CN109413724B - MEC-based task unloading and resource allocation scheme - Google Patents

MEC-based task unloading and resource allocation scheme Download PDF

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CN109413724B
CN109413724B CN201811181211.4A CN201811181211A CN109413724B CN 109413724 B CN109413724 B CN 109413724B CN 201811181211 A CN201811181211 A CN 201811181211A CN 109413724 B CN109413724 B CN 109413724B
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李虎
张海波
陈善学
刘开健
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/02—Power saving arrangements
    • H04W52/0209—Power saving arrangements in terminal devices
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/53—Allocation or scheduling criteria for wireless resources based on regulatory allocation policies
    • 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
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

Mobile Edge Computing (MEC) has brought the advantages of low latency, low power consumption and high reliability by providing IT service environment and cloud computing capability at the edge of a mobile network, and thus has become a hot spot of future 5G research. A task unloading and resource allocation scheme based on MEC is developed and disclosed, and the task unloading and resource allocation scheme comprises a combined optimization problem of unloading decision and resource allocation; optimizing the unloading decision by using a coordinate descent method; the sub-channel allocation is carried out on the users by adopting an improved Hungarian algorithm and a greedy algorithm under the condition of meeting the user time delay; and converting the energy consumption minimization problem into a power minimization problem, and converting the energy consumption minimization problem into a convex optimization problem to obtain the optimal transmission power of the user. The invention can meet the requirements of different users on different time delays, can minimize the total energy consumption of the system and effectively improve the system performance.

Description

MEC-based task unloading and resource allocation scheme
Technical Field
The invention relates to the technical field of mobile edge computing and wireless communication, in particular to a task unloading and resource allocation scheme based on MEC.
Background
In recent years, with the continuous upgrading of mobile networks and intelligent mobile devices, the number of mobile internet users has been increasing explosively. Currently, fifth generation mobile communications (5G) face new challenges with explosive data traffic growth and coexistence with mass device connectivity. Meanwhile, the newly added service scenes of the 5G network, such as interactive motion sensing games, face recognition, unmanned driving, virtual reality, industrial internet of things communication and the like, have higher requirements on indexes such as time delay, energy consumption, reliability and the like, and in order to meet the corresponding development requirements brought by the high-speed development of the mobile internet, the future 5G communication needs to meet various performance requirements such as ultra-low time delay, ultra-low power consumption, ultra-high reliability, ultra-high density connection and the like, so that the wireless cellular network is required to have high-speed data transmission capacity in the future mobile communication, and the data is required to be processed by strong computing capacity.
At present, new services such as Augmented Reality (AR), online games, smart cities, and emerging internet of things industries are rapidly developing. However, the existing mobile devices have been unable to meet the requirements of these new internet and intelligent services for low latency, high complexity, and high reliability due to limited battery power, insufficient computing power, and other factors, thereby affecting user experience. Although mobile cloud computing meets the performance requirements of users for the services to a certain extent, the mobile cloud computing allows a mobile device to partially or completely offload locally complex and large amount of computing tasks to a cloud data center located in a core network for execution, so that the problem of resource shortage of the mobile device is solved, and the energy consumption of the device during local execution of the tasks is saved to a certain extent. However, when a large amount of services need to be offloaded to a cloud data center located in a core network, backhaul link resources are consumed, backhaul congestion is caused when a large amount of services need to be offloaded to a cloud server, and extra delay overhead is generated, so that in a future emerging 5G scenario, a single cloud computing mode cannot meet requirements of services for low delay and high reliability as much as possible. Recently, Mobile Edge Computing (MEC) has been proposed as one of the key technologies of 5G, and MEC systems allow mobile devices to offload computing tasks to network edge nodes, such as base stations, wireless access points, etc., through a wireless cellular network. Compared with the traditional mobile cloud computing, the MEC deploys the edge server at the edge of the radio access network closer to the user end, so that the distance between the cloud computing server and the mobile device is greatly shortened. Therefore, the backhaul congestion can be greatly reduced, and the time delay overhead of the user is also reduced. In addition, the edge server can provide strong computing processing capacity for users, and therefore task computing time delay is greatly shortened. Secondly, under the condition that the energy of the equipment battery is limited, the network architecture of the MEC shortens the distance between the edge server and the mobile equipment, greatly reduces the energy consumed by wireless transmission during unloading, and greatly prolongs the service cycle of the equipment of the Internet of things. Research results show that the MEC can prolong the service life of the equipment battery by 30-50% for different AR equipment.
