of fig. 5 are a comparison of the performance of the HIER algorithm with the numerical algorithms slsrqp, PVI and SEP, where the mean and minimum values of the solutions of each algorithm are obtained statistically after 20 repeated solutions to the problem. Wherein the SLQP algorithm is a sequential least squares programming method; the PVI algorithm is a partial variable iteration algorithm that optimizes the total latency expectation of the task by updating the offload decisions first, then updating the transmission bandwidth allocation, then continuing to update the offload decisions, … so that the update is repeated; the SEP algorithm is a split iteration algorithm, which is an algorithm that optimizes separately the expectation of the total transmission delay of the task from the expectation of the computation delay. From the comparison result of the minimum value of the solution, it can be seen that the HIER algorithm has a slightly worse solving effect than slslqp and PVI when the problem scale is 4, but the best solving effect is not lower than the effects of slqp and PVI when the problem scale is larger. From the comparison result of the mean values of the solutions, the SLSLQP algorithm has the best mean effect when the problem scale is small, and as the problem scale is large, the mean value of the solution 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 to each other under various scales, so that the solutions have the same stability and mean solution effect.
FIG. 6 illustrates a comparison of the solution time consumption of the HIER, PVI and SLSLSLQP algorithms. Wherein the abscissa of the coordinate system is the number of servers, i.e., the scale of the problem; each point in the graph is the time consumption of solving the corresponding algorithm under the specified problem scale, and the lines are regression approximations for displaying the increasing trend of the corresponding algorithm. As can be seen from the figure, the time consumption of the SLSLSLQP and PVI algorithms increases exponentially with the problem size, while the time consumption of the HIER increases linearly. At problem size 2, the solution time of all three algorithms is in the range of tens to hundreds of milliseconds, while when the problem size increases to 13, the solution time of the slslsrp and PVI algorithms already reaches the order of one thousand seconds, while the time of one HIER solution is still between 1 and 10 seconds. HIER exhibits a very significant efficiency advantage. On one hand, the original problem can be decomposed into numerous small-scale sub-problems only by layering and grouping the edge trees by utilizing the special properties of the tree network, so that the size of the learning space 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 the upper-layer subproblem in the edge tree on the lower-layer subproblem is avoided, and the complexity of solving the subproblem is further reduced.

Claims (8)

