CN112291335A - Optimized task scheduling method in mobile edge calculation - Google Patents

Optimized task scheduling method in mobile edge calculation Download PDF

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CN112291335A
CN112291335A CN202011162207.0A CN202011162207A CN112291335A CN 112291335 A CN112291335 A CN 112291335A CN 202011162207 A CN202011162207 A CN 202011162207A CN 112291335 A CN112291335 A CN 112291335A
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edge server
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CN112291335B (en
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屈毓锛
吴帆
路栋于
陈贵海
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Shanghai Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L67/00—Network arrangements or protocols for supporting network services or applications
    • H04L67/01—Protocols
    • H04L67/10—Protocols in which an application is distributed across nodes in the network
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/48—Program initiating; Program switching, e.g. by interrupt
    • G06F9/4806—Task transfer initiation or dispatching
    • G06F9/4843—Task transfer initiation or dispatching by program, e.g. task dispatcher, supervisor, operating system
    • G06F9/4881—Scheduling strategies for dispatcher, e.g. round robin, multi-level priority queues
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/50—Allocation of resources, e.g. of the central processing unit [CPU]
    • G06F9/5061—Partitioning or combining of resources
    • G06F9/5072—Grid computing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/14—Network analysis or design
    • H04L41/142—Network analysis or design using statistical or mathematical methods

Abstract

An optimized task scheduling method in mobile edge computing estimates the number of task migration failures according to historical data, models a task scheduling problem into an optimized problem about minimization of a computing resource allocation variable and a task scheduling variable, converts the optimized problem into an aggregation function optimized problem only about the task scheduling variable, obtains a primary scheduling strategy applicable to all conditions according to a linear approximation function of an objective function obtained through construction, further obtains a secondary scheduling strategy according to a sub-model approximation function of the objective function obtained through construction when the computing capacity of a user is weak relative to the computing capacity of a server, and finally obtains the optimized task scheduling strategy through the primary scheduling strategy and the secondary scheduling strategy. The invention enables the delay of the computational tasks to be kept low in the face of hardware and software failures that may occur.

Description

Optimized task scheduling method in mobile edge calculation
Technical Field
The invention relates to a technology in the field of mobile edge calculation, in particular to an optimized task scheduling method in mobile edge calculation.
Background
Due to the rapid development of various mobile applications and the internet of things (IoT), cloud infrastructures and wireless networks face stringent requirements such as ultra-low latency, high reliability and continuity of user experience. These requirements make the end users at the edge of the network urgent for highly localized services, and one of the fundamental and critical issues in mobile edge computing is the scheduling problem of user requests, i.e., determining which task should be migrated to which edge node for remote execution to meet various performance requirements.
Compared to mobile cloud computing, mobile edge computing faces the following unique uncertainties in task migration. First, unlike mobile cloud computing, which mostly completes task migration through reliable wired links, since edge servers are typically deployed on local wireless access points or cellular base stations, mobile edge computing tasks are typically migrated to edge nodes through unreliable wireless links. Furthermore, uncertainties such as wireless network connection failures, low reliability of edge servers, etc. can cause any pre-optimized task migration policy to fail, resulting in significant performance loss, such as large response times.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an optimized task scheduling method in mobile edge calculation, which can keep the delay of a calculation task at a lower level when facing the possible hardware and software faults.
The invention is realized by the following technical scheme:
the invention relates to an optimized task scheduling method in mobile edge computing, which predicts the number of task migration failures according to historical data, models a task scheduling problem into an optimized problem about minimization of a computing resource allocation variable and a task scheduling variable, converts the optimized problem into an aggregation function optimized problem only about the task scheduling variable, obtains a primary scheduling strategy applicable to all conditions according to a linear approximation function of an objective function obtained by construction, further obtains a secondary scheduling strategy according to a sub-module approximation function of the objective function obtained by construction when the computing capacity of a user is weak relative to the computing capacity of a server, and finally obtains the optimized task scheduling strategy through the primary scheduling strategy and the secondary scheduling strategy.