Meanwhile, network densification has been widely accepted by the industry and academia as one of the main means for meeting the 1000-fold challenge of capacity increase of the future 5G wireless network. Future 5G network needs to support dozens of Tbit s-1·km-2Traffic density of greater than a million connections per square kilometer. The network is densified mainly by densely laying micro-cells, pico-cells, home base stations, etc. having low power and low cost. The method can shorten the distance between the user and various base stations, thereby realizing the improvement of the spatial multiplexing rate of the spectrum resources, providing larger bandwidth and higher data rate for the users in hot spot areas, medium and small enterprises and houses, ensuring the user experience, and achieving the aims of improving the network capacity and the like. Compared with the traditional macro cellular network architecture, the ultra-dense networking network architecture can improve coverage, increase system capacity and increase user satisfaction.
Therefore, in order to meet the new service requirements of future 5G ultra-low time delay, ultra-low power consumption, ultra-high reliability and ultra-high density connection, ultra-dense networking and mobile edge computing will be indispensable key technologies of future 5G.
Disclosure of Invention
Aiming at the defects of the prior art, the invention considers the calculation unloading in the MEC scene of the intensive networking, considers the total energy consumption of the system aiming at the influence of the unloading decision and the interference in the intensive networking on the system performance, proposes the combined solution problem of the unloading decision and the resource allocation to optimize the energy consumption of the system, and minimizes the total energy consumption of the system under the different time delay constraint conditions of different users. The invention relates to a task unloading and resource allocation scheme based on MEC, which comprises the following steps:
step 101: formulating a joint optimization problem of unloading decision and resource allocation;
step 102: optimizing the unloading decision by using a coordinate descent method;
step 103: the sub-channel allocation is carried out on the users by adopting an improved Hungarian algorithm and a greedy algorithm;
step 104: converting the energy consumption minimization problem into a power minimization problem, and converting the energy consumption minimization problem into a convex optimization problem to obtain the optimal sending power of a user;
preferably, the formulating the joint optimization problem of the offloading decision and the resource allocation comprises: consider a 5G heterogeneous MEC network consisting of one macro base station and N Small Base Stations (SBS). MEC servers are deployed at the edge of heterogeneous networks and can perform multiple compute-intensive tasks simultaneously. In order to multiplex the spectrum, it is considered that SBS are deployed in the same frequency manner in this heterogeneous network and are connected with a macro base station in a wired manner, the frequency band of each SBS is divided into K orthogonal sub-channels, where K {1,2, …, K } represents a set of sub-channels, each user in the same cell uses the orthogonal sub-channels, and users in different cells can multiplex the same sub-channels, so that users in different cells can interfere with each other. For ease of analysis, we consider here the case where there are only 1 user per SBS, defining N ═ {1, …, N } to represent the set of all users. In the network, each user n is considered to have a task which is computationally intensive and sensitive to delay to be completed, and the user can select local execution or uninstall to the MEC for execution according to the current network state and the requirement of the user. Definition anE {0,1} is the user's offload decision, with 0 representing the user's choice for local execution and 1 representing the user's choice for offload to MEC execution. Therefore, we use a ═ a1,...,aNIndicates all users' offload decisions;
when a user selects an unloading task, considering the interference of an adjacent SBS user in uplink transmission, and when a user n allocates a sub-channel k for data transmission, the signal-to-interference-and-noise ratio of the user n on the sub-channel k is as follows:
Figure BDA0001825002250000041
calculating the transmission rate of the user n on the subchannel k as follows:
Figure BDA0001825002250000042
the total rate of uplink transmission when the user n unloads the task is as follows:
Figure BDA0001825002250000043
where, B denotes a sub-channel bandwidth,
Figure BDA0001825002250000044
is a binary variable, if subchannel k is assigned to user n
Figure BDA0001825002250000045
Otherwise, the reverse is carried out
Figure BDA0001825002250000046
Figure BDA0001825002250000047
And
Figure BDA0001825002250000048
respectively representing the transmit power of users n and m on subchannel k,
Figure BDA0001825002250000049
and
Figure BDA00018250022500000410
respectively represent SBSnUser n and SBSmUser m to SBSn channel gain, ω0Representing the background noise power.
Consider that each user n has a delay-sensitive computational task
Figure BDA00018250022500000411
wnRepresenting the CPU cycles required to compute the task, dnRepresenting the size of the input dataThe program code, including the program code and the entered parameters,
Figure BDA00018250022500000412
representing the maximum delay that the user can tolerate. We discuss the computational models of energy consumption and latency for local execution and offloading to MEC execution below.
(1) When the user selects local execution, the computing task will be computed on each user device
Figure BDA0001825002250000051
Representing the computing power of the user equipment, the locally computed delay is then:
Figure BDA0001825002250000052
the local computing energy consumption is:
Figure BDA0001825002250000053
the size of the k value depends on the chip structure of the mobile device, where we take k to 10(-26). Energy consumption with user computing power in view of local computing
Figure BDA0001825002250000054
May be increased, the computing power of the user may be minimized locally by dynamically adjusting the computing power of the user through a Dynamic Voltage Scaling (DVS) technique. Thus, under the time delay constraint, the optimal computing power is distributed in local computing
Figure BDA0001825002250000055
Can be expressed as:
Figure BDA0001825002250000056
wherein the content of the first and second substances,
Figure BDA0001825002250000057
representing the maximum computing power of user n.