1. A task load balancing method based on grouping and delay estimation in a tree edge network is characterized by comprising the following steps:
step S1, considering the constraint of two resources of calculation and bandwidth, formalizing the load balance problem of the edge network into a nonlinear programming problem with linear constraint, the objective of the problem is to minimize the calculation delay and the transmission delay in the edge network, and the solution of the problem is the unloading decision and the transmission bandwidth allocation between the nodes in the edge network;
step S2, based on the characteristics of the tree network, applying specific limits to the unloading decision and the transmission bandwidth allocation, decomposing the original load balancing problem into a plurality of subproblems, and designing a delay estimation function to solve the subproblems;
and step S3, the solutions of all the subproblems are integrated to analyze the solution of the original load balancing problem.
2. The method for task load balancing based on packet and delay estimation in tree edge network according to claim 1, wherein said step S2 includes:
step S21, according to the minimum principle of resource nonuniformity, sub-nodes owned by nodes with the degree greater than 2 in the tree edge network are regrouped, and the original tree network is converted into a binary tree;
and step S22, starting from the root node of the binary tree, sequentially constructing and solving the load balancing subproblems corresponding to each node according to the sequence of first root traversal.
3. The method for task load balancing based on packet and delay estimation in tree edge network according to claim 2, wherein said step S21 includes:
step S21a, selecting nodes with degree greater than 2 in the tree network in sequence, grouping the subnodes owned by the nodes according to the principle of minimizing the unevenness of resources, wherein the number of the subnodes owned by each group is not more than 2, creating a new Node for each group, and connecting the corresponding subnodes in the group to the new Node;
step S21b, if the new Node number is equal to 2, the newly created Node is directly connected to the father Node, if the new Node number is greater than 2, the newly created Node is continuously grouped and a new Node is created for the new group, and until the new Node number in the last grouping is equal to 2, the two nodes are connected to the father Node.
4. The method for task load balancing based on grouping and delay estimation in tree edge network as claimed in claim 3, wherein the resource non-uniformity is defined as:
Figure FDA0003205738660000011
wherein s isjRepresenting the jth node in the tree edge network; let G be the edge tree containing nodes and connections between nodestree，gkRepresents GtreeThe domain is a subtree corresponding to a node in the edge tree; sj∈gkRepresentation node sjBelongs to the domain gk；
Wherein the content of the first and second substances,
Figure FDA0003205738660000021
Figure FDA0003205738660000022
cjis node sjAmount of computing resources owned, βhRepresenting the expectation of the calculated amount h of the task,
Figure FDA0003205738660000023
Figure FDA0003205738660000024
is field gkSum of the amount of tasks that can be processed per unit time, m, for all nodes in the systemvIs the sub-field gvNumber of nodes, gvIs gkA sub-field of (1), the sub-field being field gkAt the edge tree GtreeSub-tree of the corresponding tree in (1), mkRepresents the field gkThe number of nodal points.
5. The method for task load balancing based on packet and delay estimation in tree edge network according to claim 2, wherein said step S22 includes:
step S22a, according to the resource information owned by the child node of the current node and the solution of the load balancing child problem corresponding to the parent node, generating the resource constraint of the child problem corresponding to the node;
step S22b, constructing an objective function based on delay estimation by using a delay estimation function;
s22c, solving a feasible solution with the minimum objective function value under the resource constraint condition by using a sequence least square planning algorithm;
and S22d, finding the next non-leaf node according to the sequence of the first root traversal, if so, returning to S22a, and if not, ending the step S22.
6. The method for task load balancing based on grouping and delay estimation in tree edge network as claimed in claim 5, wherein the objective function of the sub-problem of load balancing is:
Figure FDA0003205738660000025
in the formula, sjRepresenting the jth node in the tree edge network; let G be the edge tree containing nodes and connections between nodestree，gkRepresents GtreeThe domain is a subtree corresponding to a node in the edge tree; gvIs gkA sub-field of (1), the sub-field being field gkAt the edge tree GtreeA sub-tree of the corresponding tree in (1); sj∈gvRepresentation node sjBelonging to sub-domain gv；
Wherein the content of the first and second substances,
Figure FDA0003205738660000031
Figure FDA0003205738660000032
Figure FDA0003205738660000033
Figure FDA0003205738660000034
Figure FDA0003205738660000035
Figure FDA0003205738660000036
cj is node sjAmount of computing resources owned, βhRepresenting the expectation of the calculated amount h of the task, betadExpectation of data quantity d representing task, mvIs gvThe number of the nodes is counted,
Figure FDA0003205738660000037
and
Figure FDA0003205738660000038
each represents gvInput bandwidth and output bandwidth of;
Ψ is a shorthand for the following equation:
Figure FDA0003205738660000039
wherein sigmahRepresenting the standard deviation of the task calculation amount h;
αjis node sjThe number of tasks generated in the unit time is increased;
Figure FDA00032057386600000310
is field gkThe total load of the medium tasks, namely the sum of the task quantities received by all nodes in a unit time domain:
Figure FDA00032057386600000311
wherein λjIs node sjThe sum of the task quantities to be processed received per unit time;
e is field gkConnection of (b)eIs the amount of bandwidth owned by connection e.
7. The method for task load balancing based on packet and delay estimation in tree edge network according to claim 1, wherein said step S3 includes:
step S31, for each subproblem, according to the quantitative relation between the solution of the subproblem and the solution of the original problem, constructing a linear equation set which takes partial solution of the original problem as variable and the solution of the subproblem as parameter;
and step S32, solving the linear equation system, and filling the obtained solution into the solution of the original problem.
8. The method for task load balancing based on grouping and delay estimation in tree edge network as claimed in claim 7, wherein the linear equation set in the step S31 includes:
the system of offload decision equations between nodes:
Figure FDA0003205738660000041
Figure FDA0003205738660000042
sjrepresenting the jth node in the tree edge network; let G be the edge tree containing nodes and connections between nodestree，gkRepresents GtreeThe domain is a subtree corresponding to a node in the edge tree; gv、guIs gkA sub-field of (1), the sub-field being field gkAt the edge tree GtreeA sub-tree of the corresponding tree in (1); si∈guRepresentation node siBelonging to sub-domain gu，sj∈gvRepresentation node sjBelonging to sub-domain gv；ai，jRefers to a slave node s per unit timeiOffloading to node sjThe average of the task amount of (a);
γjis the sub-field gvAccepted external input task variables, ΓvIs the sub-field gvThe amount of the input task of (a),
Figure FDA0003205738660000043
representing the slave sub-field guTo subfield gvAn offload decision; thetaiIs guThe amount of task, Θ, output outwarduIs the sub-field guThe output task amount of (1);
system of transmission bandwidth equations between nodes:
Figure FDA0003205738660000044
Figure FDA0003205738660000045
Figure FDA0003205738660000046
is a slave node siTo node sjThe transmission bandwidth of (a) is,
Figure FDA0003205738660000047
is a slave node sjTo node siThe transmission bandwidth of (a) is,
Figure FDA0003205738660000048
is from subfield gvTo subfield guThe decision to unload(s) of (c),
Figure FDA0003205738660000049
is the sub-field guTo subfield gvThe allocation of the transmission bandwidth of (a),
Figure FDA00032057386600000410
is the sub-field gvTo subfield guThe transmission bandwidth allocation of (1).
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Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140098670A1 (en) * 2012-10-09 2014-04-10 Samsung Electronics Co., Ltd. Method and apparatus for distributing load in wireless communication system
CN105049268A (en) * 2015-08-28 2015-11-11 东方网力科技股份有限公司 Distributed computing resource allocation system and task processing method
CN107333281A (en) * 2017-05-15 2017-11-07 北京邮电大学 Mobile computing unloads cooperative control system and method
US20180159922A1 (en) * 2016-12-05 2018-06-07 International Business Machines Corporation Job assignment using artificially delayed responses in load-balanced groups
US20180352023A1 (en) * 2017-06-01 2018-12-06 Salesforce.Com, Inc. Decentralized, resource aware load distribution in a distributed system
CN110062026A (en) * 2019-03-15 2019-07-26 重庆邮电大学 Mobile edge calculations resources in network distribution and calculating unloading combined optimization scheme
CN111352731A (en) * 2020-02-19 2020-06-30 宜通世纪物联网研究院(广州)有限公司 Method, system, apparatus and medium for distributing tasks in edge computing network
CN111813539A (en) * 2020-05-29 2020-10-23 西安交通大学 Edge computing resource allocation method based on priority and cooperation

