CN112101728A - Energy optimization distribution method for mobile edge computing system - Google Patents

Energy optimization distribution method for mobile edge computing system Download PDF

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Publication number
CN112101728A
CN112101728A CN202010829335.XA CN202010829335A CN112101728A CN 112101728 A CN112101728 A CN 112101728A CN 202010829335 A CN202010829335 A CN 202010829335A CN 112101728 A CN112101728 A CN 112101728A
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energy
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task
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林伟伟
许银海
黄天晟
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South China University of Technology SCUT
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06312—Adjustment or analysis of established resource schedule, e.g. resource or task levelling, or dynamic rescheduling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/06—Electricity, gas or water supply
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S10/00—Systems supporting electrical power generation, transmission or distribution
    • Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications

Abstract

The invention discloses an energy optimization distribution method of a mobile edge computing system, which comprises the following steps: assuming that the time intervals of the arrival events are exponentially distributed, converting the MEC system energy distribution problem into a Markov decision model of the contact time; the Markov decision model comprises six elements of a system state s, a system action a, an award r (s, a), a strategy pi, a value function V(s) and a state transition probability p (s' | s, a); obtaining the exact state transition probability, and solving the Model by adopting a Model-Based method; and solving the accurate solution of each state value function by a value iteration method to obtain the optimal strategy of energy distribution. The invention relates to a mobile edge computing system energy allocation problem, which is converted into a continuous time Markov decision model, and an accurate solution of each state value function is solved by a value iteration method, so that an optimal strategy of energy allocation is found, and long-term sustainable computation of an MEC system is realized.

Description

Energy optimization distribution method for mobile edge computing system
Technical Field
The invention belongs to the technical field of energy distribution of a mobile edge computing system, and particularly relates to an energy optimization distribution method of the mobile edge computing system.
Background
With the wide popularization of internet technology and the vigorous development of mobile communication technology, the mobile internet has become an important part of people's daily life. Smart mobile terminals such as smart phones, tablet computers, smart wearable devices, and in-vehicle mobile devices have gradually replaced personal computers, and have become main tools used by people in work, study, social contact, and entertainment. In order to solve the problem of energy limitation of mobile devices, a new network architecture, Mobile Edge Computing (MEC), is proposed. According to the ETSI definition, the moving edge is calculated as: and providing a cloud computing function and an IT service environment required by an application opener and a content service provider at the edge of the network so as to reduce the time delay of network operation and service delivery and improve the user experience.
Mobile Edge Computing (MEC) requires the distribution of millions of small servers in a city, with too much power overhead to rely on traditional power grid facilities. Due to advances in Energy Harvesting (EH) technology, renewable energy sources such as solar radiation and wind energy have become viable and promising power sources for MEC systems. However, the attainment of these energy sources is highly random and therefore requires the storage of the collected energy sources in the MEC system cells. If there is not enough available energy, the system may not operate properly, and therefore, the energy usage plan calculated for each request may have a profound effect on the sustainable operation of the system. For example, if not enough energy is provided to handle the incoming request, the computation speed may not meet the user's demand. Conversely, if too much energy is allocated, the MEC system may miss several subsequent requests due to low battery power. Therefore, reasonable distribution of the energy of the MEC system is realized, and long-term sustainable energy calculation of the MEC system is guaranteed to become a new challenge.
Disclosure of Invention
The invention mainly aims to overcome the defects and shortcomings of the prior art and provides an energy optimization allocation method for a mobile edge computing system, which converts the energy allocation problem of the mobile edge computing system into a continuous-time Markov decision model and solves the accurate solution of each state value function by a value iteration method, thereby finding the optimal strategy of energy allocation and realizing the long-term sustainable calculation of an MEC system.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides an energy optimization distribution method of a mobile edge computing system, which comprises the following steps:
assuming that the time intervals of arrival events are exponentially distributed, converting the energy distribution problem of the mobile edge computing MEC system into a Markov decision model of the contact time; the MEC system comprises a scheduler, wherein the scheduler is used for judging whether the MEC system receives tasks or not and distributing virtual machines and energy sources for the received tasks; the Markov decision model comprises six elements of a system state s, a system action a, an award r (s, a), a strategy pi, a value function V(s) and a state transition probability p (s' | s, a); when a new arrival event arrives, the MEC system generates state transition, wherein the arrival event comprises a task arrival event, an energy arrival event and a task completion event; the probability of the state transition is the same as the probability of the occurrence of the next arrival event, and the value is determined by the ratio of the probability of the specific arrival event to the total events of the system arrival;
obtaining the exact state transition probability according to the state transition probabilities under different system states and different system action conditions, and solving the Model by adopting a Model-Based method;
and solving the accurate solution of each system state value function by a value iteration method to obtain the optimal strategy of energy distribution.