(2) When the user selects to unload the task for calculation, the user equipment is accessed to the corresponding SBS through the wireless network to unload the task to the MEC for calculation. For a user unloading a task, corresponding transmission delay and energy consumption are generated when the task is transmitted to the MEC in an uplink mode through a wireless network, and according to a communication model, the uplink transmission delay when the user n unloads the task is obtained as follows:
Figure BDA0001825002250000058
when a computing task is offloaded to the MEC, the MEC will allocate certain computing resources to process the task, using fcRepresenting the computing speed of the MEC allocation, here we consider that the computing speed of the MEC allocation to each user during the task execution is fixed, and then the time delay of the MEC executing the task is:
Figure BDA0001825002250000059
the total energy consumption of the user in transmitting the calculation task is:
Figure BDA0001825002250000061
wherein
Figure BDA0001825002250000062
Represents the total transmit power of the user;
Figure BDA0001825002250000063
representing the circuit power consumption in the user idle state.
Each user device will evaluate the locally calculated costs during task offloading and then report to the MEC. At the same time, the MEC will also evaluate the cost of each user device when it is off-loaded. The MEC then makes a corresponding offloading decision by comparing the local and offloading costs, the offloading decision being expressed as:
Figure BDA0001825002250000064
here we use NcIndicating the number of users offloaded, by NcRepresenting an offloaded set of users, the number of locally computed users is N-Nc。
Considering the latency requirements and limited battery power of users, we will minimize the total energy consumption of users by optimizing the offloading decision a and the subchannel allocation C and the power allocation P, we give the objective function that we need to optimize:
Figure BDA0001825002250000065
Figure BDA0001825002250000066
Figure BDA0001825002250000067
Figure BDA0001825002250000068
Figure BDA0001825002250000069
Figure BDA00018250022500000610
wherein the content of the first and second substances,
Figure BDA00018250022500000611
and
Figure BDA00018250022500000612
respectively representing the latency of user n in local and offload computations,
Figure BDA00018250022500000613
representing the maximum delay that can be accepted by user n,
Figure BDA00018250022500000614
indicating the case of the channel assignment and,
Figure BDA00018250022500000615
indicating that the kth sub-channel is assigned to the nth user,
Figure BDA00018250022500000616
it means that the k-th sub-channel is not allocated,
Figure BDA00018250022500000617
indicating the transmission power of the nth user on the kth sub-channel, C1 indicating the maximum delay requirement that the user can tolerate when calculating the task, C2 indicating that the transmission power of the user cannot be greater than its maximum transmission power, C3 indicating that the transmission power on each sub-channel is non-negative, C4 indicating that the allocation status of the channel is present, and C5 indicating that the offloading decision is a binary variable.
Preferably, the optimizing the unloading decision by using the coordinate descent method comprises: a ═ a1,a2,...,aN]Representing offload decisions for all users, given an initial offload decision A0Is a full 1 matrix, Al-1Represents the unloading decision at the l-1(l 1, 2..) iteration, corresponding to V (a)l-1) Indicating a decision at a given offload as al-1Optimal value of the time objective function, defining
Figure BDA0001825002250000078
For the benefit obtained after changing the current unload decision at the first iteration, then
Figure BDA0001825002250000079
Wherein A isl-1(n) represents the offload decision after user n changes the current decision, and the update rule is as follows:
Figure BDA0001825002250000071
wherein the content of the first and second substances,
Figure BDA0001825002250000072
the modulo two addition method is shown.
Coordinate descent method with one variable a along each timenThe direction of the target function is continuously optimized, so that the local minimum value of the target function is found, the algorithm can be converged through finite iterations, and an optimal unloading decision is obtained. In the first iteration, we obtain the unload decision AlBy calculation, if the profit is obtained
Figure BDA0001825002250000073
Then
Figure BDA0001825002250000074
Wherein the content of the first and second substances,
Figure BDA0001825002250000075
representing the user who gets the most profit in the l-th iteration.
Preferably, the sub-channel allocation is performed on the users by adopting an improved hungarian algorithm and a greedy algorithm: in the sub-channel allocation process, it is desirable to allocate the sub-channel with the best channel quality to the user each time to maximize the uplink transmission rate of the user. Meanwhile, it is desirable to allocate as few subchannels as possible to each user to avoid serious interference due to excessive frequency reuse of the users while satisfying the user delay requirement. Therefore, according to constraints C1 and C3, the sub-channel allocation problem for each user can be formulated as follows:
Figure BDA0001825002250000076
Figure BDA0001825002250000077
Figure BDA0001825002250000081
Figure BDA0001825002250000082
Figure BDA0001825002250000083
for the above sub-channel allocation problem, it can be equivalent to NcThe method comprises the following steps that firstly, an improved Hungarian algorithm is adopted to carry out channel matching for one time, then, a greedy algorithm is adopted to continuously allocate enough sub-channels to users under the condition of meeting the requirement of the lowest rate, and the algorithm steps are as follows:
1) constructing a benefit matrix required for a first iteration
Figure BDA0001825002250000084
2) If the number of users is greater than the number of sub-channels, i.e. NcIf > K, N is addedc-K virtual subchannels, changing the benefit matrix to Nc×NcSquare matrix, if the number of users is less than the number of sub-channels, i.e. NcIf < K, K-N is addedcAnd each user changes the benefit matrix into a K multiplied by K square matrix.
