CN112000481A - Task unloading method for maximizing computing capacity of D2D-MEC system - Google Patents

Task unloading method for maximizing computing capacity of D2D-MEC system Download PDF

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CN112000481A
CN112000481A CN202010864792.2A CN202010864792A CN112000481A CN 112000481 A CN112000481 A CN 112000481A CN 202010864792 A CN202010864792 A CN 202010864792A CN 112000481 A CN112000481 A CN 112000481A
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tasks
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CN112000481B (en
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孙一鹏
李峰
苏聪聪
杜佩儒
刘杰民
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Northeastern University Qinhuangdao Branch
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Abstract

The invention discloses a task unloading method for maximizing computing capacity of a D2D-MEC system, which comprises the following steps: s1: building a system model and a task allocation model to establish an execution position of each calculation task on each local device; s2: constructing a local computing model, a wireless channel model, a D2D unloading model and an MEC server unloading model to obtain the execution delay and energy consumption of each computing task in the system; s3: establishing an objective function P1 for solving the maximum computing capacity of the system; s4: the objective function P1 is decomposed and divided into two parts, P2 and P3, and solved. The invention utilizes the D2D technology to expand the computing capacity of the traditional MEC server, more computing tasks are unloaded to the D2D equipment to be executed, and the D2D equipment suitable for the computing tasks is selected, thereby realizing the maximization of the computing capacity.

Description

Task unloading method for maximizing computing capacity of D2D-MEC system
Technical Field
The invention relates to the technical field of mobile edge computing, in particular to a task unloading method for maximizing computing capacity of a D2D-MEC system.
Background
In recent years, with the increase of computing power of mobile devices and the rapid development of a large number of IoT devices, data required to be computed in a network is in an explosive growth trend. Although the cloud computing mode can compute and store a large amount of data, the transmission delay from the user side to the cloud center is long, so that the computing with high real-time requirements cannot be processed. And the appearance of a large number of mobile devices such as mobile phones, sensors and wearable devices makes the calculation data amount more huge, and the traditional centralized storage mode is easy to cause network congestion. And the current appearance of the internet of things, the internet of vehicles and the smart city makes the requirement of the user on calculating the time delay more and more urgent, and the requirement of the user is more biased to the real-time property. This has prompted the emergence of a low-latency and practical computational paradigm, Mobile Edge Computing (MEC), which shifts the original computational task from the center side to the Edge side. The computing paradigm deploys an edge server with some computing and storage capability closer to the end of the mobile user, such as a base station connected to a cell phone or a home wireless network access point. Compared to the more distant and computationally centric cloud computing model, the MEC computing paradigm is closer to the mobile edge devices, which are closer in distance and have nearly the same computing and storage capabilities as cloud computing.
Currently, the research on computational offloading in the MEC is to optimize the time delay of the processing task inside the system, or optimize the energy consumption of the processing task of the mobile device, or optimize both in a weighted manner. The offloading only considers the computation offloading to the MEC server, but the MEC server is built near one end of the mobile device, and does not always have a large amount of computation resources and high-speed bandwidth like a cloud server. The computational and bandwidth resources of the servers in the MEC system are limited and the total amount of their processing computational tasks is limited.
Disclosure of Invention
The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a task offloading method for maximizing the computing power of a D2D-MEC system, which utilizes a D2D technology to expand the computing power of a traditional MEC server, offload more computing tasks to D2D devices for execution, and select D2D devices suitable for the computing tasks, thereby maximizing the computing power.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a task offloading method for maximizing computing power of a D2D-MEC system, the D2D-MEC system comprising an MEC server, a plurality of local devices and a plurality of D2D devices, each local device generating a plurality of computing tasks; the method comprises the following steps:
s1: building a system model and a task allocation model to establish an execution position of each computing task on each local device;
s2: constructing a local computing model, a wireless channel model, a D2D unloading model and an MEC server unloading model to obtain the execution delay and energy consumption of each computing task in the system;
s3: establishing an objective function P1 for solving the maximum computing capacity of the system;
s4: the objective function P1 is decomposed: firstly, solving the problem of maximizing the number of tasks executed on D2D equipment matched with a single local equipment, namely P2, obtaining the maximum number of computing tasks on all local equipment placed on the D2D equipment, and meanwhile, solving task unloading strategies of the computing tasks according to the part of tasks; secondly, for the rest tasks which cannot be executed on the D2D device, the local device unloads the tasks to the MEC server for execution, and the target P3 is solved.