Further, the system state s is specifically represented as follows:
Figure BDA0002637350370000021
wherein b is the residual energy of the MEC system in the current system state and represents the number of the distributed running virtual machines,
Figure BDA0002637350370000022
representing the number of running virtual machines, k, allocated to a unit of energynRepresenting the amount of unit energy allocated to the virtual machine;
in any system state, the arrival event e satisfies:
Figure BDA0002637350370000031
wherein A isr、AeAnd
Figure BDA0002637350370000032
respectively representing a task arrival event, an energy arrival event and a task completion event.
Further, when a task arrival event arrives, i.e., e ═ arIf the system action a is equal to 0, the MEC scheduler refuses the task arrival event, and if the system action a is equal to knThen it means that the MEC system assigns a value k to the arriving task requestnA virtual machine of a unit energy; bringing q for the MEC system each time when the energy arrival event arriveseJ energy source; when other events arrive, the MEC scheduler does not perform any substantive operation.
Further, the system award r (s, a) is specifically expressed as follows:
r(s,a)＝g(s,a)-c(s,a)τ(s,a)
wherein g (s, a) represents a direct reward, c (s, a) and τ (s, a) represent cost rate and dwell time between the current task arrival event and the next task arrival event, respectively, and c (s, a) τ (s, a) represents the added delay of all computation requests between two successive arrival event time points;
the direct prize g (s, a) is specifically expressed as follows:
Figure BDA0002637350370000033
wherein U represents the local computation time to the task;
the cost rate c (s, a) is specifically expressed as follows:
Figure BDA0002637350370000034
wherein the content of the first and second substances,
Figure BDA0002637350370000035
representing the number of running virtual machines in the MEC system, the number of virtual machines not changing between event arrivals; 1{a＞0}Is shown in system state a>0 is equal to 1, otherwise 0.
Further, the task arrival event and the energy arrival event are respectively subject to a parameter lambdar、λePoisson distribution of (a); the interval time obeying parameter of the task arrival event and the task completion event is muc(kn) Index distribution of (d), muc(kn) Specifically, the following are shown:
Figure BDA0002637350370000041
where φ represents the average data size of the offload request, v represents the number of CPU cycles required to compute a bit of offload request data, and κ represents the effective switch capacitance of the MEC system processor.
Further, the residence time between arrival events follows an exponential distribution with a parameter β (s, a), which represents the sum of the occurrence rates of all possible events, and is specifically expressed as follows:
Figure BDA0002637350370000042
wherein λ isr、λeRespectively representing probability expectations of task arrival events and energy arrival events;
the probability density function of the dwell time between arrival events is specifically as follows:
Figure BDA0002637350370000043
when the MEC scheduler accepts a task arrival event, a new virtual machine needs to be opened, i.e.
Figure BDA0002637350370000044
And is formed byIt is assigned kjThe energy source of (2), when the energy source is distributed kjBecomes the task completion rate of the virtual machine
Figure BDA0002637350370000045
When a task completion event is reached, i.e.
