CN110830294A - Edge calculation task allocation method based on branch-and-bound method - Google Patents
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Abstract
The invention provides an edge calculation task allocation method based on a branch-and-bound method, and belongs to the field of edge calculation. The invention minimizes the total energy consumption of task allocation under the condition of considering the constraints of task completion time, DAG parallel system reliability requirement and the like. Firstly, relaxing the optimization problem, and solving a temporary solution by using an interior point method; and then taking discrete values for the decision variables of the first task in the temporary solution and meeting the constraint that one task can only be executed on one edge server, namely only one of the decision variables is taken as 1, and the others are all 0, traversing the value taking situation from the first edge server to the last edge server, continuously adopting an interior point method for the rest tasks to solve and calculate the energy consumption values of different solutions, taking the solution with the minimum energy consumption value, and repeating the step until the last task. The invention has the advantages of good convergence, small calculated amount and the like.
Description
Technical Field
The invention relates to the field of edge calculation, in particular to an edge calculation task distribution method based on a branch-and-bound method.
Background
With the further exuberance of new production requirements such as internet of things and industrial internet of things, a centralized data processing technology taking a cloud computing model as a core cannot efficiently process a large amount of data generated by edge devices. Edge computing is a new type of computing model that performs computing at the edge of a network, and the edge of edge computing refers to any computing and network resources between the path from a data source to a cloud computing center. For example, a smart home gateway may be considered an edge between an in-home electronic device and a cloud computing center. The basic principle of edge computing is to migrate the computing task to the edge device that produces the source data.
With the development of edge computing in the application of the internet of things, more and more terminal devices are added into an edge computing mode. Most of traditional cloud computing adopts a centralized management method, and transmission of mass data from the edge of a network to a cloud computing center causes long network delay and does not meet application programs with real-time requirements. Meanwhile, if the intermediate network is attacked when the data is transmitted to the cloud computing center, the problems of security and privacy disclosure of network edge data can be caused. Finally, with more and more user applications running in the cloud computing center, the requirements of the large-scale data center on energy consumption will be difficult to meet in the future.
In summary, in order to meet the service quality requirement of the user terminal, the edge computing platform is used to push the cloud service to the network edge, when the user terminal initiates a request, the task is decomposed into a group of parallel tasks, and the parallel tasks are processed by the edge server, so that the requirements of real-time performance, safety, low energy consumption and the like of data processing are ensured. In order to realize the edge computing processing of the user terminal, the tasks are described by using a DAG task graph, and under the condition that the task priority and the constraint condition are met, the parallel tasks are distributed to different edge servers for execution by a branch-and-bound method, so that the total energy consumption of task execution is reduced.
Disclosure of Invention
The invention provides an edge computing task allocation method based on a branch-and-bound method, which is mainly applied to the aspect of edge computing and has the main advantages of optimizing the total energy consumption of task execution by considering the distributed processing of parallel tasks.
1. An edge calculation task distribution method based on a branch-and-bound method at least comprises the following steps:
step one, arranging an edge calculation scene, wherein the scene is composed of a network model formed by a user terminal and a plurality of edge servers;
step two, describing the tasks initiated by the user terminal by using a DAG task graph G ═ T, P, wherein the vertex of the graph is described by using a set T ═ T1,t2,...,tmRepresents the tasks needed to be executed by the edge server, the number of the tasks in the task graph is m, and the tasks tiByDefinition of wherein pi、eiAndrespectively representing the number of CPU cycles required for executing the task, the transmission power of the task and the maximum tolerance time for completing the task; p ═ Pij|ti,tjE T represents a set of communication edges between tasks, PijRepresenting slave tasks tiTo task tjThe task has priority, and the subsequent task must start processing after all the predecessor tasks are finished;
step three, a network model formed by connecting a plurality of edge servers is described by a mesh network N ═ (A, D), wherein a vertex set A ═ a of the network model1,a2,...,anIndicates the edge server, the number of edge servers in the network model is n, the edge server ajFrom a to aj(vj,ej,ej,init,hj) Definition of wherein vj、ej、ej,initAnd hjRespectively representing the processing rate of the edge server, the energy consumption per unit time, the initial capacity and the constant failure rate per unit time, and the edge set D ═ DijMeans forCommunication distances between different edge servers;
step four, distributing the tasks in the DAG task graph in the step two to the network model formed by the interconnection of the edge servers in the step three, wherein the task t isiCompletion time ofWherein lijRepresenting slave edge server ajTransmitted for performing task tiB represents the network bandwidth; task tiAt edge server ajTotal energy consumption of upper executionReliability of DAG task graphIn order to minimize the energy consumption of the edge server for executing all tasks and meet the constraint condition, a task allocation matrix X is obtained by a branch-and-bound methodm×nEach element x in the matrixijRepresenting a task tiWhether or not at edge server ajIs executed if task tiAt ajUpper execution, then xijIs 1, otherwise is 0.
