CN112654058A - Mobile edge computing offload and resource allocation algorithm in D2D multicast network - Google Patents

Mobile edge computing offload and resource allocation algorithm in D2D multicast network Download PDF

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CN112654058A
CN112654058A CN202011490867.1A CN202011490867A CN112654058A CN 112654058 A CN112654058 A CN 112654058A CN 202011490867 A CN202011490867 A CN 202011490867A CN 112654058 A CN112654058 A CN 112654058A
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陈雷
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China Criminal Police University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/02—Traffic management, e.g. flow control or congestion control
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
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Abstract

A mobile edge computing unloading and resource allocation algorithm in a D2D multicast network belongs to the technical field of mobile edge computing in a D2D multicast network, firstly, in order to improve the stability of multicast transmission links and increase computing resources, a D2MD cluster head selection and clustering selection strategy is provided, and the social attributes, available energy and transmission rate of D2MD users are jointly considered in the cluster head selection strategy. And secondly, under the conditions of user selection, calculation unloading strategy and calculation resource allocation, the maximum user income is used as an optimization problem to be formulated. And further converting the optimization problem into two sub-problems, namely a user selection optimization USO problem and a resource allocation optimization RAO problem, wherein the RAO problem is a convex optimization problem, and the optimal solution is obtained by adopting a Lagrange multiplier method. And the provided algorithm is verified in a simulation mode, so that the energy consumption and the calculation cost can be effectively reduced while the user profit is maximized.

Description

Mobile edge computing offload and resource allocation algorithm in D2D multicast network
Technical Field
The invention belongs to the technical field of mobile edge computing in a D2D (Device-to-Device communication) multicast network, and particularly relates to a mobile edge computing unloading and resource allocation algorithm in a D2D multicast network.
Background
With the explosive growth of data volume and computation-sensitive traffic, Mobile Edge Computing (MEC) technology and D2D multicast (D2MD) technology have begun to be known. However, existing research often overlooks the problem of limited battery power and computing power of D2MD users.
With the rapid development of mobile communication technology, more and more intelligent devices are provided with mobile applications, such as multicast video sharing, real-time online game and the like, which generate a large amount of data of various types[1],[2]. As data traffic explosively grows, mobile devices will face access requests of different broadband intensive and widely computing wireless networks. These new applications and services increase the transmission burden on the backhaul link between the core network and the base station. At the present stage, a great deal of research work focuses on unloading of mass data and transmission of intensive computing tasks to the cloud end for execution[3],[4]. However, when the mobile device performs computations by connecting to the cloud through the base station, it will face a longer delay, and therefore, this will not be sufficient for transmission-sensitive tasks.
D2D communication is an attractive technology to meet the above-mentioned large data transmission requirements and achieve high network capacity. In an actual cellular network, the transmission tasks of the D2D users to the base station are carried out under the control of the base station, and the D2D users directly use the authorized frequency spectrum for communication, so that the D2D users will not generate interference with the users of the cellular network[5]. The D2D multicast (D2MD) communication technology can realize the common sharing of interested contents or the online game of multiple persons, such as the computing task of 4K video or real-time VR (Virtual Reality). In the D2MD mode, factors such as geographical position and social attributes are factors influencing D2MD cluster head selection and D2MD clustering[6],[7]. Moreover, mobile devices are also subject to certain unavoidable circumstances, such as: energy limited, capacity limited, and computing power limited, etc. In recent years, the problem of limited computing power has been solved by the proposal of Mobile Edge Computing (MEC)[8],[9]. By locating computing services at the edge of the network, a system supporting MEC may enable a user to offload computing tasks to an MEC server for execution, which may provide the user with a large number of wireless connectionsResources and computational power, which can help users reduce transmission delays and provide higher computational performance.
Based on the computing power on the mobile device and the use of the MEC server on the base station side, there are some studies on computing offload of D2MD networks supporting MEC at the present stage[10]-[15]. Document [10 ]]Research has been conducted to offload computing tasks to neighboring mobile terminals for execution in a D2D network supporting MEC, considering the limitation of computing resources, and to propose an optimization problem to minimize the average communication cost and the computing service cost. Document [11]In a D2D network supporting MEC, a D2D selection strategy, an unloading rate and computing resource allocation are comprehensively considered, an optimization problem of maximizing user benefits is provided, and the optimization problem is divided into two sub-optimization problems to be solved. Document [12 ]]By simultaneously utilizing the advantages of the D2D technology and the MEC technology, the method proposes that the number of supportable devices can be maximized by optimizing the D2D communication pair under the condition that the communication resources and the computing resources are limited. Document [13 ]]A network of multi-MEC servers based on D2D communication was studied, analyzing the assignment of their tasks to multiple off-load devices by local users in TDMA (time division multiple access) systems, and minimizing computational delay by jointly considering transmission time, transmission rate and download results. Document [14]MEC networks based on D2D communication were investigated, and in order to minimize the overall energy consumption of MEC systems and to meet the delay constraints of the equipment, an optimization problem was presented that combines collaborator selection and allocation of computational resources. Document [15 ]]An MEC network based on D2D communication was studied to define the consumption of task execution as a weight of total task execution delay and energy consumption and to propose a joint optimization problem to minimize the consumption of energy when executing a task. Previous work was done in the case of D2D unicast, but not in the multicast scenario.
At this stage, the computing offload of the D2D user is limited by the energy and computing power of the D2D user. Current research work rarely considers the problem of both D2MD clusterhead selection and the limited computational power of MECs. For the task offloading problem, it is mostly assumed that the MEC has enough software and hardware resources to support the computation task. In fact, however, such assumptions are not feasible in actual MEC operation.
Disclosure of Invention
The invention aims to provide a mobile edge computing offload and resource allocation algorithm in a D2D multicast network, which is used for researching the computing offload and resource allocation problem of delay-sensitive tasks when the resource limitation is considered in a D2MD network supporting MEC.
Firstly, in order to improve the stability of multicast transmission links and increase computing resources, a D2MD cluster head selection and clustering selection strategy is proposed, in which social attributes, available energy and transmission rate of D2MD users are jointly considered.
Secondly, under the condition of considering user selection, calculation unloading strategy and calculation resource allocation, the maximum user benefit is formulated as an optimization problem. Further, the Optimization problem is converted into two sub-problems, namely a User Selection Optimization (USO) problem and a Resource Allocation Optimization (RAO) problem, wherein the RAO problem is a convex Optimization problem, and the optimal solution is obtained by using a lagrangian multiplier method.