Figure BDA0002637350370000046
When an event occurs, the system will shut down the virtual machine running this task, at which point k is assignedjBecomes (σ) the task completion rate of the virtual machinekj-1)μc(kj)。
Further, the obtaining of the exact state transition probability specifically includes:
the state transition probabilities under different system states and different system operating conditions are as follows:
when in use
Figure BDA0002637350370000047
When the temperature of the water is higher than the set temperature,
Figure BDA0002637350370000051
wherein s' represents the next system state;
when in use
Figure BDA0002637350370000052
In time, namely, the new arriving event is the energy arriving event, the probability of occurrence of the three arriving events will not change:
Figure BDA0002637350370000053
wherein the content of the first and second substances,
Figure BDA0002637350370000054
equivalent to min (b +1, b)m)；
When in use
Figure BDA0002637350370000055
When the temperature of the water is higher than the set temperature,
Figure BDA0002637350370000056
further, the reward function adopts a discount model, and the prospective discount reward is derived as follows:
Figure BDA0002637350370000061
where η is the discount factor.
Further, when the fixed policy pi is followed, the discount reward in an infinite time range is obtained, which is specifically expressed as follows:
Figure BDA0002637350370000062
wherein, tpRepresents the start time, s, of the p-th action of the MEC systempRepresents the system state at the p-th action of the MEC system,
Figure BDA0002637350370000063
is shown in system state spThe reward of following the policy pi is then,
Figure BDA0002637350370000064
is shown at tpFollowing the system actions taken by the policy π time MEC system, the rewards obtained all require a discount function
Figure BDA0002637350370000065
The continuous-time markov model target is a strategy for achieving a maximum reward, expressed as follows:
Figure BDA0002637350370000066
wherein, pi*Representing an optimal strategy;
Figure BDA0002637350370000067
for all system states S ∈ S, the bellman optimal equation is satisfied, which is as follows:
Figure BDA0002637350370000068
wherein the content of the first and second substances,
Figure BDA0002637350370000069
further, the value iteration specifically includes the following steps:
initialization, for all system states S ∈ S, q ═ 0, Vq(s)＝0；
The update value function, for the system state S e S,
Figure BDA0002637350370000071
q ═ q +1, if | Vq-Vq-1Ii >, return to the update value function step;
and searching an optimal energy distribution strategy, and for all system states S E S,
Figure BDA0002637350370000072
compared with the prior art, the invention has the following advantages and beneficial effects:
the invention converts the energy distribution problem of the mobile edge computing system into a Markov decision model of continuous time by assuming that the time interval of the arrival event is exponentially distributed, solves the accurate solution of each state value function by adopting a model-based method of value iteration, finds the optimal strategy of energy distribution, solves the problems of task loss, unsatisfied delay and the like of the mobile edge computing system, and realizes the long-term sustainable computation of the MEC system.
Drawings
FIG. 1 is a simplified schematic diagram of an energy allocation model of a mobile edge computing system in accordance with the method of the present invention;
FIG. 2 is a median iterative solution algorithm of the method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Examples
Three alternative energy scores for incoming requests are considered-1, 2 and 3 energy units. The MEC system starts from its initial state (a battery containing one energy unit) and receives an additional energy unit upon encountering an energy arrival event. A task request then arrives at the MEC system, which decides to reserve 1 energy unit for the task request, with system action a being 1. Accordingly, the battery charge will be reduced by 1, the number of currently operating 1 unit of energy allocation VM (recorded as α)1) Jump to 1. After receiving another unit of energy, the computation in the VM has been completed (task completion event arrives), then α1A jump to 0 will occur. The last event is another task arrival event, but this time the MEC system schedules 2 units of energy allocation for it, i.e. a-2.
As shown in fig. 1, the invention relates to a method for optimizing and allocating energy of a mobile edge computing system, comprising the following steps:
s1, assuming that the time intervals of arriving events are distributed exponentially, converting the MEC system energy allocation problem into a markov decision model of continuous events, where the model includes six elements, namely a system state S, a system action a, a reward r (S, a), a policy pi, a value function v (S), and a state transition probability p (S' | S, a):
A) a system state s, said system state s being represented as follows:
Figure BDA0002637350370000081
b is the remaining energy of the MEC system in the current state,
Figure BDA0002637350370000082
representing the number of allocated running virtual machines, e representing an arrival event, the arrival of a new event generating a system state transition, the arrival event comprising a task arrival event, an energy arrival event and a task completion event.
In any system state, the arrival event e satisfies:
Figure BDA0002637350370000083
wherein A isr、AeAnd
Figure BDA0002637350370000084
respectively representing a task arrival event, an energy arrival event and a task completion event.