The estimation according to historical data is as follows: and estimating the number of task migration failures which possibly occur in the future by using a logistic linear regression method according to the condition that the task migration failures occur in the historical data.
The optimization problem regarding minimization of computing resource allocation variables and task scheduling variables includes:
optimizing the target: minimizing total latency of computational tasks
Figure BDA0002744712010000011
Wherein:
Figure BDA0002744712010000021
the limiting conditions are as follows:
Figure BDA0002744712010000022
wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all the edge servers, N is the set of all the computing tasks, xnsIdentification variables for whether to migrate task n to edge server s, for the scheme of task scheduling, fnsThe computing resources allocated to the edge server s with task n, the solution to the computing resource allocation,
Figure BDA0002744712010000023
to migrate the task n to the total latency of the edge server s processing,
Figure BDA0002744712010000024
the time required to upload task n to the edge server,
Figure BDA0002744712010000025
the time required to download the results of the computation of task n from the edge server s to the user device,
Figure BDA0002744712010000026
for the total delay of the local processing of task n, αnIs the input data size, beta, of task nnFor the size of the output data of task n,
Figure BDA0002744712010000027
for the upstream bandwidth of the edge server s,
Figure BDA0002744712010000028
downstream bandwidth, γ, for edge server snsIs the signal-to-noise ratio, γ ', of the uplink between user device n and edge server s'nsFor the signal-to-noise ratio, w, of the downlink between the user equipment n and the edge server snIn order to be a computational load for the task n,
Figure BDA0002744712010000029
in order to be the computing power of the user equipment n,
Figure BDA00027447120100000210
is the computing power of the edge server s.
The transformation is that: the optimization problem of the minimization of the computing resource allocation variables and the task scheduling variables is expressed as an optimization problem only containing the task scheduling variables, namely:
minimization
Figure BDA00027447120100000211
The limiting conditions are as follows:
Figure BDA00027447120100000212
constructing a task scheduling set A and a task scheduling variable xnsThe relationship of (1): a { (n, s) | x ns1, N belongs to N, S belongs to S, the objective function is marked as g (A), and then the variable x is markednsIs restricted by
Figure BDA00027447120100000213
Into constraints on set A
Figure BDA00027447120100000214
Wherein: 1(n,s)∈ATo indicate a function, the function value is 1 when (n, s) ∈ A holds, otherwise it is 0, and this constraint is a pseudo-matrix constraint, denoted τ.
The problem of the set function optimization only related to the task scheduling variables can be solved into the optimal closed solution of computing resource allocation
Figure BDA00027447120100000215
Wherein:
Figure BDA00027447120100000216
indicating that the edge server s allocates the computing resource of task n for optimal computing resource allocation when the task scheduling variable is X, XnsIdentification variable, w, for whether to migrate task n to edge server snIs the computational load of task n.
The linear approximation function of the objective function is
Figure BDA00027447120100000217
The primary scheduling policy obtained according to the constructed linear approximation function of the objective function specifically includes:
i) initializing a set A, taking a full set from a gamma as an empty set
Figure BDA00027447120100000218
Wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all the edge servers, N is the set of all the computing tasks, and the element (N, S) in the set is the migration of the computing task N to the edge server S.
ii) repeating steps iii, iv, v when Γ is not equal to Ω, otherwise performing step vi.
iii) taking the set of singletons
Figure BDA0002744712010000031
Wherein: v is the element in the set Ω \ Γ, argmax is the operation to take the set of single elements that maximizes the function value, and e is the element in the set of single elements that maximizes the function value.
iv) when A { e }. is ∈ τ, the update set A is A { e }.
v) the update set Γ is Γ { v }.
vi) for each element (n, s) in the set A, the task n is migrated to the edge server s.