3) And performing maximum weight matching by adopting a Hungarian algorithm to obtain primary channel allocation.
4) Updating a subchannel allocation matrix according to the result of the allocated subchannels
Figure BDA0001825002250000085
And interference matrix
Figure BDA0001825002250000086
5) And checking whether each user meets the minimum rate requirement, and if so, terminating the algorithm. If not, updating the users needing to continuously distribute the sub-channels to be Nc'。
6) Checking channel allocation matrices
Figure BDA0001825002250000087
To Nc'each user in' uses a greedy algorithm to select the sub-channel with the least interference from the remaining sub-channels to allocate to the user.
7) Repeat steps 4) -6) until all users meet the minimum rate requirement or
Figure BDA0001825002250000088
The algorithm terminates.
Preferably, the sub-channel allocation is performed on the users by adopting an improved hungarian algorithm and a greedy algorithm: in the case of obtaining the offload decision and channel allocation, the original optimization objective is still a non-convex optimization problem, and considering that the constraint condition C1 of the objective function is the maximum delay constraint, the energy consumption minimization problem can be converted into the minimum power consumption problem under the delay constraint, so we convert the original problem into:
Figure BDA0001825002250000091
Figure BDA0001825002250000092
Figure BDA0001825002250000093
Figure BDA0001825002250000094
since the above optimization problem is still a non-convex optimization problem, we now let us make use of variable substitution
Figure BDA0001825002250000095
Then:
Figure BDA0001825002250000096
we therefore turn the optimization problem into:
Figure BDA0001825002250000097
Figure BDA0001825002250000098
Figure BDA0001825002250000099
Figure BDA00018250022500000910
Figure BDA00018250022500000911
here we change the original equation to the inequality constraint C3 in order to transform this non-convex problem into a convex problem, and this change does not affect the optimal solution of the problem, since the data rate of user n on subchannel k cannot be less than optimal
Figure BDA0001825002250000101
Drawings
FIG. 1 is a flowchart of a preferred embodiment of MEC-based task offload and resource allocation in a dense networking system according to the present invention;
FIG. 2 is a diagram of a MEC-based task offloading system model for use in dense networking;
FIG. 3 illustrates the variation of the number of users selected for offloading according to different time delay constraints as the number of users increases;
FIG. 4 is a comparison graph of the total energy consumption simulation of the system of the present invention as the number of users increases;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a preferred embodiment of the present invention for MEC-based task offloading and resource allocation scheme, the method comprising the steps of:
step 101: formulating a joint optimization problem of unloading decision and resource allocation;
step 102: optimizing the unloading decision by using a coordinate descent method;
step 103: the sub-channel allocation is carried out on the users by adopting an improved Hungarian algorithm and a greedy algorithm;
step 104: converting the energy consumption minimization problem into a power minimization problem, and converting the energy consumption minimization problem into a convex optimization problem to obtain the optimal sending power of a user;
fig. 2 is a diagram of a MEC-based task offloading system model in dense networking used in the present invention, including: considering a 5G heterogeneous MEC network composed of a macro base station and N Small Base Stations (SBS), a system model is shown in the figure. MEC servers are deployed at the edge of heterogeneous networks and can perform multiple compute-intensive tasks simultaneously. To multiplex the spectrum, we consider that SBS are deployed in the same frequency in this heterogeneous network and connected in a wired manner to the macro base station, and the frequency band of each SBS is divided into K orthogonal sub-channels, where K ═ 1,2, …, K represents a set of sub-channelsEach user in the same cell uses orthogonal sub-channels, and users in different cells can multiplex the same sub-channels, so that users in different cells can interfere with each other. For ease of analysis, we consider here the case where there are only 1 user per SBS, defining N ═ {1, …, N } to represent the set of all users. In the network, each user n is considered to have a task which is computationally intensive and sensitive to delay to be completed, and the user can select local execution or uninstall to the MEC for execution according to the current network state and the requirement of the user. Definition anE {0,1} is the user's offload decision, with 0 representing the user's choice for local execution and 1 representing the user's choice for offload to MEC execution. Therefore, we use a ═ a1,...,aNDenotes the offload decision of all users.