2. The method of claim 1, wherein the task is executed in a sequence determined by traversing the set of tasks in the DAG task graph, wherein if a task is a predecessor of another task, the task is processed preferentially, and if multiple tasks have the same execution sequence, the tasks are processed randomly.
3. The method for task allocation based on branch-and-bound method in edge computing as claimed in claim 1, wherein the task allocation matrix X is obtained by branch-and-bound method according to the objectives and constraints mentioned in step fourm×nAt least comprises the following steps:
1) establishing an optimization problem model P1:Constraint conditions are as follows: R(G)≥Rreq(G) whereinMeaning that a task can only be executed on one edge server, Rreq(G) Representing the reliability requirements of the task graph G;
2) initializing parameters, randomly initializing task allocation matrix Xm×nSolution set Solution fetchTaking the optimal value optVal to be + ∞;
3) relaxation Xm×nBinary decision variable x in (1)ijE {0,1} is a real variable xij∈[0,1]Obtaining a relaxation optimization problem model P2;
4) Solving by adopting an interior point method to obtain temporary solution X'm×nAnd the current energy consumption value tempVal;
5) judging whether the tempVal is larger than the optVal or not and whether the current problem has a feasible solution or not, if the tempVal is larger than the optVal or the current problem has no feasible solution, pruning the current problem, and ending, otherwise, executing the step 6);
6) judging X'm×nElement x ofijWhether the discrete value is 0 or 1 is taken, if so, the Solution set Solution is updated, otherwise, the current problem is branched and X 'is set'm×nThe initial value i of the row number is 1;
7) prepared from X'm×nElement x of the ith rowijTake discrete values of 0 or 1 and satisfyThat is, only one element in the ith row takes a value of 1, and the rest are all 0, at this time, the element in the ith row can be obtainedUnder the condition of n different discrete values, the elements in the remaining m-i rows still take continuous values and are solved by adopting an interior point method to respectively obtain n solutions X 'of the element in the ith row under n different discrete conditions'm×nAnd resolving the tempVal corresponding to the n-th tempVal, comparing the n-th tempVal, and taking X 'corresponding to the minimum tempVal'm×nDissolving other n-1 pieces of the mixture into X'm×nPruning and taking the tempVal as a lower bound;
8) repeating the step 7) until i is m, updating the Solution set Solution, and enabling the X 'corresponding to the minimum tempVal in the Solution'm×nIs given to Xm×nX obtained at this timem×nI.e. the matrix is assigned to the task being solved.