The fact that the computing power of the user is weaker than that of the server means that:
Figure BDA0002744712010000032
Figure BDA0002744712010000033
wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all the edge servers, N is the set of all the computing tasks,
Figure BDA0002744712010000034
the time required to upload task n to the edge server,
Figure BDA0002744712010000035
time required for downloading the result of the task n calculation from the edge server s to the user device, wnIn order to be a computational load for the task n,
Figure BDA0002744712010000036
in order to be the computing power of the user equipment n,
Figure BDA0002744712010000037
is the computing power of the edge server s.
The sub-model approximation function of the objective function is
Figure BDA0002744712010000038
Figure BDA0002744712010000039
Wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all the edge servers, N is the set of all the computing tasks,
Figure BDA00027447120100000310
the time required to upload task n to the edge server,
Figure BDA00027447120100000311
time required for downloading the result of the task n calculation from the edge server s to the user device, wnIn order to be a computational load for the task n,
Figure BDA00027447120100000312
in order to be the computing power of the user equipment n,
Figure BDA00027447120100000313
for the computing power of the edge server s, 1(n,s)∈AIndicating a function, the value of (n, s) ∈ A is 1, otherwise the value is 0.
And obtaining a secondary scheduling strategy comprising two-step greedy according to the constructed sub-model approximation function of the objective function.
The two-step greedy specifically includes selecting an element corresponding to a scheduling policy which maximizes an objective function in a greedy process of the first step, selecting an element corresponding to a scheduling policy which maximizes an edge value of the objective function in a greedy process of the second step, and taking a union of sets obtained in the two steps as a result of a task scheduling policy of the algorithm, and the specific steps include:
i) initializing set A1And A2And is provided with a gamma1，Γ2For the empty collection, take the complete collection
Figure BDA00027447120100000314
ii) when r is1If not, repeating the steps iii, iv and v, otherwise executing the step vi.
iii) taking the set of singletons
Figure BDA00027447120100000315
Wherein: v is the element in the set Ω \ Γ, argmax is the operation to take the set of single elements that maximizes the function value, and e is the element in the set of single elements that maximizes the function value.
iv) when A1E ∈ τ and | A1When U { e } | is less than or equal to k, updating the set A1Is A1∪{e}。
v) updating the set Γ1Is gamma1∪{e}。
vi) when set Γ2Is not equal to omega \ A1Then, omega \ A1Is set to omega and A1Repeat steps vii, viii, ix, otherwise perform step x.
vii) taking a set of singletons
Figure BDA0002744712010000041
Wherein: v is an element in the set Ω \ Γ, e represents argmax represents an operation to take the set of single elements that maximizes the function value, and e is an element in the set of single elements that maximizes the function value.
viii) when A1∪A2When the [ e ] belongs to [ tau ], updating the set A2Is A2And E, otherwise, skipping the step.
ix) update set Γ2Is gamma2∪{e}。
x) taking A ═ A1∪A2And for each element (n, s) in a, migrate task n to edge server s.
Technical effects
The invention integrally solves the problems that in the prior art, when facing hardware and software faults possibly occurring in a mobile edge computing environment, uncertain factors in the mobile edge computing environment are not considered, and no design with robustness is available, so that the hardware and software faults possibly occurring can cause great service performance loss, such as longer task response time and higher delay of computing tasks.
Compared with the prior art, the invention can keep the delay of the computing task at a lower level when facing hardware and software faults possibly occurring in the mobile edge computing environment by using the robust optimization task scheduling method in the mobile edge computing.
Drawings
FIG. 1 is a schematic diagram of an edge computing network;
fig. 2 is a schematic diagram of total task latency under different numbers of task migration failures of a simulation experiment.