Further, in step S1, the system model is:
the local devices are represented by the set K {1, 2.,. K }, the computing tasks on each local device are represented by the set M {1, 2.,. M }, and the D2D devices that each local device can match are represented by the set Ik＝{i1,i2,i3,...,inRepresents; the remaining energy consumption of each D2D device is integrated into
Figure BDA0002649381590000031
Using three-dimensional vectors for a single computational task
Figure BDA0002649381590000032
Represents;
wherein, bm，kWhich represents the size of the computing task,
Figure BDA0002649381590000033
representing the number of CPU cycles required to compute a task,
Figure BDA0002649381590000034
represents the maximum computation tolerance time of the computation task;
further, in step S1, the task allocation model is:
in the D2D-MEC system, each computation task execution of each local device is divided into three positions, namely the local device, the D2D device or the MEC server; the parameter pi is used as a task allocation policy to first decide where to perform each computational task:
Figure BDA0002649381590000035
Figure BDA0002649381590000036
wherein pi (m, k) ═ 0 represents that the computation task m fails to execute; pi (m, k) ═ 1 represents that the calculation task m is successfully calculated; pi (m, k) ═ xl,m,kMeaning that the computing task m is executed in the local device, pi (m, k) ═ xD,m,k,iIndicating that the computing task m is executed in the D2D device through the D2D link, pi (m, k) ═ xS,m,kIndicating that the computing task m is executed in the MEC server.
Further, in step S2, the local computation model is:
if the computation task m is executed in the local device k, pi (m, k) ═ xl,m,kThen the local device k is localThe time taken to perform the task is:
Figure BDA0002649381590000037
in the formula (f)kRepresents the computational resources of the local device k;
in addition, the energy consumption of the local device k for processing and executing the task is as follows:
Figure BDA0002649381590000038
wherein, the effective capacitance parameter is related to the chip structure of the device.
Further, in the step S2, in the D2D offload model and the MEC server offload model, an orthogonal frequency division multiple access method is used for channel access; the wireless channel model comprises a D2D wireless channel model and an MEC server wireless channel model:
(2-1) D2D Wireless channel model
The MEC server allocates a bandwidth B quota between each local device k and the D2D device over the D2D linkDFor each local device k, the data rate is:
Figure BDA0002649381590000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002649381590000042
transmission Power offloaded for D2D between local device k and device i, HD,k,iIt is shown that the channel gain is,
Figure BDA0002649381590000043
representing the transmission distance between a local device k and a device i, beta representing a path loss parameter, and N representing a gain white Gaussian noise;
(2-2) MEC Server Wireless channel model
For MEC clothesServer offload mode, MEC server allocates sub-bandwidth to local device k
Figure BDA0002649381590000044
And computing resources, then the local device k allocates its tasks to the MEC server at the data rate:
Figure BDA0002649381590000045
in the formula (I), the compound is shown in the specification,
Figure BDA0002649381590000046
is the uplink transmission power, H, between the local device k and the serverS,kRepresenting the channel gain between the local device k and the server,
Figure BDA0002649381590000047
represents the transmission distance between the local device k and the server, BS,kRepresents the bandwidth allocated to the local device k by the MEC service, and bandwidth BS,kThe conditions are satisfied:
Figure BDA0002649381590000048
in the formula (I), the compound is shown in the specification,
Figure BDA0002649381590000049
representing the total bandwidth available to the MEC server.
Further, in step S2, the D2D unloading model is:
for a task that is not executing in the local device, it is first offloaded to the neighboring D2D device, and the execution time of each D2D device is:
Figure BDA0002649381590000051
in the formula (f)iRepresenting the computing resources that D2D device i can provide;
corresponding energy consumption consumed by D2D device i:
Figure BDA0002649381590000052
uplink transmission delay between local device k and D2D device i:
Figure BDA0002649381590000053
the corresponding transmission energy consumption is as follows:
Figure BDA0002649381590000054
the new set of a single local device k and its matching D2D devices is:
Yi,k＝{i1,i2,...,in,k}
wherein the new set of computing resources of each D2D device is:
Figure BDA0002649381590000055
wherein the remaining energy consumption set of each D2D device is:
Figure BDA0002649381590000056
the conditions are satisfied for the computational tasks offloaded onto D2D device i:
Figure BDA0002649381590000057
the above conditions indicate that the overall energy consumption of a single D2D device to perform a task cannot exceed the remaining energy of the device.