When a user selects an unloading task, considering the interference of an adjacent SBS user in uplink transmission, and when a user n allocates a sub-channel k for data transmission, the signal-to-interference-and-noise ratio of the user n on the sub-channel k is as follows:
Figure BDA0001825002250000111
calculating the transmission rate of the user n on the subchannel k as follows:
Figure BDA0001825002250000112
the total rate of uplink transmission when the user n unloads the task is as follows:
Figure BDA0001825002250000113
where, B denotes a sub-channel bandwidth,
Figure BDA0001825002250000114
is a binary variable, if subchannel k is assigned to user n
Figure BDA0001825002250000115
Otherwise, the reverse is carried out
Figure BDA0001825002250000116
Figure BDA0001825002250000117
And
Figure BDA0001825002250000118
respectively representing the transmit power of users n and m on subchannel k,
Figure BDA0001825002250000119
and
Figure BDA00018250022500001110
respectively represent SBSnUser n and SBSmUser m to SBSnChannel gain of (a) (. omega)0Representing the background noise power.
We consider that each user n has a delay-sensitive computational task
Figure BDA0001825002250000121
wnRepresenting the CPU cycles required to compute the task, dnRepresenting the size of the input data, including program code and parameters of the input,
Figure BDA0001825002250000122
representing the maximum delay that the user can tolerate. We discuss the computational models of energy consumption and latency for local execution and offloading to MEC execution below.
(1) When the user selects local execution, the computing task will be computed on each user device
Figure BDA0001825002250000129
Representing the computing power of the user equipment, the locally computed delay is then:
Figure BDA0001825002250000123
the local computing energy consumption is:
Figure BDA0001825002250000124
the size of the k value depends on the chip structure of the mobile device, where we take k to 10(-26). Energy consumption with user computing power in view of local computing
Figure BDA00018250022500001210
May be increased, the computing power of the user may be minimized locally by dynamically adjusting the computing power of the user through a Dynamic Voltage Scaling (DVS) technique. Thus, under the time delay constraint, the optimal computing power is distributed in local computing
Figure BDA0001825002250000125
Can be expressed as:
Figure BDA0001825002250000126
wherein the content of the first and second substances,
Figure BDA0001825002250000127
representing the maximum computing power of user n.
(2) When the user selects to unload the task for calculation, the user equipment is accessed to the corresponding SBS through the wireless network to unload the task to the MEC for calculation. For a user unloading a task, corresponding transmission delay and energy consumption are generated when the task is transmitted to the MEC in an uplink mode through a wireless network, and according to a communication model, the uplink transmission delay when the user n unloads the task is obtained as follows:
Figure BDA0001825002250000128
when a computing task is offloaded to the MEC, the MEC allocates certain computing resources to process the task,by fcRepresenting the computing speed of the MEC allocation, here we consider that the computing speed of the MEC allocation to each user during the task execution is fixed, and then the time delay of the MEC executing the task is:
Figure BDA0001825002250000131
the total energy consumption of the user in transmitting the calculation task is:
Figure BDA0001825002250000132
wherein
Figure BDA0001825002250000133
Represents the total transmit power of the user;
Figure BDA0001825002250000134
representing the circuit power consumption in the user idle state.
Each user device will evaluate the locally calculated costs during task offloading and then report to the MEC. At the same time, the MEC will also evaluate the cost of each user device when it is off-loaded. The MEC then makes a corresponding offloading decision by comparing the local and offloading costs, the offloading decision being expressed as:
Figure BDA0001825002250000135
here we use NcIndicating the number of users offloaded, by NcRepresenting an offloaded set of users, the number of locally computed users is N-Nc。
Considering the latency requirements and limited battery power of users, we will minimize the total energy consumption of users by optimizing the offloading decision a and the subchannel allocation C and the power allocation P, we give the objective function that we need to optimize:
Figure BDA0001825002250000136
Figure BDA0001825002250000137
Figure BDA0001825002250000138
Figure BDA0001825002250000139
Figure BDA00018250022500001310
Figure BDA00018250022500001311
wherein, C1 represents the maximum delay requirement that the user can tolerate when calculating the task, C2 represents that the user's transmission power cannot be greater than its maximum transmission power, C3 represents that the transmission power on each sub-channel is non-negative, C4 represents the allocation status of the channel, and C5 represents that the offloading decision is a binary variable.
Wherein step 102 optimizes the unload decision using a coordinate descent method comprising: we are with A ═ a1,a2,…,aN]Representing offload decisions for all users, given an initial offload decision A0Is a full 1 matrix, Al-1Represents the unloading decision at the l-1(l 1, 2..) iteration, corresponding to V (a)l-1) Indicating a decision at a given offload as al-1Optimal value of the time objective function, defining
Figure BDA0001825002250000146
For the benefit obtained after changing the current unload decision at the first iteration, then
Figure BDA0001825002250000147
Wherein A isl-1(n) represents the offload decision after user n changes the current decision, and the update rule is as follows:
Figure BDA0001825002250000141
wherein the content of the first and second substances,
Figure BDA0001825002250000142
the modulo two addition method is shown.