Compared with the prior art, the invention has the advantages that:
(1) the invention minimizes the energy consumption for completing the edge computing task under the condition of comprehensively considering time and reliability, reflects the requirements in various aspects in the process of executing the edge computing network task, and the task allocation scheme obtained by the method can improve the comprehensive performance for completing the task;
(2) the method takes 1 from each decision variable according to only one value to carry out a branching strategy on the original problem, then adopts an interior point method to solve, and prunes the solution, compared with a traversal algorithm, the computational complexity is O (n)m) Reduction to o (mn);
(3) the method is a deterministic solution and has the advantages of good convergence, stable calculation result and the like.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of an edge computation scenario;
FIG. 3 is a task allocation process diagram;
fig. 4 is a schematic branching diagram.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
Task collection: an application program running on a terminal device is represented by a DAG task graph G ═ (T, P), and each member is defined as follows:
T={t1,t2,...,tmthe representation of the task set that needs the edge server to execute, the task number in the task graph is m, in fig. 3, there are 6 tasks; p ═ Pij|ti,tjE T represents a set of communication edges between tasks, PijRepresenting slave tasks tiTo task tjIn FIG. 3, task t1To task t2One directed edge of is P12。
Edge network: the edge network formed by the edge server is represented by a mesh network N ═ (a, D), and each member is defined as follows:
A={a1,a2,...,anindicates an edge server set, where the number of edge servers is n, and in fig. 3, there are 4 edge servers in total; d ═ DijDenotes the communication distance between different edge servers, in fig. 3, edge server a1To the edge server a2Has a communication distance d12。
The task allocation of the edge calculation is generally divided into three steps, namely, firstly, the execution sequence of task nodes is determined, a task allocation matrix is initialized, then, an optimization problem model is established, and finally, the tasks are allocated to proper edge servers according to the proposed branch-and-bound method.
Step one, determining an execution sequence of tasks, and generating a task allocation matrix:
1) determining the execution order of tasks from the DAG task graph as { t }1}、{t2,t3,t4}、{t5}、{t6};
2) The rows of the task allocation matrix correspond to tasks and need to be arranged from top to bottom according to the execution sequence of the tasks; if a task precedes another task in the DAG task graph, the row corresponding to the task is above; if the tasks have the same execution sequence, randomly arranging rows corresponding to the tasks;
3) the columns of the task assignment matrix correspond to edge servers, for each row, only 1 column takes 1 and the rest all take 0.
4) Through the steps, the initial task allocation matrix is obtained as follows:
step two, establishing an optimization problem model:
the whole optimization problem model can be expressed as the total energy consumption for the whole task distribution is minimized on the premise of meeting the total task completion time constraint and the task reliability constraint.
And step three, distributing the tasks to proper edge equipment according to the proposed branch and bound method.
1) Relaxation task assignment matrix X6×4Binary decision variable x in (1)ijE {0,1} is a real variable xij∈[0,1]The random initialization task allocation matrix is as follows:
2) solving by adopting an interior point method to obtain a temporary solutionPrepared from X'6×4Maximum value of each row
Taking 1 and all the rest as 0 to obtain an approximate solutionAnd the current energy consumption value tempVal;
3) if the tempVal is larger than the optVal or the current problem has no feasible solution, pruning the current problem, and ending, otherwise, executing the step 4);
4) judging X'6×4Element x ofijWhether the discrete values are 0 and 1, if so, updating Solution, otherwise, branching the current problem and setting X'6×4The initial value i of the row number is 1;
5) prepared from X'6×4Element x of the ith rowijTake discrete values of 0 or 1 andin this case, the i-th element can take 4 different discrete values, case 1: get xi1=1,xi2=0,xi3=0,xi40; case 2: get xi1=0,xi2=1,xi3=0,xi40; case 3: get xi1=0,xi2=0,xi3=1,xi40; case 4: get xi1=0,xi2=0,xi3=0,xi41 is ═ 1; the elements in the remaining 6-i rows are still continuous values and are solved by adopting an interior point method to obtain 4 solutions X 'of the elements in the ith row under 4 different discrete conditions'6×4And resolving the corresponding tempVal, comparing the 4 tempVals, and taking X 'corresponding to the minimum tempVal'6×4And dissolving the other 3 of the three residues by X'6×4Pruning and taking the tempVal as a lower bound;
6) repeating the step 5) until i is 6, updating the Solution set Solution, and enabling the X 'corresponding to the minimum tempVal in the Solution'6×4Is given to X6×4X obtained at this time6×4I.e. the matrix is assigned to the task being solved.