Further, in step S2, the MEC server uninstall model is:
if the computing task data is large enough, the maximum tolerant delay is small, or the local device in the system does not have an additional D2D device, unloading the residual tasks m of the local device k to the MEC server; then the MEC server calculates the delay as:
Figure BDA0002649381590000061
in the formula (f)S,kComputing resources allocated to the local device k for the MEC server;
the transmission delay of the local device k when unloading the task to the MEC server is as follows:
Figure BDA0002649381590000062
the corresponding energy consumption is as follows:
Figure BDA0002649381590000063
further, in step S3, the number of tasks processed by the system is represented as the computing capacity of the system, the problem of maximizing the computing capacity of the whole system is modeled as an objective function P1, and an optimal offloading policy, an optimal bandwidth allocation policy, and a computing resource allocation policy are solved while ensuring various constraints:
P1:
Figure BDA0002649381590000064
conditions are as follows:
C1：
Figure BDA0002649381590000065
C2：
Figure BDA0002649381590000066
C3：
Figure BDA0002649381590000067
C4：
Figure BDA0002649381590000068
C5：
Figure BDA0002649381590000069
C6：
Figure BDA0002649381590000071
C7：
Figure BDA0002649381590000072
C8：
Figure BDA0002649381590000073
C9：
Figure BDA0002649381590000074
C10：
Figure BDA0002649381590000075
C11：
Figure BDA0002649381590000076
among the constraints mentioned above, constraints C1, C2, and C3 are integer constraints that ensure that each computation task m selects only one position for computation; constraint C4 ensures that each local device and D2D device is assigned at least one task; constraint C5 ensures that each computation task m completes within the maximum tolerated delay; constraint C6, C7
Figure BDA0002649381590000078
Representing the remaining energy of the local device k,
Figure BDA0002649381590000079
representing the residual energy of the local device i, and ensuring that the energy consumed by the computing tasks of the device k and the device i does not exceed the residual energy of the device itself by the constraints C6 and C7; constraint C8 ensures that the computing resources allocated by the MEC server to all local users cannot exceed the total amount of computing resources of the server, i.e., the total amount of computing resources of the MEC server.
Further, in step S4, in order to maximize the computing capacity of the system and improve the utilization rate of the wireless resources, when performing task offloading decision, tasks are preferentially allocated to the D2D device for execution, and the computing capacity of D2D is maximized first; for this purpose, the objective function P1 is decomposed, and the modeling problem of the maximum computing power of D2D is extracted, so that the problem of the maximum computing power of D2D is modeled as the objective function P2:
P2:
Figure BDA0002649381590000077
conditions are as follows:
C12：
Figure BDA0002649381590000081
C13：
Figure BDA0002649381590000082
the goal of P2 is to be x (m, k) ═ xD,m,k,iThe calculation tasks of (2) are used for solving the maximum value of the sum, which means that the more calculation tasks are distributed to the D2D, the more the target value is, the better the target value is, the target is an integer linear programming problem, and in order to solve the target value, the number of the calculation tasks distributed to the D2D is enabled to reach the maximum value, the calculation tasks are firstly distributed according to the energy remained on the D2D equipment;
the solving algorithm of the target is as follows: firstly, the task sets M are arranged in descending order according to the size of bytes, and then the residual energy consumption sets O are arrangedESize of (D2D) to D2D device set IkPerforming ascending ranking, then putting the larger computing task into the D2D device with smaller residual energy, and then putting the small computing task, and marking the D2D device in which each computing task is specifically placed(ii) a Thus, the residual energy of the D2D equipment can be maximally utilized to put more calculation tasks, and the goal of P2 is achieved;
after the D2D equipment in which each calculation task is placed is obtained, the tasks and the equipment can be marked, and an optimal D2D unloading strategy set pi is obtained;
finally, the computing task set M remained after the computing tasks executed by the D2D equipment reach the maximum value*＝{m1,m2,m3,...,miThe tasks are executed at the local device or the MEC server, and the target P3 is a policy set for maximizing the number of executed computing tasks:
P3:
Figure BDA0002649381590000083
conditions are as follows:
C14：
Figure BDA0002649381590000084
C15：
Figure BDA0002649381590000085
C16：
Figure BDA0002649381590000086
C17：
Figure BDA0002649381590000091
c14 is the maximum tolerated time for the MEC server to compute and transmit the sum of the delays and meet the task, the single device based multitask execution on the server is assumed to be executed in parallel; c15 is that the transmission power allocated to D2D and the transmission power of the MEC server satisfy the local device's own maximum transmission power constraint; c16 is the remaining energy of the device that must be satisfied for the task to be delivered to the server;
the above function is a linear programming problem, two boundary values of the programming problem are considered, and therefore a corresponding unloading strategy solution can be obtained.