Coordinate descent method with one variable a along each timenThe direction of the target function is continuously optimized, so that the local minimum value of the target function is found, the algorithm can be converged through finite iterations, and an optimal unloading decision is obtained. In the first iteration, we obtain the unload decision AlBy calculation, if the profit is obtained
Figure BDA0001825002250000143
Then
Figure BDA0001825002250000144
Wherein the content of the first and second substances,
Figure BDA0001825002250000145
representing the user who gets the most profit in the l-th iteration.
Step 103, performing subchannel allocation on the user by adopting an improved hungarian algorithm and a greedy algorithm, and comprising: in the sub-channel allocation process, it is desirable to allocate the sub-channel with the best channel quality to the user each time to maximize the uplink transmission rate of the user. Meanwhile, it is desirable to allocate as few subchannels as possible to each user to avoid serious interference due to excessive frequency reuse of the users while satisfying the user delay requirement. Therefore, according to the constraints C1 and C3 of the optimization goal, the sub-channel allocation problem for each user can be formulated as follows:
Figure BDA0001825002250000151
Figure BDA0001825002250000152
Figure BDA0001825002250000153
Figure BDA0001825002250000154
Figure BDA0001825002250000155
for the above sub-channel allocation problem, it can be equivalent to NcThe problem of matching of each user with K sub-channels is that firstly, an improved Hungarian algorithm is adopted for channel matching once, then a greedy algorithm is adopted to continuously allocate enough sub-channels to the users under the condition of meeting the requirement of the lowest rate, and the algorithm steps are as follows:
101A: constructing a benefit matrix required for a first iteration
Figure BDA0001825002250000156
101B: if the number of users is greater than the number of sub-channels, i.e. NcIf > K, N is addedc-K virtual subchannels, changing the benefit matrix to Nc×NcSquare matrix, if the number of users is less than the number of sub-channels, i.e. NcIf < K, K-N is addedcThe user changes the benefit matrix into a K multiplied by K square matrix;
101C: performing maximum weight matching by adopting a Hungarian algorithm to obtain primary channel allocation;
101D: based on the result of the allocated sub-channelsNew subchannel allocation matrix
Figure BDA0001825002250000157
And interference matrix
Figure BDA0001825002250000158
101E: and checking whether each user meets the minimum rate requirement, and if so, terminating the algorithm. If not, updating the users needing to continuously distribute the sub-channels to be Nc'。
101F: checking channel allocation matrices
Figure BDA0001825002250000159
To Nc'each user in' uses a greedy algorithm to select the sub-channel with the least interference from the remaining sub-channels to allocate to the user.
101G: repeat steps 101D) -101F) until all users meet the minimum rate requirement or
Figure BDA00018250022500001510
The algorithm terminates.
Step 104, converting the energy consumption minimization problem into a power minimization problem, and converting the power minimization problem into a convex optimization problem to obtain the optimal transmission power of the user, wherein the specific implementation method is as follows: considering that the constraint C1 is a maximum latency constraint, the minimization problem of energy consumption can be converted into a minimum power consumption problem under the latency constraint, so we convert the original optimization objective into:
Figure BDA0001825002250000161
Figure BDA0001825002250000162
Figure BDA0001825002250000163
Figure BDA0001825002250000164
since the above optimization problem is still a non-convex optimization problem, we now let us make use of variable substitution
Figure BDA0001825002250000165
Then:
Figure BDA0001825002250000166
we therefore turn the optimization problem into:
Figure BDA0001825002250000167
Figure BDA0001825002250000168
Figure BDA0001825002250000169
Figure BDA00018250022500001610
Figure BDA00018250022500001611
here we change the original equality relationship into the inequality constraint C3 in order to transform this non-convex problem into a convex problem, and this change does not affect the optimal solution to the problem, since the data rate of user n on sub-channel k cannot be less than optimal
Figure BDA0001825002250000171
Theorem: the above problem is a convex optimization problem at high signal to interference and noise ratios.
And (3) proving that: since the objective function is in the form of an exponential summation and is therefore a convex function, it can be seen that the constraints C1, C2, and C4 are all convex, and for the inequality constraint C3, the constraint C3 is non-convex due to the non-convexity of the throughput function. Under high SINR conditions, a common approach to throughput function non-convexity is an efficient approximation, such that log (1+ x) is approximately equal to log (x). Thus, constraint C3 may translate to:
Figure BDA0001825002250000172
wherein the content of the first and second substances,
Figure BDA0001825002250000173
is exponential and logarithmic and is therefore convex. In conclusion, it can be obtained that under the condition of high signal to interference and noise ratio, the above optimization problem is a convex optimization problem, and the certification is completed. For the convex optimization problem, the optimal power distribution result can be solved by using an interior point method.