Detailed Description
As shown in fig. 1, this embodiment relates to an optimized task scheduling method in edge computing, which simulates and schedules 100 computing tasks in an edge computing network with 50 edge servers, sets the value range of input data size of the tasks to [420,1000] KB, sets the ratio of the task computation amount to the input data to [330,960] cycles/byte, sets the computation capability of the user equipment to [0.2,1.5] GHz, sets the value range of the computation capability of the edge servers to about 20GHz, sets a Random algorithm (Random), an iterative optimization algorithm (JSAC' 18), and a Heuristic algorithm (Heuristic) as comparison terms, and takes 10 groups for comparison, where this embodiment specifically includes the following steps:
firstly, estimating the number k of possible task migration failures by a logistic linear regression method according to historical data, and recording the size of input data of a research task n as alphanAnd the size of the output data of the research task n is recorded as betanThe upstream bandwidth of the edge server s is recorded as
Figure BDA0002744712010000042
The downstream bandwidth of the edge server s is recorded as
Figure BDA0002744712010000043
The signal-to-noise ratio of the uplink between the user equipment n and the edge server s is recorded as gammansAnd the signal-to-noise ratio of the downlink between the research user device n and the edge server s is recorded as gamma'nsThe calculated amount of the investigation task n is recorded as wnThe computing power of the user device n is recorded as
Figure BDA0002744712010000044
The computing power of the edge server s is recorded as
Figure BDA0002744712010000045
As shown in fig. 1, to explain an example of this standard, there are N computing tasks, S edge servers, and tasks may be migrated to the edge servers over a wireless network.
Secondly, establishing an optimization problem about minimization of a computing resource allocation variable and a task scheduling variable for computing resource allocation and task scheduling, specifically:
optimizing the target: minimizing total latency of computational tasks
Figure BDA0002744712010000051
Wherein:
Figure BDA0002744712010000052
the limiting conditions are as follows:
Figure BDA0002744712010000053
wherein: x is the number ofnsAn identification variable indicating the scheduling of the task, f, for whether to migrate the task n to the edge server snsThe edge server s is assigned the computational resources of the task n, representing a scheme of computational resource allocation,
Figure BDA0002744712010000054
to migrate the task n to the total latency of the edge server s processing,
Figure BDA0002744712010000055
the time required to upload task n to the edge server,
Figure BDA0002744712010000056
the time required to download the results of the computation of task n from the edge server s to the user device,
Figure BDA0002744712010000057
is the total latency of task n processing locally.
And thirdly, representing the optimization problem in the second step as an optimization problem only containing task scheduling variables and solving to obtain an optimal closed-form solution of the computing resource allocation, wherein the method specifically comprises the following steps:
minimization
Figure BDA0002744712010000058
The limiting conditions are as follows:
Figure BDA0002744712010000059
constructing a task scheduling set A and a task scheduling variable xnsThe relationship of (1): a { (n, s) | xns1, N belongs to N, S belongs to S, the objective function is marked as g (A), and then the variable x is markednsIs restricted by
Figure BDA00027447120100000510
Into constraints on set A
Figure BDA00027447120100000511
Wherein: 1(n,s)∈ATo indicate a function, the function value is 1 when (n, s) ∈ A holds, otherwise it is 0, and this constraint is a pseudo-matrix constraint, denoted τ.
The optimal closed-form solution is
Figure BDA00027447120100000512
The original problem can be represented as an optimization problem containing only task scheduling variables:
fourthly, constructing a linear approximate function of the objective function
Figure BDA00027447120100000513
Obtaining a task scheduling strategy through a primary scheduling strategy, and the method specifically comprises the following steps:
i) initializing a set A, taking a full set from a gamma as an empty set
Figure BDA00027447120100000514
ii) repeating steps iii, iv, v when Γ is not equal to Ω.
iii) taking the set of singletons
Figure BDA00027447120100000515
iv) when a { e }. is ∈ τ, then the update set a ═ a { e }.
v) update set Γ ═ γ { v }.
vi) the algorithm results in a, and for each element (n, s) in a, the task n is migrated to the edge server s.