Further, in the step S4, the following two boundary value conditions are considered:
(1) when the MEC server does not allocate bandwidth resources and computational resources to the local device, the computational tasks generated by the local device are all performed locally or by the D2D device, i.e.
Figure BDA0002649381590000092
In this case, according to the constraint conditions:
xs,m,k＝0，xl,m,k＝1 (16)
(2) when all resources of the whole D2D-MEC system are fully allocated, the various resources of the MEC server are full, and at this time, the number of system processing tasks is maximized, that is, when bandwidth resources, computing resources and transmission power are fully allocated:
Figure BDA0002649381590000101
in this case, according to the constraint conditions:
xs,m,k＝1，xl,m,k＝0 (18)
the computing resources and bandwidth resources of the MEC server are fixed, and if some tasks cannot be completed in the scheduling, the MEC server waits for the next suboptimal scheduling to be completed in the task queue.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
the invention introduces the D2D technology into an MEC unloading system to form a D2D-MEC system, and utilizes adjacent idle equipment to increase the computing capacity in the system. The invention realizes that the computing task processing of the local device and the D2D device reaches the maximum, and simultaneously considers the time delay constraint and the energy consumption constraint, thereby being more close to the practical situation.
The D2D-MEC system constructed by the invention comprises a server, a plurality of mobile devices and a plurality of computing tasks. The computing tasks generated by each local device may choose to select different locations for execution based on the proposed optimal offloading policy algorithm. The computing tasks in the local task queue are executed locally by decision selection, D2D execution, or MEC server execution. The computing tasks selected for offloading by D2D may be offloaded to one D2D device or to multiple D2D devices for execution.
Drawings
FIG. 1 is a D2D-MEC system diagram of the present invention;
FIG. 2 is a diagram of a computational model of the present invention.
Detailed Description
The above description is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clear, the present invention is further described below with reference to the accompanying drawings and embodiments.
As shown in fig. 1, the D2D-MEC system includes one MEC server, a plurality of local devices, each generating a plurality of computing tasks, and a plurality of D2D devices.
As shown in FIG. 2, the invention discloses a task unloading method for maximizing the computing capacity of a D2D-MEC system, which comprises the following steps:
s1: a system model is built, and a task allocation model is built to establish the execution location of each computing task on each local device.
For the computing task on each local device, the execution position is unique but not fixed, and in order to represent the execution position of each task, a task allocation model as described in (2.1) below is constructed.
S2: and constructing a local computing model, a wireless channel model, a D2D unloading model and an MEC server unloading model to obtain the execution delay and energy consumption of each computing task in the system.
To meet the energy consumption constraint, the maximum computation task per equipment load cannot exceed the remaining energy consumption of the equipment. Second, after each computing task has selected an execution location, both the transmission and execution of the computing task must be completed within the maximum tolerated latency of the task.
S3: according to the following descriptions (2.2) to (2.5), an objective function P1 for solving the maximum calculation power of the system is established.
The objective function P1 is to solve the maximum computing power of the system, which is expressed by the number of tasks that can be performed. The solution of the objective function is complex, and in order to solve the optimization problem of the objective, the method is decomposed into two parts for solution.
S4: the objective function P1 is decomposed: firstly, solving the problem of maximizing the number of tasks executed on D2D equipment matched with a single local equipment, namely P2, obtaining the maximum number of calculation tasks on all local equipment placed on the D2D equipment, and simultaneously solving task unloading strategies of the calculation tasks aiming at the part of the tasks; secondly, for the rest tasks which cannot be executed on the D2D device, the local device unloads the tasks to the MEC server for execution, and the target P3 is solved.
The solution of the P2 problem is obtained by using iterative algorithm 1, and after the result is obtained, the summation of all local devices obtains the maximum number of computing tasks placed on the D2D device on all local devices, and the task unloading strategy can also be obtained for the part of tasks, namely (2.1) below. For the remaining tasks that are not executed on the D2D device, the local device will offload the computing tasks to the MEC server for execution. Where the MEC server allocates a corresponding task upload bandwidth resource, transmission power to each local device, and Virtual Machines (VMs) allocated for each device to perform the computational tasks, the server allocates corresponding computational resources. This part can be seen clearly in fig. 2.