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140098670A1 (en) * 2012-10-09 2014-04-10 Samsung Electronics Co., Ltd. Method and apparatus for distributing load in wireless communication system
CN105049268A (en) * 2015-08-28 2015-11-11 东方网力科技股份有限公司 Distributed computing resource allocation system and task processing method
US20180159922A1 (en) * 2016-12-05 2018-06-07 International Business Machines Corporation Job assignment using artificially delayed responses in load-balanced groups
CN107333281A (en) * 2017-05-15 2017-11-07 北京邮电大学 Mobile computing unloads cooperative control system and method
US20180352023A1 (en) * 2017-06-01 2018-12-06 Salesforce.Com, Inc. Decentralized, resource aware load distribution in a distributed system
CN110062026A (en) * 2019-03-15 2019-07-26 重庆邮电大学 Mobile edge calculations resources in network distribution and calculating unloading combined optimization scheme
CN111352731A (en) * 2020-02-19 2020-06-30 宜通世纪物联网研究院(广州)有限公司 Method, system, apparatus and medium for distributing tasks in edge computing network
CN111813539A (en) * 2020-05-29 2020-10-23 西安交通大学 Edge computing resource allocation method based on priority and cooperation

Non-Patent Citations (8)

* Cited by examiner, † Cited by third party
Title
CAN WANG ET AL.: "Joint server assignment and resource management for edge-based MAR system", 《IEEE/ACM TRANSACTIONS ON NETWORKING》 *
KEQIANG HE ET AL.: "Presto: Edge-based Load Balancing for Fast Datacenter Networks", 《ACM SIGCOMM COMPUTER COMMUNICATION REVIEW》 *
SHIQIANG WANG ET AL.: "Online placement of multi-component applications in edge computing environment", 《IEEE ACCESS》 *
XIAOLIANG WANG ET AL.: "Nem:toward fine-grained load balancing through RNIC EC offloading", 《2018 IEEE 19TH INTERNATIONAL CONFERENCE ON HIGH PERFORMANCE SWITCHING AND ROUTING》 *
周鹏等: "工业物联网中基于边缘计算的跨域计算资源分配与任务卸载", 《物联网学报》 *
屈志昊等: "面向边缘计算的资源优化技术研究进展", 《大数据》 *
李文中等: "服务组合中一种自适应的负载均衡算法", 《软件学报》 *
闫伟: "移动边缘计算网络中的计算卸载及负载均衡算法研究", 《中国优秀硕士学位论文全文数据库》 *

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