The fifth step, as shown in fig. 2, is a schematic diagram of the total task delay under different numbers of task migration failures. When the computing power of the user is weak relative to that of the server, that is, the following condition is satisfied
Figure BDA0002744712010000061
Figure BDA0002744712010000062
Constructing a submodel approximation function of the target function; wherein: n denotes the number of compute tasks, S denotes the number of edge servers, S denotes the set of all edge servers, N denotes the set of all compute tasks,
Figure BDA0002744712010000063
the time required to upload task n to the edge server,
Figure BDA0002744712010000064
time required for downloading the result of the task n calculation from the edge server s to the user device, wnIn order to be a computational load for the task n,
Figure BDA0002744712010000065
in order to be the computing power of the user equipment n,
Figure BDA0002744712010000066
is the computing power of the edge server s.
The sub-module is close toThe similarity function is:
Figure BDA0002744712010000067
Figure BDA0002744712010000068
obtaining a task scheduling strategy through a secondary scheduling strategy, and the specific steps comprise:
i) initializing set A1，A2，Γ1，Γ2For the empty collection, take the complete collection
Figure BDA0002744712010000069
ii) when r is1And when not equal to omega, repeating the steps iii, iv and v.
iii) taking the set of singletons
Figure BDA00027447120100000610
iv) when A1E ∈ τ and | A1U { e } | is less than or equal to k, and the set A is updated1＝A1∪{e}。
v) updating the set Γ1＝Γ1∪{e}。
vi) when set Γ2Is not equal to omega \ A1When so, repeat steps vii, viii, ix.
vii) taking a set of singletons
Figure BDA00027447120100000611
viii) when A1∪A2E, E belongs to tau, and the set A is updated2＝A2∪{e}。
ix) update set Γ2＝Γ2∪{e}。
x) taking A ═ A1∪A2The output algorithm result is a, and for each element (n, s) in a, the task n is migrated to the edge server s.
The secondary scheduling strategy is preferentially used in the above case; when the above conditions are not satisfied, only the primary scheduling policy can be used, and the secondary scheduling policy cannot be used. In this embodiment, the experimental setting satisfies the above conditions, so we show the effect of the primary scheduling policy and the secondary scheduling policy at the same time. It can be seen that under the condition of different numbers of failed task scheduling, the performance of the optimized task scheduling strategy obtained by the primary scheduling strategy and the secondary scheduling strategy is obviously superior to that of other comparison algorithms. Specifically, the total task delay of the robust algorithm provided by the invention is reduced by 2218.2ms,27976.9ms and 5285.8ms relative to a random algorithm, an iterative optimization algorithm and a heuristic algorithm respectively.
Through specific practical experiments, when the number of the task migration failures is 1 to 10, the total task time delays that can be achieved through the robust task primary scheduling strategy are 40.5s,48.1s,55.8s,59.6s,63.2s,66.8s,70.4s,73.9s,77.4s, and 80.8s, respectively; the total task delay which can be achieved by the robust task secondary scheduling strategy is 41.9s,49.6s,57.1s,60.8s,64.4s,68.0s,71.5s,75.0s,78.5s and 81.8s respectively. Fig. 2 is a schematic diagram of the total task latency under different numbers of task migration failures. It can be seen that the performance of the method is significantly better than that of other comparison algorithms under the condition of different numbers of failed task scheduling. Specifically, the total task delay of the method is reduced by 2218.2ms,27976.9ms and 5285.8ms relative to a random algorithm, an iterative optimization algorithm and a heuristic algorithm respectively.