In this embodiment, the MEC system includes an MEC scheduler.
B) System actions a,; when the task arrives, i.e. e ═ ArIf the system action a is equal to 0, the MEC scheduler refuses the task arrival event, and if the system action a is equal to knThen it means that the MEC system assigns a value k to the arriving task requestnA virtual machine of a unit energy;
in this embodiment, it is assumed that the energy arrival event arrives, bringing 1 unit (q) for the MEC system each timeeJ) The energy source of (1). When other events arrive, the MEC scheduler does not perform any substantive operation.
C) A system reward r (s, a), which is specifically expressed as follows:
r(s,a)＝g(s,a)-c(s,a)τ(s,a)
wherein g (s, a) represents a direct reward, c (s, a) and τ (s, a) represent the cost rate and residence time between the current task arrival event and the next task arrival event, respectively, and c (s, a) τ (s, a) represents the added delay of all computation requests within two consecutive arrival event time points;
the direct prize g (s, a) is specifically expressed as follows:
Figure BDA0002637350370000091
wherein U represents the local computation time to the task; in other words, using MEC calculations, the MEC system will save U units of time for the requester.
In this embodiment, the different local computation times caused by the different capacities of the local mobile devices are not taken into account, i.e. the immediate payback expectation for each request is the same.
The cost rate c (s, a) is specifically expressed as follows:
Figure BDA0002637350370000092
wherein the content of the first and second substances,
Figure BDA0002637350370000093
representing the number of running virtual machines in the MEC server, which does not change between event arrivals; 1{a＞0}Is shown in system a>0 is equal to 1, otherwise 0.
In this embodiment, the sum of the computation service delay times of the current task request will be increased by c for each secondtSecond, wherein ctThe total number of the existing virtual machines.
The task arrival event and the energy arrival event are respectively obeyed with a parameter lambdar、λePoisson distribution of (a); the interval time obeying parameter of the task arrival event and the task completion event is muc(kn) Index distribution of (d), muc(kn) Specifically, the following are shown:
Figure BDA0002637350370000101
where φ represents the average data size of the offload request, v represents the number of CPU cycles required to compute data for the offload request, and κ represents the effective switched capacitance of the MEC system processor.
The residence time between arrival events obeys an exponential distribution with a parameter β (s, a) representing the sum of the occurrence rates of the possible events, as follows:
Figure BDA0002637350370000102
wherein λ isr、λeRespectively representing probability expectations of task arrival events and energy arrival events;
the probability density function of the dwell time between arrival events is specifically as follows:
Figure BDA0002637350370000103
in this embodiment, when the MEC scheduler accepts a task arrival event, a new virtual machine needs to be opened, i.e., a new virtual machine is opened
Figure BDA0002637350370000104
And assign k theretojThe energy source of (2), when the energy source is distributed kjBecomes the task completion rate of the virtual machine
Figure BDA0002637350370000105
When a task completion event is reached, i.e.
Figure BDA0002637350370000106
When an event occurs, the system will shut down the virtual machine running this task, at which point k is assignedjBecomes (σ) the task completion rate of the virtual machinekj-1)μc(kj)。
The reward function adopts a discount model, and the expected discount reward is deduced as follows:
Figure BDA0002637350370000107
Figure BDA0002637350370000111
where η is the discount factor. In the present embodiment, e is in the form of an index-ηtThe expected value can be simplified as a discount compared to etat.