Finally, the algorithm provided by the method is verified through simulation, and the energy consumption and the calculation cost can be effectively reduced while the user income is maximized.
Compared with the previous research, the technical scheme researches a transmission and calculation unloading strategy in a D2MD network supporting MEC to serve high-speed and delay-sensitive traffic. Therefore, the main contributions of the present solution are the following two aspects.
1) A D2MD cluster head selection strategy is provided on the basis of considering the social attributes of users, the energy available for the users and the transmission rate. In this strategy, a user who wants to become a cluster head needs to obtain the cluster head according to a Chinese Restaurant Process (CRP) algorithm and a corresponding weighting factor.
2) A joint computation offloading and resource optimal allocation strategy is proposed. Under the condition of considering user selection, calculation unloading strategy and calculation resource allocation, the maximized user benefit is formulated as an optimization problem. And obtaining a solution of the optimization problem by solving the USO problem and the RAO problem.
Drawings
Fig. 1 is a D2D multicast system model supporting mobile edge computation.
Fig. 2 shows a D2D multicast subscriber distribution.
Fig. 3 shows D2D after clustering and cluster head determination of multicast users.
FIG. 4 is a graph of the impact of different ratios of consumption to power consumption per unit on user revenue.
Fig. 5 shows the total user revenue for different average data amounts.
FIG. 6 is a graph of the impact of the number of users on the total revenue for the users.
Fig. 7 is a graph of the impact of the number of cluster heads of D2MD on the total revenue for a user. Where the abscissa FD is Full Duplex, indicating Full Duplex.
Fig. 8 shows the effect of the maximum tolerated delay of a task on the total user gain.
Detailed Description
Mobile edge computing offload and resource allocation algorithm in D2D multicast network:
1 system model.
System model as shown in fig. 1, users are divided into a plurality of clusters D2MD according to geographical location within the coverage area of a base station. In each cluster, a unique user is selected as a D2MD cluster head, and the D2MD cluster head has a full-duplex antenna and is connected to the user terminal and the base station terminal in a wireless manner. These D2MD clusterheads can help user terminals connect to the network and assist users in transferring tasks to the MEC server at the base station side. The cluster head actively stores some content (some content represents data transmitted from the base station to the multicast user, the data can be any form of data such as text, voice, image, video and the like, the data is transmitted to the cluster head firstly, and the data is multicast to other users in the same cluster after being received by the cluster head), and the content can be multicast to the users in the same cluster. When the user requires some content, the cluster head transmits in a multicast mode. To achieve efficient distribution caching, the users are each separatelyBelonging to and unique from one cluster. The set of D2D users is denoted as K ═ {1,2, L, K }. The set of D2D clusters is denoted as M ═ {1,2, L, M }. By using
Figure BDA0002840647090000031
Wherein x i,m1 denotes the D2MD cluster head m used by the user equipment i. X ═ Xi,mDenotes a set of user equipments using the cluster head m.
2 cluster head selection and clustering strategies combining social attributes, energy and rate.
D2MD plays an important role in increasing system capacity, reducing transmission delay, and improving resource utilization. This section proposes a D2MD cluster head selection strategy, and proposes a clustering strategy based on this. In one cluster, the D2MD cluster head acts as a relay to transfer content to users in its cluster. If the D2MD clusterhead and the D2MD users do not trust each other, it may be difficult to transmit and receive the same content between them. If the D2MD clusterhead does not have sufficient energy, communication may be interrupted. In addition, if both the cluster head and the user are at the cell edge, their channel quality may be difficult to meet the conditions required for transmission. Therefore, the social attributes of the users, the available energy and the transmission rate between the base station and the users are comprehensively considered in the cluster head selection.
In the cluster head selection, a well-known Chinese Restaurant Process (CRP) model, which is a well-known stochastic model widely used in non-parametric modeling, is used. In cluster cnThe probability that user j selects user i as the cluster head can be expressed as:
Figure BDA0002840647090000041
where a iswParameter for CRP, m (m.gtoreq.3) is cluster cnThe number of users in the group,
Figure BDA0002840647090000042
is the probability that user j selects user i as the cluster head.
The probability matrix that the user is selected as the cluster head can therefore be expressed as:
Figure BDA0002840647090000043
here, the ith row represents the probability of the user i being selected as the cluster head, and the sum of the elements in the ith row represents the selection probability of the user i, wherein the user with the highest selection probability is the cluster head.
Thus, in cluster cnThe probability that the user j selects the user i as the cluster head can be calculated by formula (3).
Figure BDA0002840647090000044
Herein, the
Figure BDA0002840647090000045
Is the influence factor of user i on user j.
Figure BDA0002840647090000046
Can be expressed as:
Figure BDA0002840647090000047
where w isS+wE+wR＝1。
Figure BDA0002840647090000048
And
Figure BDA0002840647090000049
respectively representing the social influence factor, the energy influence factor and the transmission rate influence factor of the user i on the user j. The influencing factors are described in detail below.
2.1 social influence factor.
Figure BDA00028406470900000410
Representing the social impact factor of user i on user j. By analyzing the social relationship between users, a social similarity factor between user i and user j is proposed, which is expressed as:
Figure BDA00028406470900000411
herein, the
Figure BDA0002840647090000051
Representing a social similarity factor between user i and user j.
Figure BDA0002840647090000052
Higher values of (c) indicate higher similarity. If it is not
Figure BDA0002840647090000053
This indicates that user i and user j will not establish a D2D communication link. For user cluster cnThe normalized social influence factor may be expressed as:
Figure BDA0002840647090000054
herein, the
Figure BDA0002840647090000055
Represents a user cluster cnAnd (4) the sum of social influence factors of the rest users on the user i.
2.2 energy impact factor.
Figure BDA0002840647090000056
Represents a user cluster cnThe energy impact of user i on user j. The maximum available transmission time that user i can measure on user j is expressed as:
Figure BDA0002840647090000057
herein, the
Figure BDA0002840647090000058
Representing the energy available to user i, P0Indicating the circuit loss of the user i,
Figure BDA0002840647090000059
representing the transmission power of user i.