The foregoing embodiments may be modified in many different ways by those skilled in the art without departing from the spirit and scope of the invention, which is defined by the appended claims and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (8)

1. An optimized task scheduling method in mobile edge computing is characterized in that the number of task migration failures is estimated according to historical data, a task scheduling problem is modeled into an optimized problem about minimization of a computing resource allocation variable and a task scheduling variable, then the optimized problem is converted into an aggregation function optimized problem only about the task scheduling variable, a primary scheduling strategy applicable to all conditions is obtained according to a linear approximation function of a constructed objective function, a secondary scheduling strategy is obtained according to a sub-model approximation function of the constructed objective function when the computing capacity of a user is weak relative to that of a server, and finally the optimized task scheduling strategy is obtained through the primary scheduling strategy and the secondary scheduling strategy;
the estimation according to historical data is as follows: and estimating the number of task migration failures which possibly occur in the future by using a logistic linear regression method according to the condition that the task migration failures occur in the historical data.
2. The method as claimed in claim 1, wherein the optimization problem regarding minimization of the computing resource allocation variable and the task scheduling variable comprises:
optimizing the target: minimizing total latency of computational tasks
Figure FDA0002744710000000011
Wherein:
Figure FDA0002744710000000012
Figure FDA0002744710000000013
the limiting conditions are as follows:
Figure FDA0002744710000000014
wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all the edge servers, N is the set of all the computing tasks, xnsIdentification variables for whether to migrate task n to edge server s, for the scheme of task scheduling, fnsThe computing resources allocated to the edge server s with task n, the solution to the computing resource allocation,
Figure FDA0002744710000000015
total delay for migrating task n to edge server s processingThe latest time of the day is,
Figure FDA0002744710000000016
the time required to upload task n to the edge server,
Figure FDA0002744710000000017
the time required to download the results of the computation of task n from the edge server s to the user device,
Figure FDA0002744710000000018
for the total delay of the local processing of task n, αnIs the input data size, beta, of task nnFor the size of the output data of task n,
Figure FDA0002744710000000019
for the upstream bandwidth of the edge server s,
Figure FDA00027447100000000110
downstream bandwidth, γ, for edge server snsIs the signal-to-noise ratio, γ ', of the uplink between user device n and edge server s'nsFor the signal-to-noise ratio, w, of the downlink between the user equipment n and the edge server snIn order to be a computational load for the task n,
Figure FDA00027447100000000111
in order to be the computing power of the user equipment n,
Figure FDA00027447100000000112
is the computing power of the edge server s.
3. The method as claimed in claim 1, wherein the converting is: the optimization problem of the minimization of the computing resource allocation variables and the task scheduling variables is expressed as an optimization problem only containing the task scheduling variables, namely:
minimization
Figure FDA0002744710000000021
The limiting conditions are as follows:
Figure FDA0002744710000000022
constructing a task scheduling set A and a task scheduling variable xnsThe relationship of (1): a { (n, s) | xns1, N belongs to N, S belongs to S, the objective function is marked as g (A), and then the variable x is markednsIs restricted by
Figure FDA0002744710000000023
Into constraints on set A
Figure FDA0002744710000000024
Wherein: 1(n，s)∈ATo indicate a function, the function value is 1 when (n, s) ∈ A holds, otherwise it is 0, and this constraint is a pseudo-matrix constraint, denoted τ.
4. The method as claimed in claim 1, wherein the aggregation function optimization problem only regarding task scheduling variables is solved to obtain an optimal closed-form solution of the allocation of the computing resources as
Figure FDA0002744710000000025
Figure FDA0002744710000000026
Wherein:
Figure FDA0002744710000000027
indicating that the edge server s allocates the computing resource of task n for optimal computing resource allocation when the task scheduling variable is X, XnsIdentification variable, w, for whether to migrate task n to edge server snIs the computational load of task n.