Claims (3)
1. An edge calculation task distribution method based on a branch-and-bound method at least comprises the following steps:
step one, arranging an edge calculation scene, wherein the scene is composed of a network model formed by a user terminal and a plurality of edge servers;
step two, describing the tasks initiated by the user terminal by using a DAG task graph G ═ T, P, wherein the vertex of the graph is described by using a set T ═ T1,t2,...,tmRepresents the tasks needed to be executed by the edge server, the number of the tasks in the task graph is m, and the tasks tiByDefinition of wherein pi、eiAndrespectively representing the number of CPU cycles required for executing the task, the transmission power of the task and the maximum tolerance time for completing the task; p ═ Pij|ti,tjE T represents a set of communication edges between tasks, PijRepresenting slave tasks tiTo task tjThe task has priority, and the subsequent task must start processing after all the predecessor tasks are finished;
step three, a network model formed by connecting a plurality of edge servers is described by a mesh network N ═ (A, D), wherein a vertex set A ═ a of the network model1,a2,...,anIndicates the edge server, the number of edge servers in the network model is n, the edge server ajFrom a to aj(vj,ej,ej,init,hj) Definition of wherein vj、ej、ej,initAnd hjRespectively representing the processing rate of the edge server, the energy consumption per unit time, the initial capacity and the constant failure rate per unit time, and the edge set D ═ DijDenotes the communication distance between different edge servers;
step four, distributing the tasks in the DAG task graph in the step two to the network model formed by the interconnection of the edge servers in the step three, wherein the task t isiCompletion time ofWherein lijRepresenting slave edge server ajTransmitted for performing task tiB represents the network bandwidth; task tiAt edge server ajTotal energy consumption of upper executionReliability of DAG task graphIn order to minimize the energy consumption of the edge server for executing all tasks and meet the constraint condition, a task allocation matrix X is obtained by a branch-and-bound methodm×nEach element x in the matrixijRepresenting a task tiWhether or not at edge server ajIs executed if task tiAt ajUpper execution, then xijIs 1, otherwise is 0.
2. The method of claim 1, wherein the task is executed in a sequence determined by traversing the set of tasks in the DAG task graph, wherein if a task is a predecessor of another task, the task is processed preferentially, and if multiple tasks have the same execution sequence, the tasks are processed randomly.
3. The method for task allocation based on branch-and-bound method in edge computing as claimed in claim 1, wherein the task allocation matrix X is obtained by branch-and-bound method according to the objectives and constraints mentioned in step fourm×nAt least comprises the following steps:
1) establishing an optimization problem model P1:Constraint conditions are as follows:xij∈{0,1},R(G)≥Rreq(G) whereinxijE {0,1} indicates that a task can only be executed on one edge server, Rreq(G) Representing the reliability requirements of the task graph G;
2) initializing parameters, randomly initializing task allocation matrix Xm×nSolution set Solution fetchTaking the optimal value optVal to be + ∞;
3) relaxation Xm×nBinary decision variable x in (1)ijE {0,1} is a real variable xij∈[0,1]Obtaining a relaxation optimization problem model P2;
4) Solving by adopting an interior point method to obtain temporary solution X'm×nAnd the current energy consumption value tempVal;
5) judging whether the tempVal is larger than the optVal or not and whether the current problem has a feasible solution or not, if the tempVal is larger than the optVal or the current problem has no feasible solution, pruning the current problem, and ending, otherwise, executing the step 6);
6) judging X'm×nElement x ofijWhether the discrete value is 0 or 1 is taken, if so, the Solution set Solution is updated, otherwise, the current problem is branched and X 'is set'm×nThe initial value i of the row number is 1;
7) prepared from X'm×nElement x of the ith rowijTake discrete values of 0 or 1 and satisfyxijE {0,1}, j e {1, 2., n }, i.e. only one element in the ith row takes a value of 1, and the rest are 0, at this time, the element in the ith row can obtain n different discrete value conditions, the elements in the remaining m-i rows still take continuous values and are solved by adopting an interior point method, and n solutions X 'of the element in the ith row under n different discrete conditions are obtained respectively'm×nAnd resolving the tempVal corresponding to the n-th tempVal, comparing the n-th tempVal, and taking X 'corresponding to the minimum tempVal'm×nPruning other n-1 solutions X' and taking the tempVal as a lower bound;
8) repeating the step 7) until i is m, updating the Solution set Solution, and enabling the X 'corresponding to the minimum tempVal in the Solution'm×nIs given to Xm×nX obtained at this timem×nI.e. the matrix is assigned to the task being solved.
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