Figure BDA00028406470900000510
Where σ is2Representing the noise power, gamma0Representing the received signal-to-noise threshold. To ensure transmission quality, the actual received SNR of the user needs to be greater than γ0。
Figure BDA00028406470900000511
Represents the channel gain between user i and user j, and is represented as:
Figure BDA00028406470900000512
Figure BDA0002840647090000061
indicating Rayleigh fading, alphahThe parameters of the path loss are represented,
Figure BDA0002840647090000062
representing the distance between user i and user j.
Substituting equations (8) and (9) into equation (7) can obtain the maximum transmission time between user i and user j as:
Figure BDA0002840647090000063
herein, the
Figure BDA0002840647090000064
A higher value indicates a greater energy impact of user i on user j. Consider the entire user cluster cnA normalized impact factor can be expressed as:
Figure BDA0002840647090000065
herein, the
Figure BDA0002840647090000066
Represents a user cluster cnAnd (4) summing the energy influence factors of the rest users on the user i.
2.3 Transmission Rate Effect factor.
Figure BDA0002840647090000067
Represents a user cluster cnThe transmission rate of user i. If the base station transmits data at a fixed amount of power, the transmission rate of user i can be expressed as:
Figure BDA0002840647090000068
herein, the
Figure BDA0002840647090000069
Representing the channel gain, P, between the base station and user iBWhich represents the transmit power of the base station,
Figure BDA00028406470900000610
denotes a distance between the user i and the base station, W denotes a channel bandwidth between the user i and the base station,
Figure BDA00028406470900000611
representing Rayleigh fading, alpha, between user i and base stationBRepresenting a path loss parameter. The higher the transmission rate, the greater the impact on user i. Consider the entire user cluster cnA normalized impact factor can be expressed as:
Figure BDA00028406470900000612
herein, the
Figure BDA0002840647090000071
Represents a user cluster cnThe sum of the transmission rate impact of the remaining users on user i.
In summary, substituting equations (6), (11) and (13) into equation (4) can obtain the influence factor of user i on user j as follows:
Figure BDA0002840647090000072
the probability of selecting user i as the cluster head can be obtained by substituting equation (14) for (3). And arranging according to the descending order of the probability, and selecting the cluster head with the maximum probability.
2.4 clustering strategy.
Initializing each cluster
Figure BDA0002840647090000073
The remaining set of users is represented as
Figure BDA0002840647090000074
When in use
Figure BDA0002840647090000075
Time cycle: from
Figure BDA0002840647090000076
Calculating an average impact factor for each cluster
Figure BDA0002840647090000077
Selecting
Figure BDA0002840647090000078
Updating
Figure BDA0002840647090000079
And (3) outputting: obtaining a user clustering result Km,1≤m≤M。
3 computation offload and resource allocation.
3.1D 2MD system communication model and computational model supporting MEC.
It is assumed herein that the tasks are split and transmitted to the MEC servers at the local user side and the base station side simultaneously. Definition of Li＝(σi,si,Ti) Indicating the task that the user equipment i needs to handle, where δi(cycles of CPU work per megabit) indicates that the processing task requires total computational resources, si(bits) representing the amount of data of the task that needs to be performed, TiIndicating the maximum delay value that the task can accept. It should be noted that due to limited computing power, all tasks cannot be completed within the maximum tolerable delay time. Thus, the user equipment will transmit a part of the task to the MEC.
The steps of the computation task offload of the D2MD network supporting MEC are: first, the user equipments send a certain proportion of the tasks to their associated D2MD clusterhead. Secondly, the D2MD cluster head will use the same frequency band of the forward link to transmit further to the MEC in the base station after receiving the task. For user i, its calculated unload rate may be denoted as oi∈[0,1]Wherein o isi＝1(oi0) indicates that the task is offloaded to MEC execution (indicating that the task is executing locally).
1) A communication model.
It is assumed that the forward and reverse links of the user equipment and the D2MD clusterhead operate on orthogonal frequency spectrums. And therefore do not interfere with each other. The bandwidth of the forward link is the same as the bandwidth of the reverse link and may be denoted by B.
The transmission rate that can be achieved on the link from the user (i e K) to the D2MD clusterhead (M e M) can be expressed as:
Figure BDA0002840647090000081
where p isiIndicating the transmit power of user equipment i. gi,mIndicating the channel gain from the user equipment i to the D2MD cluster head m. SI denotes self-interference of a full-duplex antenna, and SI ═ Ibi,mpmWhere I is the gain of the remaining SI, pmIs the power allocated by cluster head m of D2MD, bi,mIs the power ratio of cluster head m of D2 MD. SI is a constant of the interference cancellation technique.
Similarly, the data rate of the reverse link from D2MD cluster head m to the base station may be expressed as:
Figure BDA0002840647090000082
where p ismRepresenting the maximum transmission power of the D2MD cluster head m. bi,m∈(0,1]Indicating the allocated power ratio at which the user equipment i needs to offload tasks. gmRepresenting the channel gain of D2MD cluster head m to the base station.
Therefore, according to the study of the document [16], the uplink data rate of the ue i transmitted to the D2MD cluster head m can be expressed as:
Figure BDA0002840647090000083
full duplex communication requires that the transmission rate of the input link be higher than the transmission rate of the output link. There may therefore be:
Figure BDA0002840647090000084
order to
Figure BDA0002840647090000085
Wherein
Figure BDA0002840647090000086
Representing the transfer rate of the offloaded task to the MEC.
2) And calculating the model.
Definition of
Figure BDA0002840647090000098
For the local computation capability of the user equipment i (per megabit of CPU working period), the local computation execution delay of the terminal when all tasks are computed locally can be expressed as:
Figure BDA0002840647090000091
the task is transmitted from the user equipment i to the D2MD cluster head, and the computation execution delay of the task at the D2MD cluster head can be expressed as:
Figure BDA0002840647090000092
the total computation execution latency in processing tasks on the mobile edge computation server can therefore be expressed as:
Figure BDA0002840647090000093
wherein weRepresenting the computing power on the MEC server. a isiRepresenting the calculation factor on the MEC server for executing the task on the user device i.