Algorithm 2 is an overall algorithm for the above process, and in order to obtain the allocation strategy of each task, the server allocates the bandwidth resource, transmission power and calculation resource to the local device. By centering on the tasks and distributing the tasks, the number of the tasks executed in the system can be maximized, and the optimization result of the target P1 can be obtained. The unknowns in target P1 are policy x, bandwidth resource B, compute resource f, which
Firstly, a system model:
the D2D-MEC system of the present invention includes an MEC server, a plurality of local devices, each generating a plurality of computing tasks, and a plurality of D2D devices. The invention takes the task as the center, optimizes the execution position of the task: namely, local execution, D2D device execution, and MEC server execution.
The D2D-MEC system is shown in fig. 1, where K1-K5 are local devices and I1-I3 are D2D devices, all of which are under the coverage of one MEC server. The K1 equipment generates a calculation task and transmits the calculation task to the I1 equipment by using D2D; the computing task generated by the K2 equipment is transmitted to the MEC server to be executed; the computation task generated by K3 is executed locally; the computational tasks generated by K4 may be transmitted to multiple D2D devices, such as I2, I3. This system diagram illustrates the present invention as task centric, where the task itself can be selected for execution. The computing tasks selected for offloading by D2D may be offloaded to one D2D device, such as the K1 device in FIG. 1, or to multiple D2D devices for execution, such as the K4 device in FIG. 1.
FIG. 2 is a model diagram of a task offloading method for maximizing computing power of a D2D-MEC system according to the present invention. And the computing task generated by the local equipment selects different equipment to execute through decision. To the computing tasks of the MEC server, the server allocates the corresponding bandwidth and computing resources and provides a Virtual Machine (VM) for each device to perform the computing tasks.
Second, mathematic model
The local devices are represented by the set K {1, 2.. K, }, the computing tasks on each local device are represented by the set M {1, 2...., M }, and the D2D devices that each local device can match are represented by the set Ik＝{i1,i2,i3,...,inRepresents; these matching D2D devices will help the local user perform the computing task when the local user is unable to perform the computing task on time. The remaining energy consumption of each D2D device is integrated into
Figure BDA0002649381590000131
Using three-dimensional vectors for a single computational task
Figure BDA0002649381590000132
Represents;
wherein, bm，k(bits) denotes the size of the computational task,
Figure BDA0002649381590000133
indicating the number of CPU cycles required to compute the task,
Figure BDA0002649381590000134
representing the maximum computation tolerance time of the computation task.
In the system of the present invention, each local device can only connect to nearby devices through a D2D link, while each D2D device can only provide computational assistance when it is done its own task or has spare computational resources. Furthermore, each computing task m can only compute locally, on a D2D device or on an MEC server.
For a single computing task on a single device, the goal is to find the most suitable execution location, first considering which device in the D2D set, the remaining tasks will be executed locally or uploaded to the MEC server for execution, and the MEC server will allocate sub-bandwidth, computing resources, transmission power according to the total amount of remaining tasks on these devices.
In addition, the system also has some limitations: (1) each local device has a channel connected with the MEC server or D2D device, and is stable and not interfered with each other; (2) the computing resources of the MEC server are fixed and limited; (3) there is one hop to route the distance between local devices and the D2D device; (4) all tasks are independent; (5) maximum tolerated time for all tasks
Figure BDA0002649381590000144
Are all the same.
(2.1) task assignment model
In the D2D-MEC system of the present invention, each computing task execution of each local device can be divided into three locations, namely local, D2D, or MEC server. Therefore, first a decision is made where to perform each computational task, for which the invention employs the parameter π as a task allocation policy.
Figure BDA0002649381590000141
Figure BDA0002649381590000142
Wherein pi (m, k) ═ 0 represents that the computation task m fails to execute; pi (m, k) ═ 1 represents that the calculation task m is successfully calculated; pi (m, k) ═ xl,m,kMeaning that the computing task m is executed in the local device, pi (m, k) ═ xD,m,k,iIndicating that the computing task m is executed in the D2D device through the D2D link, pi (m, k) ═ xS,m,kIndicating that the computing task m is executed in the MEC server.
(2.2) local computation model
If the computation task m is executed in the local device k, pi (m, k) ═ xl,m,kThen the time it takes local device k to perform the task locally is:
Figure BDA0002649381590000143
in the formula (f)k(CPU cycles/s) represents the computing resources of local device k.
In addition, the energy consumption of the local device k for processing and executing the task is as follows:
Figure BDA0002649381590000151
wherein, the effective capacitance parameter is related to the chip structure of the device.