Fig. 3 shows the variation of the number of offloads of the user under different time delay conditions. It can be seen from the figure that in the case where the user's latency constraint is low, the user has more choices to offload tasks to MEC computation, and in the case where the latency constraint is high, the user has more choices to perform local computation. This is because the algorithm herein considers the delay requirement of the user, guarantees the minimum rate requirement of the user when allocating resources, and when the delay constraint is small, the rate requirement of the user is high, more wireless resources will be allocated, the transmission delay is low, and the energy consumption is correspondingly small, while the local computation has a low delay constraint, the CPU cycle frequency consumed by the user is high, the corresponding energy consumption is high, and then the user can obtain a higher performance improvement compared with the local computation, so the user can select more offload computations. On the contrary, if the user delay constraint is larger, the corresponding divided wireless resources are less, the energy consumption during the unloading calculation is higher, and the CPU cycle frequency consumed by the user during the local calculation is lower, at this time, the performance of the local calculation is better than that of the unloading calculation, so that the user can select the local calculation more.
Fig. 4 depicts the variation in total energy consumption of the system as the number of users increases. Here we compare the algorithm here with the local computation, total offload and join algorithms, which only consider channel assignments and do not consider the different latency requirements of users. It can be seen from the figure that the algorithm herein has a lower total system energy consumption than other algorithms. Compared with the join algorithm, the algorithm considers the whole task unloading optimization scheme, effectively allocates channels for users under the condition of meeting the time delay constraint, and minimizes the transmission power of the users under the condition of considering the total energy consumption of the system. The algorithm herein can obtain better offloading decision and resource allocation scheme than the join algorithm, and thus has significant improvement in system performance.

Claims (4)

1. A task unloading and resource allocation method based on MEC is characterized by comprising the following steps:
step 101: formulating a joint optimization problem of unloading decision and resource allocation;
step 102: optimizing the unloading decision by using a coordinate descent method;
step 103: the sub-channel allocation is carried out on the users by adopting an improved Hungarian algorithm and a greedy algorithm;
step 104: converting the energy consumption minimization problem into a power minimization problem, and converting the energy consumption minimization problem into a convex optimization problem to obtain the optimal transmission power of a user, wherein the method comprises the following steps:
in the case of obtaining the offload decision and channel allocation, the original optimization objective is still a non-convex optimization problem, and considering that the constraint condition C1 of the objective function is a maximum delay constraint, the minimization problem of energy consumption can be converted into a minimum power consumption problem under the delay constraint, and the original problem is converted into:
Figure FDA0003152030530000011
Figure FDA0003152030530000012
Figure FDA0003152030530000013
Figure FDA0003152030530000014
since the above optimization problem is still a non-convex optimization problem, we now let us make use of variable substitution
Figure FDA0003152030530000015
Then the following results are obtained:
Figure FDA0003152030530000016
we therefore turn we next the above optimization problem into:
Figure FDA0003152030530000017
Figure FDA0003152030530000018
Figure FDA0003152030530000021
Figure FDA0003152030530000022
Figure FDA0003152030530000023
for the transformed convex optimization problem, the optimal power distribution result can be solved by using an interior point method;
wherein the content of the first and second substances,
Figure FDA0003152030530000024
denotes the transmission power, N, of the nth user on the kth sub-channelcIndicating the number of users to be offloaded,
Figure FDA0003152030530000025
a set of users that are to be offloaded is represented,
Figure FDA0003152030530000026
representing a set of sub-channels, RnRepresenting the total rate of uplink transmission of user n while offloading tasks, dnRepresenting the size of the input data, fcRepresenting the calculated speed of MEC allocation, wnRepresenting the CPU cycles, T, required to compute the taskn maxRepresenting the maximum time delay, P, acceptable to user nmaxWhich represents the maximum transmit power of the user,
Figure FDA0003152030530000027
representing the transmission rate of user n on subchannel k,
Figure FDA0003152030530000028
represents SBSnUser n to SBSnThe channel gain of (a) is determined,
Figure FDA0003152030530000029
represents SBSmUser m to SBSnChannel gain of (a) (. omega)0Representing the background noise power, B representing the subchannel bandwidth,
Figure FDA00031520305300000210
representing the equivalent transmit power of the nth user on the kth sub-channel,
Figure FDA00031520305300000211
represents the equivalent transmission power of the mth user on the kth sub-channel;
Figure FDA00031520305300000212
representing the data rate, R, of user n on subchannel knRepresenting the total rate of uplink transmission for user n while offloading tasks.