Task L transmitted from user i to D2MD clusterhead mi＝(σi,si,Ti) The transmission delay of (d) may be expressed as:
Figure BDA0002840647090000094
task L passed from user i to MEC through D2MD clusterhead mi＝(σi,si,Ti) Is delayedCan be expressed as:
Figure BDA0002840647090000095
as mentioned above, tasks are processed separately. Order to
Figure BDA0002840647090000096
And
Figure BDA0002840647090000097
indicating the proportion of tasks offloaded to MEC and D2MD clusterhead, respectively. Thus, when a task is offloaded onto the D2MD cluster head and MEC, the processing time of the remaining tasks locally can be expressed as:
Figure BDA0002840647090000101
Figure BDA0002840647090000102
the total execution latency of the offloaded task from user i to D2MD cluster head m and MEC can be expressed as:
Figure BDA0002840647090000103
Figure BDA0002840647090000104
assuming that the task is allocated to be executed on both the local mobile terminal and the MEC server, the task L is executediIs the largest of the local execution time and the execution time on the MEC server or D2MD cluster head, so when a task is offloaded to the MEC, the total completion time is expressed as:
Figure BDA0002840647090000105
when a task is offloaded to the D2MD clusterhead, the total completion time is expressed as:
Figure BDA0002840647090000106
3.2 revenue maximization problem.
To maximize the revenue for users within the D2MD cluster, the problem of maximum revenue is modeled and solved. First, the utility function is defined as a subtraction function between the service revenue and cost. Based on the utility function, a maximum profit problem is formulated. Secondly, the original optimization problem is decomposed into two optimization problems. Finally, a greedy algorithm is adopted for solving.
1) Utility functions and optimization problem formulas.
The utility function is expressed as a decreasing function between the service revenue and the cost. The service revenue may be expressed to include how much task data is obtained and how much computing resources are used. The cost includes the price of the allocated computing resources and the power required to transmit the data to the MEC. Task L thereforei＝(σi,si,Ti) The utility function of (a) can be expressed as:
Figure BDA0002840647090000107
wherein d ismRepresents the current state of cluster head m, D, of D2MD m1 means in operation, otherwise d m0 means in idle state. Where κ and η represent the revenue factor per unit of offloaded data and the revenue factor per unit of power of the D2MD cluster head, respectively. ρ and β represent the price coefficient of the computing resource per unit and the price coefficient of the computing power allocated per unit time, respectively.
Figure BDA0002840647090000111
Figure BDA0002840647090000112
Figure BDA0002840647090000113
Figure BDA0002840647090000114
Figure BDA0002840647090000115
Figure BDA0002840647090000116
Figure BDA0002840647090000117
Where the constraint C1 indicates that the tasks on the MEC server and on the local user device are computed in parallel. The restriction C2 indicates that the user equipment is guaranteed to be connected to only one full-duplex D2MD clusterhead at a time. The restriction condition C3 indicates that the number of user equipments required to be simultaneously accessed by each D2MD cluster head cannot exceed its maximum acceptable value. The restriction condition C4 indicates that the allocated power of each D2MD cluster head cannot exceed its maximum transmission power. The constraint C5 indicates that the computational resources allocated to the MEC cannot exceed the maximum computational capacity of the MEC. The restriction C6 indicates that the transmission rate of the reverse link is smaller than the transmission rate of the forward link for each user equipment.
2) And optimizing problem transformation.
Due to the fact that
Figure BDA0002840647090000118
Is a binary variable, so the objective function (30) (i.e., equation 30) is a non-convex function. The original problem was a hybrid discrete non-convex optimization problem, which was therefore an NP-hard (NP-hard) problem. The reconstructed original problem is decomposed into two sub-problems, namely a User Selection Optimization (USO) problem and a Resource Allocation Optimization (RAO) problem. NP in the question refers to a non-deterministic polynomial (NP for short). By non-deterministic, it is meant that a certain number of operations can be used to solve a problem that can be resolved in polynomial time.
For a fixed value X, the RAO problem can be expressed as:
Figure BDA0002840647090000121
s.t.C1,C2,C5,C6
order to
Figure BDA0002840647090000122
Equation (31) can be reconstructed as:
Figure BDA0002840647090000123
s.t.C1,C2,C5,C6
proposition 1: li will be offloaded to MEC or D2MD clusterhead for task with optimal offload rate
Figure BDA0002840647090000124
Is that
Figure BDA0002840647090000125
The total execution time for compute offload is Ti。
And (3) proving that: first, analyzing the computational offload over the MEC, by rewriting the constraints C1, one can obtain:
Figure BDA0002840647090000126
herein, the
Figure BDA0002840647090000127
Representing the channel gain from the D2MD cluster head to the MEC reverse link.
Due to the fact that
Figure BDA0002840647090000128
Therefore, there must be a point
Figure BDA0002840647090000129
Equation (34) is satisfied.
Figure BDA00028406470900001210
When in use
Figure BDA00028406470900001211
From
Figure BDA00028406470900001212
When the value is decremented to 0, the value,
Figure BDA00028406470900001213
the start of the increment is incremented and,
Figure BDA00028406470900001214
begins to decrement. Optimum value
Figure BDA00028406470900001215
Is that
Figure BDA00028406470900001216
Is obtained because
Figure BDA00028406470900001217
And is
Figure BDA00028406470900001218
Thus can obtain
Figure BDA0002840647090000131
In conjunction with equation (22), the total execution delay of the offload task can be rewritten as:
Figure BDA0002840647090000132
as can be seen from the equation (36),
Figure BDA0002840647090000133
larger means larger allocated transmission power or more consumed computing resources. When in use
Figure BDA0002840647090000134
The larger the user's increased cost will replace the revenue obtained. Therefore, it is optimal
Figure BDA0002840647090000135
Should be that
Figure BDA0002840647090000136
And finishing proposition certification.
When the computational load is assigned to the D2MD clusterhead, the gain from completing the task will be reduced based on equation (32) because of the increased proportion of the task load.
Order to
Figure BDA0002840647090000137
Integrating equations (30) and (31) and substituting the relevant variables can result in:
Figure BDA0002840647090000138
Figure BDA0002840647090000139
equation (32) can be rewritten as:
Figure BDA00028406470900001310
Figure BDA00028406470900001311
Figure BDA0002840647090000141
Figure BDA0002840647090000142
3) and (5) solving an optimization problem.