5. According to claim 1The method for scheduling the optimization task in the mobile edge calculation is characterized in that the linear approximation function of the objective function is
Figure FDA0002744710000000028
The primary scheduling policy obtained according to the constructed linear approximation function of the objective function specifically includes:
i) initializing a set A, taking a full set from a gamma as an empty set
Figure FDA0002744710000000029
Wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all the edge servers, N is the set of all the computing tasks, and the element (N, S) in the set is to migrate the computing task N to the edge server S;
ii) repeating steps iii, iv, v when Γ is not equal to Ω, otherwise performing step vi;
iii) taking the set of singletons
Figure FDA00027447100000000210
Wherein: v is an element in the set omega \ Γ, argmax is an operation of taking the single-element set which enables the function value to be maximum, and e is an element in the single-element set which enables the function value to be maximum;
iv) updating the set A to be A { e }, when A { e }, [ tau ];
v) the update set Γ is Γ { v };
vi) for each element (n, s) in the set A, the task n is migrated to the edge server s.
6. The method as claimed in claim 1, wherein the user's computing power is weaker than the server's computing power by:
Figure FDA00027447100000000211
wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all edge servers, N is all countersThe set of computing tasks is computed by a computer,
Figure FDA0002744710000000031
the time required to upload task n to the edge server,
Figure FDA0002744710000000032
the time required for downloading the result of the computation of task n from the edge server s to the user equipment, wn is the amount of computation of task n,
Figure FDA0002744710000000033
in order to be the computing power of the user equipment n,
Figure FDA0002744710000000034
is the computing power of the edge server s.
7. The method as claimed in claim 1, wherein the sub-model approximation function of the objective function is
Figure FDA0002744710000000035
Figure FDA0002744710000000036
Wherein: n is the serial number of the computing task, S is the serial number of the edge server, S is the set of all the edge servers, N is the set of all the computing tasks,
Figure FDA0002744710000000037
the time required to upload task n to the edge server,
Figure FDA0002744710000000038
time required for downloading the result of the task n calculation from the edge server s to the user device, wnIn order to be a computational load for the task n,
Figure FDA0002744710000000039
in order to be the computing power of the user equipment n,
Figure FDA00027447100000000310
for the computing power of the edge server s, 1(n，s)∈AIndicating a function, the value of (n, s) ∈ A is 1, otherwise the value is 0.
8. The method for scheduling optimization tasks in mobile edge computing according to claim 1 or 7, wherein the secondary scheduling strategy comprising two-step greedy is obtained according to the constructed sub-model approximation function of the objective function;
the two-step greedy specifically includes selecting an element corresponding to a scheduling policy which maximizes an objective function in a greedy process of the first step, selecting an element corresponding to a scheduling policy which maximizes an edge value of the objective function in a greedy process of the second step, and taking a union of sets obtained in the two steps as a result of a task scheduling policy of the algorithm, and the specific steps include:
i) initializing set A1And A2And is provided with a gamma1，Γ2For the empty collection, take the complete collection
Figure FDA00027447100000000311
ii) when r is1If not, repeating the steps iii, iv and v, otherwise, executing the step vi;
iii) taking the set of singletons
Figure FDA00027447100000000312
Wherein: v is an element in the set omega \ Γ, argmax is an operation of taking the single-element set which enables the function value to be maximum, and e is an element in the single-element set which enables the function value to be maximum;
iv) when A1E ∈ τ and | A1When U { e } | is less than or equal to k, updating the set A1Is A1∪{e}；
v) updating the set Γ1Is gamma1∪{e}；
vi) when set Γ2Is not equal to omega \ A1Then, omega \ A1Is set to omega and A1Repeating steps vii, viii, ix, otherwise executing step x;
vii) taking a set of singletons
Figure FDA00027447100000000313
Wherein: v is an element in the set omega \ Γ, e represents argmax represents an operation of taking the set of single elements that make the function value maximum, and e is an element in the set of single elements that make the function value maximum;
viii) when A1∪A2When the [ e ] belongs to [ tau ], updating the set A2Is A2And E, otherwise, skipping the step;
ix) update set Γ2Is gamma2∪{e}；
x) taking A ═ A1∪A2And for each element (n, s) in a, migrate task n to edge server s.
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