D) And a strategy pi, wherein when the fixed strategy pi is followed, discount rewards in an infinite time range are obtained, and the strategy pi is specifically expressed as follows:
Figure BDA0002637350370000112
wherein, tpRepresents the start time, s, of the p-th action of the systempIndicating the state of the system at the p-th action of the system,
Figure BDA0002637350370000113
is shown in state spNext, following the reward of the policy pi,
Figure BDA0002637350370000114
is shown at tpFollowing the actions taken by the policy pi system, the reward obtained for each action requires a discount function
Figure BDA0002637350370000115
The continuous-time markov model target is a strategy for achieving a maximum reward, expressed as follows:
Figure BDA0002637350370000116
wherein, pi*Representing an optimal strategy; to simplify the notation, in the present embodiment, let
Figure BDA0002637350370000117
E) For all system states S ∈ S, the bellman optimal equation is satisfied, and the value function v (S) is as follows:
Figure BDA0002637350370000118
wherein the content of the first and second substances,
Figure BDA0002637350370000119
s2, obtaining the exact state transition probability, and solving the Model by adopting a Model-Based method, wherein the method specifically comprises the following steps:
F) probability of state transition p (s' | s, a)
The state transition probabilities under different system states and different system operating conditions are as follows:
when in use
Figure BDA00026373503700001110
When the temperature of the water is higher than the set temperature,
Figure BDA0002637350370000121
wherein s' represents the next system state;
when in use
Figure BDA0002637350370000122
In time, namely, the arrival event is an energy arrival event, the occurrence probability of the three events will not change:
Figure BDA0002637350370000123
wherein the content of the first and second substances,
Figure BDA0002637350370000124
equivalent to min (b +1, b)m)；
When in use
Figure BDA0002637350370000125
When the temperature of the water is higher than the set temperature,
Figure BDA0002637350370000126
s3, solving the accurate solution of each system state value function through a value iteration method to find out the optimal energy distribution scheme, which specifically comprises the following steps:
s31, initializing, wherein S e S, q is 0, V for all system statesq(s)＝0；
S32, updating the value function, for the system state S e S,
Figure BDA0002637350370000131
s33, q ═ q +1, if | Vq-Vq-1Ii >, return to step S32;
s34, finding the optimal energy distribution strategy, for all system states S belonging to S,
Figure BDA0002637350370000132
it should also be noted that in this specification, terms such as "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A method for optimizing energy distribution of a mobile edge computing system, comprising the steps of:
assuming that the time intervals of arrival events are exponentially distributed, converting the energy distribution problem of the mobile edge computing MEC system into a Markov decision model of the contact time; the MEC system comprises a scheduler, wherein the scheduler is used for judging whether the MEC system receives tasks or not and distributing virtual machines and energy sources for the received tasks; the Markov decision model comprises six elements of a system state s, a system action a, an award r (s, a), a strategy pi, a value function V(s) and a state transition probability p (s' | s, a); when a new arrival event arrives, the MEC system generates state transition, wherein the arrival event comprises a task arrival event, an energy arrival event and a task completion event; the probability of the state transition is the same as the probability of the occurrence of the next arrival event, and the value is determined by the ratio of the probability of the specific arrival event to the total events of the system arrival;
obtaining the exact state transition probability according to the state transition probabilities under different system states and different system action conditions, and solving the Model by adopting a Model-Based method;
and solving the accurate solution of each system state value function by a value iteration method to obtain the optimal strategy of energy distribution.
2. The method according to claim 1, wherein the system state s is specifically expressed as follows:
Figure FDA0002637350360000011
wherein b is the residual energy of the MEC system in the current system state and represents the number of the distributed running virtual machines,
Figure FDA0002637350360000012
representing the number of running virtual machines, k, allocated to a unit of energynRepresenting the amount of unit energy allocated to the virtual machine;
in any system state, the arrival event e satisfies:
Figure FDA0002637350360000013
wherein A isr、AeAnd
Figure FDA0002637350360000014
respectively representing a task arrival event, an energy arrival event and a task completion event.
3. The method of claim 2, wherein the task-arrival event is e-A when the task-arrival event arrivesrIf the system action a is equal to 0, the MEC scheduler refuses the task arrival event, and if the system action a is equal to knThen it means that the MEC system assigns a value k to the arriving task requestnA virtual machine of a unit energy; bringing q for the MEC system each time when the energy arrival event arriveseJ energy source; when other events arrive, the MEC scheduler does not perform any substantive operation.
4. The method of claim 2, wherein the system reward r (s, a) is expressed as follows:
r(s，a)＝g(s，a)-c(s，a)τ(s，a)
wherein g (s, a) represents a direct reward, c (s, a) and τ (s, a) represent cost rate and dwell time between the current task arrival event and the next task arrival event, respectively, and c (s, a) τ (s, a) represents the added delay of all computation requests between two successive arrival event time points;
the direct prize g (s, a) is specifically expressed as follows:
Figure FDA0002637350360000021
wherein U represents the local computation time to the task;
the cost rate c (s, a) is specifically expressed as follows:
Figure FDA0002637350360000022
wherein the content of the first and second substances,
Figure FDA0002637350360000023
representing the number of running virtual machines in the MEC system, the number of virtual machines not changing between event arrivals; 1{a＞0}Indicating a 1 when system state a > 0, otherwise 0.