The solution of the RAO problem is discussed first. To Zi,mMiddle xii,mThe second derivative of (d) can be expressed as:
Figure BDA0002840647090000143
as can be seen from the proposition 1,
Figure BDA0002840647090000144
thus, it is possible to obtain:
Figure BDA0002840647090000145
in the same way, the method for preparing the composite material,
Figure BDA0002840647090000146
and is
Figure BDA0002840647090000147
Can obtain:
Figure BDA0002840647090000148
when in use
Figure BDA0002840647090000149
When equations (37) and (38) are combined, then:
Figure BDA00028406470900001410
thus, it is possible to obtain
Figure BDA00028406470900001411
And function (39) (i.e., equation 39) is a convex function. The second derivative as the objective function (39) (i.e., equation 39) is strictly convergent. Therefore, solving the optimization problem of equation (39) can apply the KKT condition.
Karush-Kuhn-Tucker Karush Kuhn Tak (KKT) conditions.
The lagrangian expression of equation (39) is:
Figure BDA0002840647090000151
for the
Figure BDA0002840647090000152
The KKT condition is expressed as:
Figure BDA0002840647090000153
Figure BDA0002840647090000154
Figure BDA0002840647090000155
Figure BDA0002840647090000156
a 'here'i(ξi,m)＝JV/(J-Cξi,m)2Wherein
Figure BDA0002840647090000157
C＝weBTiσi，
Figure BDA0002840647090000158
Let [ y)]+Max { y,0}, in conjunction with equations (41) - (43), the lagrange multiplier can be rewritten as:
Figure BDA0002840647090000159
Figure BDA0002840647090000161
Figure BDA0002840647090000162
where t is the number of iterations and δ (t) represents the spacing of the t-th iteration. By using the KKT condition, an optimal resource allocation result can be obtained. Optimal ξ i, m can be obtained from equations (45) - (48). According to the equations (32) and (33), the optimum can be obtained
Figure BDA0002840647090000163
And
Figure BDA0002840647090000164
for the solution of the USO problem, let
Figure BDA0002840647090000165
And
Figure BDA0002840647090000166
respectively representing the power allocated and the computational resources allocated in the access scheme of user selection X. The optimal resource allocation result can be obtained through the algorithm, and the optimal resource allocation result is a 0-1 nonlinear optimization problem and is also a complete NP problem corresponding to the remaining user selection problems. Some heuristic algorithms already exist for solving the user selection, such as: ant Colony Optimization (ACO), Genetic Algorithm (GA), Simulated Annealing (SA), and greedy algorithm. The greedy algorithm approaches the globally optimal solution by obtaining a series of locally optimal solutions through a low complexity search. A greedy algorithm is used herein to obtain the optimal user selection, and the details of the specific algorithm are as follows:
the algorithm is as follows: greedy algorithm
Inputting:
the set of user equipments is represented as: k ═ 1,2, L, K }
The maximum number of iterations is: i is
The working set of D2MD clusterheads is represented as:
D＝{d1,d2,L,dM}
the tasks of the user equipment are represented as: l isi＝(σi,si,Ti)
Defining B, p simultaneouslym,pi,we,κ,ρ,η,β
And (3) outputting:
adopted resource allocation strategy A*,B*,O*
Adopted user selection policy X*
Figure BDA0002840647090000167
Figure BDA0002840647090000171
4, simulation analysis.
The system consists of 20 users and 7 full-duplex D2MD clusterheads. In the simulation scenario, the base stations are arranged at 100 × 100m2D2MD cluster heads are evenly distributed within the base station cell. The transmission power of the user equipment is pi10dBm, transmission power p of D2MD cluster head m20 dBm. For a radio link, the channel power gain of the users follows a Gaussian distribution of CN (10; 5). The thermal noise power of the user equipment is set to-100 dBm. The remaining simulation parameters are shown in table 1.
TABLE 1 simulation parameters
Figure BDA0002840647090000172
Figure BDA0002840647090000181
The full duplex based algorithm presented herein was compared to other algorithms for the needs of the simulation. The algorithm proposed by adopting the non-full duplex mode comprises the following steps: under the limitation of maximum tolerant time delay, an optimal task execution algorithm and an optimal resource allocation algorithm are provided. The other comparative algorithm is that rreora (random Ratio of Execution and Optimal Resource allocation) w.fd indicates that under the limit of maximum tolerated delay, a random allocation Execution proportion under full duplex and an Optimal Resource allocation algorithm are adopted. Meora (MEC Execution and Optimal Resource allocation) w.fd represents an Optimal Resource allocation algorithm executed on MEC in a full-duplex manner under the limitation of maximum tolerated delay.
The simulations of fig. 2 and 3(D2D multicast user clustering and determine cluster head policy) give the results of the D2MD clustering and D2MD cluster head selection policy proposed herein, as shown in fig. 3. The 20 user equipments are divided into 7 clusters in total, and the geographical positions of the clusters are observed, so that the clustering method better divides the users with similar channel quality into one cluster, and avoids the excessive power occupation of the users with poor channel quality. The cluster head selection and clustering of each cluster comprehensively consider social attribute, energy and rate factors.
Fig. 4 shows the power cost per unit versus the calculated cost in different proportions. The power cost per unit ρ is fixed and the computational cost per unit κ is varied. As can be seen from fig. 4, the user's profit decreases as the scale increases. This is because as the consumption per unit of calculation increases, the total consumption also increases.
FIG. 5 shows how much of the average input task volume has an effect on the revenue achieved by the user when employing different algorithms. It can be seen from fig. 5 that the user's profit increases with the average amount of data at the beginning of all algorithms. With the increasing amount of tasks, the additional power and computational resources consumed to meet the maximum tolerable delay for the transmission task are also increasing. The algorithm proposed herein has better user revenue in full duplex mode than other algorithms.
Fig. 6 and 7 simulate the impact of the number of user devices and the number of cluster heads of D2MD on the system yield. As can be seen from fig. 6, as the number of user devices increases, the user's gain of all algorithms increases rapidly, but the growth rate decreases slowly. This is due to the limited power of the D2MD cluster head and the limited computing power of the MEC server, so the system balances the consumption of users with maximizing the revenue of users due to the phenomenon of resource competition among users. It can be seen from fig. 7 that as the number of D2MD clusterheads increases, the user revenue for all algorithms initially increases rapidly, and then its growth rate tends to flatten out.