2. The method of claim 1, further characterized in that said step 101 of formulating a joint optimization problem for offloading decisions and resource allocation comprises:
definition anE {0,1} is an unloading decision of the user, 0 represents the user to select local execution, and 1 represents the user to select unloading to MEC execution; therefore, we use a ═ a1，...，aNRepresents the offloading decisions of all users, each user device will evaluate the cost of local computation during the task offloading process and then report to the MEC; at the same time, the MEC will also evaluate the cost of each user equipment in offloading, and then the MEC will make a corresponding offloading decision by comparing the local and offloading costs, the offloading decision being expressed as:
Figure FDA0003152030530000031
with NcIndicating the number of users to offload
Figure FDA0003152030530000032
Representing an offloaded set of users, the number of locally computed users is N-Nc，
Figure FDA0003152030530000033
Representing the energy consumption of the local calculation selected by the user n,
Figure FDA0003152030530000034
the method represents energy consumption of N selected unloading calculation of a user, N represents the number of small base stations, and the total energy consumption of the user is minimized by optimizing an unloading decision A, a sub-channel distribution matrix C and a power distribution matrix P in consideration of time delay requirements and limited battery power of the user, so that an objective function required to be optimized by the method is given:
Figure FDA0003152030530000035
Figure FDA0003152030530000036
Figure FDA0003152030530000037
Figure FDA0003152030530000038
Figure FDA0003152030530000039
Figure FDA00031520305300000310
wherein the content of the first and second substances,
Figure FDA00031520305300000311
and
Figure FDA00031520305300000312
respectively representing the latency of user n in local and offload computations,
Figure FDA00031520305300000313
representing the maximum delay that can be accepted by user n,
Figure FDA00031520305300000314
indicating the case of the channel assignment and,
Figure FDA00031520305300000315
indicating that the kth sub-channel is assigned to the nth user,
Figure FDA00031520305300000316
it means that the k-th sub-channel is not allocated,
Figure FDA00031520305300000317
denotes the transmission power, P, of the nth user on the k-th sub-channelmaxRepresenting the maximum transmit power of the user, C1 representing the maximum latency requirement that the user can tolerate when computing the task, C2 representing that the transmit power of the user cannot be greater than its maximum transmit power, C3 representing that the transmit power on each sub-channel is non-negative, C4 representing the allocation status of the channel, C5 representing that the offload decision is a binary variable,
Figure FDA00031520305300000318
representing the set of all users.
3. The method of claim 1, further characterized in that said step 102 of optimizing an unloading decision using a coordinate descent method comprises:
with A ═ a1，a2，...，aN]Representing offload decisions for all users, given an initial offload decision A0Is a full 1 matrix, Al-1Is shown inThe unloading decision in the l-1(l ═ 1, 2..) iteration is accordingly determined using V (a)l-1) Indicating a decision at a given offload as al-1Optimal value of the time objective function, defining
Figure FDA00031520305300000319
For the benefit obtained after changing the current unload decision at the first iteration, then
Figure FDA0003152030530000041
Wherein A isl-1(n) represents the offload decision after user n changes the current decision, and the update rule is as follows:
Figure FDA0003152030530000042
wherein the content of the first and second substances,
Figure FDA0003152030530000043
representing the modulo two addition method, the coordinate descent method, one variable a per edgenThe direction of the target function is continuously optimized, so that the local minimum value of the target function is found, the algorithm can be converged through finite iterations, and an optimal unloading decision is obtained.
4. The method of claim 1, further characterized in that said step 103 of employing a modified hungarian algorithm and a greedy algorithm for sub-channel assignment to users comprises:
for subchannel assignment problem, it can be equivalent to NcThe problem of matching of each user with K sub-channels is that firstly, an improved Hungarian algorithm is adopted to carry out channel matching once, then, a greedy algorithm is adopted to continuously allocate enough sub-channels to the users under the condition of meeting the requirement of the lowest rate, and the algorithm steps are as follows:
1) constructing a benefit matrix required for a first iteration
Figure FDA0003152030530000044
B denotes a sub-channel bandwidth,
Figure FDA0003152030530000045
representing the SINR of user n on sub-channel k
2) If the number of users is greater than the number of sub-channels, i.e. NcIf > K, N is addedc-K virtual subchannels, changing the benefit matrix to Nc×NcSquare matrix, if the number of users is less than the number of sub-channels, i.e. NcIf < K, K-N is addedcThe user changes the benefit matrix into a K multiplied by K square matrix;
3) performing maximum weight matching by adopting a Hungarian algorithm to obtain primary channel allocation;
4) updating a subchannel allocation matrix according to the result of the allocated subchannels
Figure FDA0003152030530000046
And interference matrix
Figure FDA0003152030530000047
5) Checking whether each user meets the minimum rate requirement, and if so, terminating the algorithm; if not, updating the user needing to continuously distribute the sub-channels as
Figure FDA0003152030530000048
6) Checking channel allocation matrices
Figure FDA0003152030530000049
To pair
Figure FDA00031520305300000410
Each user in the group selects a subchannel with the minimum interference from the rest subchannels by adopting a greedy algorithm to be distributed to the user;
7) repeat steps 4) -6) until all users meet the minimum rate requirement or
Figure FDA00031520305300000411
The algorithm terminates.
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