5. The method as claimed in claim 3, wherein the task arrival event and the energy arrival event are respectively subject to a parameter λr、λePoisson distribution of (a); the interval time obeying parameter of the task arrival event and the task completion event is muc(kn) Index distribution of (d), muc(kn) Specifically, the following are shown:
Figure FDA0002637350360000024
where φ represents the average data size of the offload requests, v represents the number of CPU cycles required to compute a bit of offload request data, and K represents the effective switched capacitance of the MEC system processor.
6. The method according to claim 4 or 5, wherein the residence time between arrival events is subject to an exponential distribution with a parameter β (s, a), where β (s, a) represents the sum of the occurrence rates of all possible events, and is specifically expressed as follows:
Figure FDA0002637350360000031
wherein λ isr、λeRespectively representing probability expectations of task arrival events and energy arrival events;
the probability density function of the dwell time between arrival events is specifically as follows:
Figure FDA0002637350360000032
when the MEC scheduler accepts a task arrival event, a new virtual machine needs to be opened, i.e.
Figure FDA0002637350360000033
And assign k theretojThe energy source of (2), when the energy source is distributed kjBecomes the task completion rate of the virtual machine
Figure FDA0002637350360000034
When a task completion event is reached, i.e.
Figure FDA0002637350360000035
When an event occurs, the system will shut down the virtual machine running this task, at which point k is assignedjBecomes (σ) the task completion rate of the virtual machinekj-1)μc(kj)。
7. The method according to claim 6, wherein the obtaining the exact state transition probability specifically comprises:
the state transition probabilities under different system states and different system operating conditions are as follows:
when in use
Figure FDA0002637350360000036
When the temperature of the water is higher than the set temperature,
Figure FDA0002637350360000041
wherein s' represents the next system state;
when in use
Figure FDA0002637350360000042
In time, namely, the new arriving event is the energy arriving event, the probability of occurrence of the three arriving events will not change:
Figure FDA0002637350360000043
wherein the content of the first and second substances,
Figure FDA0002637350360000044
equivalent to min (b +1, b)m)；
When in use
Figure FDA0002637350360000045
When the temperature of the water is higher than the set temperature,
Figure FDA0002637350360000046
8. the method of claim 6, wherein the reward function employs a discount model, and the prospective discount reward is derived as follows:
Figure FDA0002637350360000051
where η is the discount factor.
9. The method according to claim 7 or 8, wherein when the fixed policy pi is followed, the discount reward within an infinite time range is obtained, which is specifically expressed as follows:
Figure FDA0002637350360000052
wherein, tpRepresents the start time of the p-th action of the MEC system, sp represents the system state of the MEC system at the p-th action,
Figure FDA0002637350360000053
is shown in system state spThe reward of following the policy pi is then,
Figure FDA0002637350360000054
is shown at tpFollowing the system actions taken by the policy π time MEC system, the rewards obtained all require a discount function
Figure FDA0002637350360000055
The continuous-time markov model target is a strategy for achieving a maximum reward, expressed as follows:
Figure FDA0002637350360000056
wherein, pi*Representing an optimal strategy;
Figure FDA0002637350360000057
for all system states S ∈ S, the bellman optimal equation is satisfied, which is as follows:
Figure FDA0002637350360000058
wherein the content of the first and second substances,
Figure FDA0002637350360000059
10. the method according to claim 9, wherein the value iteration comprises the following steps:
initialization, for all system states S ∈ S, q ═ 0, Vq(s)＝0；
The update value function, for the system state S e S,
Figure FDA0002637350360000061
q ═ q +1, if | | | Vq-Vq-1I >, return to the update value function step;
and searching an optimal energy distribution strategy, and for all system states S E S,
Figure FDA0002637350360000062
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