Figure 8 simulates the effect of the average maximum tolerated delay of a task on the total benefit of a user. From simulations it can be seen that as the average maximum tolerated delay increases, the overall benefit to the user also increases, due to the reduction in power consumption and computational resource consumption. The algorithm proposed herein outperforms other strategies in some intervals when full duplex mode is not employed.
And 5, a conclusion is reached.
Optimization algorithms for computational offloading and resource allocation are studied herein in D2MD networks supporting MECs. First, consider the problem of optimizing user revenue when combining user selection, computing offload policies, and computing resource scheduling. Second, the optimization problem is an NP-hard problem and a non-convex problem, and thus, the original problem is converted into an optimization problem of resource allocation and an optimization problem of user selection. Finally, lagrangian-based algorithms are proposed to solve the resource allocation optimization problem and greedy-based optimization algorithms are proposed to solve the user selection problem.
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Claims (3)

  1. A mobile edge computing offload and resource allocation algorithm in a D2D multicast network, characterized by the following steps:
    firstly, in order to improve the stability of a multicast transmission link and increase computing resources, a D2MD cluster head selection and clustering selection strategy is provided, and social attributes, available energy and transmission rate of a D2MD user are jointly considered in the cluster head selection strategy;
    secondly, under the condition of considering user selection, calculation unloading strategy and calculation resource allocation, the maximum user benefit is used as an optimization problem to be formulated; further, the optimization problem is converted into two sub-problems, namely a user selection optimization USO problem and a resource allocation optimization RAO problem, wherein the RAO problem is a convex optimization problem, and the optimal solution is obtained by adopting a Lagrange multiplier method.
  2. 2. The algorithm for mobile edge computing offload and resource allocation in a D2D multicast network according to claim 1, comprising the steps of:
    1, a system model;
    in the coverage area of the base station, users are divided into a plurality of D2MD clusters according to geographic positions; in each cluster, only one user is selected as a D2MD cluster head, and the D2MD cluster head is provided with a full-duplex antenna and is connected to a user terminal and a base station terminal in a wireless mode; these D2MD clusterheads can help user terminals connect to the network and assist users in transferring tasks to the MEC server at the base station side; the cluster head actively stores some contents and can transmit the contents to users in the same cluster in a multicast way; when a user requires certain content, the cluster head transmits the content in a multicast mode; in order to realize effective distribution cache, users respectively and uniquely belong to one cluster; the set of D2D users is denoted as K ═ {1,2, L, K }; the set of D2D clusters is denoted as M ═ {1,2, L, M }; by using
    Figure FDA0002840647080000011
    Wherein xi,m1 denotes the D2MD cluster head m used by the user equipment i; x ═ Xi,mDenotes the set of user equipments using cluster head m;
    2, a cluster head selection and clustering strategy combining social attributes, energy and rate;
    in cluster head selection, a well-known Chinese restaurant process model is used, in cluster cnIn (2), the probability that the user j selects the user i as the cluster head is represented as:
    Figure FDA0002840647080000012
    where a iswParameter for CRP, m (m.gtoreq.3) is cluster cnThe number of users in the group,
    Figure FDA0002840647080000013
    is the probability that user j selects user i as the cluster head;
    the probability matrix that the user is selected as the cluster head is thus expressed as:
    Figure FDA0002840647080000014
    the ith row represents the probability of the user i being selected as the cluster head, the sum of the elements in the ith row represents the selection probability of the user i, and the user with the highest selection probability is the cluster head;
    thus, in cluster cnThe probability that the user j selects the user i as the cluster head is obtained through calculation of a formula (3);
    Figure FDA0002840647080000021
    herein, the
    Figure FDA0002840647080000022
    Is the influence factor of the user i on the user j;
    Figure FDA0002840647080000023
    expressed as:
    Figure FDA0002840647080000024
    where w isS+wE+wR＝1；
    Figure FDA0002840647080000025
    And
    Figure FDA0002840647080000026
    respectively representing social influence factors, energy influence factors and transmission rate influence factors of a user i on a user j;
    2.1 social influence factor;
    Figure FDA0002840647080000027
    representing the social influence factor of the user i on the user j; the social similarity factor between user i and user j is expressed as:
    Figure FDA0002840647080000028
    herein, the
    Figure FDA0002840647080000029
    Representing a social similarity factor between user i and user j;
    Figure FDA00028406470800000210
    higher values of (d) indicate higher similarity; if it is not
    Figure FDA00028406470800000211
    This indicates that user i and user j will not establish a D2D communication link; for user cluster cnThe normalized social influence factor is expressed as:
    Figure FDA00028406470800000212
    herein, the
    Figure FDA0002840647080000031
    Represents a user cluster cnThe sum of social influence factors of other users on the user i;
    2.2 energy impact factor;
    Figure FDA0002840647080000032
    represents a user cluster cnEnergy impact of user i on user j; the maximum available transmission time that user i can measure on user j is expressed as:
    Figure FDA0002840647080000033
    herein, the
    Figure FDA0002840647080000034
    Representing the energy available to user i, P0Indicating the circuit loss of the user i,
    Figure FDA0002840647080000035
    represents the transmission power of user i;
    Figure FDA0002840647080000036
    where σ is2Representing the noise power, gamma0Representing a received signal-to-noise threshold; to ensure transmission quality, the actual received SNR of the user needs to be greater than γ0；
    Figure FDA0002840647080000037
    Represents the channel gain between user i and user j, and is represented as:
    Figure FDA0002840647080000038
    Figure FDA0002840647080000039
    indicating Rayleigh fading, alphahThe parameters of the path loss are represented,
    Figure FDA00028406470800000310
    representing the distance between the user i and the user j;
    substituting equations (8) and (9) into equation (7) yields the maximum transmission time between user i and user j as:
    Figure FDA00028406470800000311
    herein, the
    Figure FDA00028406470800000312
    A higher value indicates a greater energy impact of user i on user j; consider the entire user cluster cnOne normalized impact factor is expressed as:
    Figure FDA0002840647080000041
    herein, the
    Figure FDA0002840647080000042
    Represents a user cluster cnThe sum of energy influence factors of other users on the user i;
    2.3 transmission rate influencing factor;
    Figure FDA0002840647080000043
    represents a user cluster cnThe transmission rate of user i; if the base station transmits data at a fixed amount of power, the transmission rate of user i is expressed as:
    Figure FDA0002840647080000044
    herein, the
    Figure FDA0002840647080000045
    Representing the channel gain, P, between the base station and user iBWhich represents the transmit power of the base station,
    Figure FDA0002840647080000046
    denotes a distance between the user i and the base station, W denotes a channel bandwidth between the user i and the base station,
    Figure FDA0002840647080000047
    representing Rayleigh fading, alpha, between user i and base stationBRepresenting a path loss parameter; the higher the transmission rate is, the greater the influence on the user i is; consider the entire user cluster cnOne normalized impact factor is expressed as:
    Figure FDA0002840647080000048
    herein, the
    Figure FDA0002840647080000049
    Represents a user cluster cnThe sum of the influence of other users on the transmission rate of the user i;
    in summary, substituting equations (6), (11) and (13) into equation (4) results in the influence factor of user i on user j being expressed as:
    Figure FDA00028406470800000410
    replacing (3) with a formula (14) to obtain the probability of selecting the user i as the cluster head; arranging according to the descending order of the probability, and selecting the cluster head with the maximum probability;
    2.4 clustering strategy;
    initializing each cluster
    Figure FDA0002840647080000051
    The remaining set of users is represented as
    Figure FDA0002840647080000052
    When in use
    Figure FDA0002840647080000053
    Time cycle: from
    Figure FDA0002840647080000054
    Calculating an average impact factor for each cluster
    Figure FDA0002840647080000055
    Selecting
    Figure FDA0002840647080000056
    Updating
    Figure FDA0002840647080000057
    And (3) outputting: obtaining a user clustering result Km,1≤m≤M；
    3 calculating unloading and resource allocation;
    3.1D 2MD system communication model and computational model supporting MEC;
    definition of Li＝(σi,si,Ti) Indicating the task that the user equipment i needs to handle, where δi(cycles of CPU work per megabit) indicates that the processing task requires total computational resources, si(bits) representing the amount of data of the task that needs to be performed, TiRepresents the maximum time delay value that the task can accept;
    the steps of the computation task offload of the D2MD network supporting MEC are: first, the ues send a certain proportion of tasks to their associated D2MD clusterhead; secondly, after receiving the task, the D2MD cluster head further transmits the frequency band same with the forward link to the MEC in the base station; for user i, its calculated unload rate is denoted as oi∈[0,1]Wherein o isi＝1(oi0) represents task offloading to MEC execution;
    1) a communication model;
    setting the forward link and the reverse link of the user equipment and the D2MD cluster head to work on orthogonal frequency spectrums; the bandwidth of the forward link is the same as the bandwidth of the reverse link, denoted by B;
    the transmission rate that can be achieved on the link from user (i e K) to the cluster head of D2MD (M e M) is expressed as:
    Figure FDA0002840647080000058
    where p isiRepresents the transmit power of user equipment i; gi,mRepresents the channel gain from user equipment i to D2MD cluster head m; SI denotes self-interference of a full-duplex antenna, and SI ═ Ibi,mpmWhere I is the gain of the remaining SI, pmIs the power allocated by cluster head m of D2MD, bi,mIs the power ratio of cluster head m of D2 MD; the SI is used as a constant of the interference cancellation technology;
    the data rate of the reverse link from D2MD cluster head m to the base station is represented as:
    Figure FDA0002840647080000061
    where p ismRepresents the maximum transmission power of the D2MD cluster head m; bi,m∈(0,1]Representing the allocated power ratio when the user equipment i needs to unload the task; gmRepresenting the channel gain of the D2MD cluster head m to the base station;
    the uplink data rate of the ue i transmitting to the cluster head m of D2MD is represented as:
    Figure FDA0002840647080000062
    full duplex communication requires that the transmission rate of the input link be higher than the transmission rate of the output link. Therefore, there are:
    Figure FDA0002840647080000063
    order to
    Figure FDA0002840647080000064
    Wherein
    Figure FDA0002840647080000065
    Representing the transfer rate of the offloaded tasks to the MEC;
    2) calculating a model;
    definition of
    Figure FDA0002840647080000066
    For the local computation capability of the user equipment i (per megabit of CPU working period), the local computation execution delay of the terminal's overall task through local computation is expressed as:
    Figure FDA0002840647080000067
    the task is transmitted from the user equipment i to the D2MD cluster head, and the computation execution delay of the task at the D2MD cluster head is expressed as:
    Figure FDA0002840647080000068
    the total computation execution latency in processing tasks on the mobile edge computation server is therefore expressed as:
    Figure FDA0002840647080000071
    wherein weRepresenting computing power on the MEC server; a isiRepresenting a calculation factor on the MEC server for executing a task on the user equipment i;
    task L transmitted from user i to D2MD clusterhead mi＝(σi,si,Ti) The transmission delay of (c) is expressed as:
    Figure FDA0002840647080000072
    task L passed from user i to MEC through D2MD clusterhead mi＝(σi,si,Ti) The transmission delay of (d) is expressed as:
    Figure FDA0002840647080000073
    order to
    Figure FDA0002840647080000074
    And
    Figure FDA0002840647080000075
    represents the proportion of tasks offloaded to MEC and D2MD clusterhead, respectively; thus, when a task is offloaded onto the D2MD cluster head and MEC, the processing time of the remaining tasks locally is expressed as:
    Figure FDA0002840647080000076
    Figure FDA0002840647080000077
    the total execution latency of the offloaded task from user i to D2MD cluster head m and MEC is represented as:
    Figure FDA0002840647080000078
    Figure FDA0002840647080000079
    assuming that the task is allocated to be executed on both the local mobile terminal and the MEC server, the task L is executediIs the largest of the local execution time and the execution time on the MEC server or D2MD cluster head, so when a task is offloaded to the MEC, the total completion time is expressed as:
    Figure FDA0002840647080000081
    when a task is offloaded to the D2MD clusterhead, the total completion time is expressed as:
    Figure FDA0002840647080000082
    3.2 the benefit maximization problem;
    firstly, defining a utility function as a subtraction function between service income and cost; based on the utility function, a maximum profit problem is formulated; secondly, decomposing the original optimization problem into two optimization problems; finally, solving is carried out by adopting a greedy algorithm;
    1) utility functions and optimization problem formulas;
    the utility function is expressed as a decreasing function between the service revenue and the cost; the service revenue is expressed to include how much task data is obtained and how much computing resources are used; the cost includes the price of the allocated computing resources and the power required to transmit the data to the MEC; task L thereforei＝(σi,si,Ti) The utility function of (a) is expressed as:
    Figure FDA0002840647080000083
    wherein d ismRepresents the current state of cluster head m, D, of D2MDm1 indicates the working stateOtherwise dm0 means idle state; where κ and η represent the revenue factor per unit of offloaded data and the revenue factor per unit of power of the D2MD cluster head, respectively; ρ and β represent a price coefficient of computing resources per unit and a price coefficient of computing power allocated per unit time, respectively;
    Figure FDA0002840647080000084
    s.t.C1：
    Figure FDA0002840647080000085
    C2:
    Figure FDA0002840647080000086
    C3:
    Figure FDA0002840647080000087
    C4:
    Figure FDA0002840647080000091
    C5:
    Figure FDA0002840647080000092
    C6:
    Figure FDA0002840647080000093
    wherein the constraint C1 indicates that the tasks on the MEC server and on the local user device are computed in parallel; the restriction condition C2 indicates that the ue is guaranteed to be connected to only one full-duplex D2MD cluster head at a time; the restriction condition C3 indicates that the number of user equipments requiring simultaneous access to each D2MD cluster head cannot exceed its acceptable maximum value; the restriction condition C4 indicates that the allocated power of each D2MD cluster head cannot exceed its maximum transmission power; the constraint C5 indicates that the computational resources allocated to the MEC cannot exceed the maximum computational capacity of the MEC; the restriction condition C6 indicates that for each user equipment, its reverse link transmission rate is less than that of the forward link;
    2) optimizing problem transformation;
    due to the fact that
    Figure FDA0002840647080000094
    Is a binary variable, so the objective function (30) (i.e., equation 30) is a non-convex function; the original problem was a hybrid discrete non-convex optimization problem, and thus the optimization problem was an NP-hard problem; the method comprises the steps that an original reconstruction problem is decomposed into two sub-problems which are named as a User Selection Optimization (USO) problem and a Resource Allocation Optimization (RAO) problem respectively;
    for a fixed value X, the RAO problem is expressed as:
    Figure FDA0002840647080000095
    order to
    Figure FDA0002840647080000096
    Equation (31) is reconstructed as:
    Figure FDA0002840647080000097
    proposition 1: for task LiWill be offloaded to MEC or D2MD clusterhead, with optimal offload rate
    Figure FDA0002840647080000101
    Is that
    Figure FDA0002840647080000102
    The total execution time for compute offload is Ti(ii) a Is proved to be
    Figure FDA0002840647080000103
    When the computational load is assigned to the D2MD clusterhead, the gain from completing the task will be reduced based on equation (32) because of the increased proportion of the task load;
    order to
    Figure FDA0002840647080000104
    Integrating equations (30) and (31), and substituting the relevant variables to obtain:
    Figure FDA0002840647080000105
    Figure FDA0002840647080000106
    equation (32) is rewritten as:
    Figure FDA0002840647080000107
    s.t.C7:
    Figure FDA0002840647080000108
    C8:
    Figure FDA0002840647080000109
    C9:
    Figure FDA00028406470800001010
    3) solving an optimization problem;
    first, the solution of the RAO problem is discussed; to Zi,mMiddle xii,mThe second derivative of (d) is expressed as:
    Figure FDA0002840647080000111
    as can be seen from the proposition 1,
    Figure FDA0002840647080000112
    thus, the following steps are obtained:
    Figure FDA0002840647080000113
    in the same way, the method for preparing the composite material,
    Figure FDA0002840647080000114
    and is
    Figure FDA0002840647080000115
    Can obtain:
    Figure FDA0002840647080000116
    when in use
    Figure FDA0002840647080000117
    When equations (37) and (38) are combined:
    Figure FDA0002840647080000118
    thus obtaining
    Figure FDA0002840647080000119
    And function (39) (i.e., equation 39) is a convex function; the second derivative as the objective function (39) (i.e., equation 39) is strictly convergent; thus, the optimization problem of equation (39) is solved;
    for the solution of the USO problem, let
    Figure FDA00028406470800001110
    And
    Figure FDA00028406470800001111
    respectively representing the power allocated and the computing resources allocated in the access scheme of the user selection X; the optimal resource allocation result obtained by the algorithm is a 0-1 nonlinear optimization problem corresponding to the remaining user selection problems, and is also a complete NP problem.
  3. 3. The algorithm for mobile edge computing offload and resource allocation in a D2D multicast network according to claim 2, comprising the steps of:
    solving the problem that equation (39) applies the KKT condition; the lagrangian expression of equation (39) is:
    Figure FDA0002840647080000121
    for the
    Figure FDA0002840647080000122
    The KKT condition is expressed as:
    Figure FDA0002840647080000123
    Figure FDA0002840647080000124
    Figure FDA0002840647080000125
    Figure FDA0002840647080000126
    a 'here'i(ξi,m)＝JV/(J-Cξi,m)2Wherein
    Figure FDA0002840647080000127
    C＝weBTiσi，
    Figure FDA0002840647080000128
    Let [ y)]+Max { y,0}, in conjunction with equations (41) - (43), the lagrange multiplier is rewritten as:
    Figure FDA0002840647080000129
    Figure FDA0002840647080000131
    Figure FDA0002840647080000132
    where t is the number of iterations and δ (t) denotes the spacing of the t-th iteration; obtaining an optimal resource allocation result by utilizing a KKT condition; optimal xii,mObtained from formulae (45) - (48); obtaining optimum according to equations (32) and (33)
    Figure FDA0002840647080000133
    And
    Figure FDA0002840647080000134
    for the solution of the USO problem, a greedy algorithm is adopted to obtain the optimal user selection, and the details of the specific algorithm are as follows:
    the algorithm is as follows: greedy algorithm
    Inputting:
    the set of user equipments is represented as: k ═ 1,2, L, K }
    The maximum number of iterations is: i is
    The working set of D2MD clusterheads is represented as:
    D＝{d1,d2,L,dM}
    the tasks of the user equipment are represented as: l isi＝(σi,si,Ti)
    Defining B, p simultaneouslym,pi,we,κ,ρ,η,β
    And (3) outputting:
    adopted resource allocation strategy A*,B*,O*
    Adopted user selection policy X*
    Figure FDA0002840647080000135
    Figure FDA0002840647080000141
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