(2.3) Wireless channel model
In the D2D offload model and the MEC server offload model, an Orthogonal Frequency Division Multiple Access (OFDMA) method is employed for channel access.
(2.3.1) D2D Wireless channel model
The MEC server is connected with each local device k and D through a D2D linkAllocating a rated bandwidth B between 2D devicesD. For each local device k, the data rate is:
Figure BDA0002649381590000152
in the formula (I), the compound is shown in the specification,
Figure BDA0002649381590000153
transmission Power offloaded for D2D between local device k and device i, HD,k,iIt is shown that the channel gain is,
Figure BDA0002649381590000154
denotes a transmission distance between the local device k and the device i, β denotes a path loss parameter, and N denotes gain white Gaussian noise AWGN (additive white Gaussian noise).
(2.3.2) MEC Server Wireless channel model
For MEC server offload mode, the MEC server allocates sub-bandwidth to local device k
Figure BDA0002649381590000158
And computing resources. The local device k then allocates its tasks to the MEC server at the data rate:
Figure BDA0002649381590000155
in the formula (I), the compound is shown in the specification,
Figure BDA0002649381590000156
is the uplink transmission power, H, between the local device k and the serverS,kRepresenting the channel gain between the local device k and the server,
Figure BDA0002649381590000157
represents the transmission distance between the local device k and the server, BS,kRepresenting the bandwidth allocated to the local device k by the MEC service.
Bandwidth BS,kMust be full ofFoot conditions:
Figure BDA0002649381590000161
Figure BDA0002649381590000162
representing the total bandwidth available to the MEC server.
(2.4) D2D unloading model
For tasks that are not executed in the local device, which will be offloaded first to the neighboring D2D device, the execution time of D2D device i is:
Figure BDA0002649381590000163
in the formula (f)i(CPU cycles/s) represents the computing resources that D2D device i can provide;
corresponding energy consumption consumed by D2D device i:
Figure BDA0002649381590000164
uplink transmission delay between local device k and D2D device i:
Figure BDA0002649381590000165
the corresponding transmission energy consumption is as follows:
Figure BDA0002649381590000166
since the return delay of the task results is very small, the delay of task return is ignored in the system model of the present invention.
The new set of a single local device k and its matching D2D devices is:
Yi,k＝{i1,i2,...,in,k}
wherein the new set of computing resources of each D2D device is:
Figure BDA0002649381590000171
wherein the remaining energy consumption set of each D2D device is:
Figure BDA0002649381590000172
the conditions are satisfied for the computational tasks offloaded onto D2D device i:
Figure BDA0002649381590000173
the above conditions indicate that the overall energy consumption of a single D2D device to perform a task cannot exceed the remaining energy of the device.
(2.5) MEC Server offload model
If the task data is large enough, the maximum tolerated delay is small, or the local devices in the system do not have additional D2D devices, the remaining computing tasks m of the local devices k are offloaded to the MEC server where they are executed. Then the MEC server calculates the delay as:
when the MEC server calculates the time delay as follows:
Figure BDA0002649381590000174
in the formula (f)S,kComputing resources allocated to the local device k for the MEC server; since the MEC server is in a continuously powered state, the energy consumption required for the MEC server computation task and the computation results returned to the local device k are not considered.
The transmission delay of the local device k when unloading the task to the MEC server is as follows:
Figure BDA0002649381590000175
the corresponding energy consumption is as follows:
Figure BDA0002649381590000176
because the calculation result processed by the MEC server is very small, the invention ignores the time delay of the return of the processing result.
Modeling method for maximum computing capacity of (III) system
The objective function adopts the calculation capability maximization of the D2D-MEC system which is closer to the reality, because in the calculation unloading of the traditional MEC system or after the D2D technology is introduced, the minimization of the processing task delay and the minimization of the energy consumption of the mobile equipment in the system are more concerned, but in the practical application, the calculation capability of the MEC server is usually limited, so how to maximize the calculation capability of the whole system under the condition of ensuring to meet the delay constraint and the energy consumption constraint is a key problem to be solved. Therefore, the task number processed by the system is represented by the computing capacity of the system, the problem of maximizing the computing capacity of the whole system is modeled as a problem P1, and the optimal unloading strategy, the optimal bandwidth allocation strategy and the optimal computing resource allocation strategy are solved under the condition of ensuring various constraints.
P1:
Figure BDA0002649381590000181
Conditions are as follows:
C1：
Figure BDA0002649381590000182
C2：
Figure BDA0002649381590000183
C3：
Figure BDA0002649381590000184
C4：
Figure BDA0002649381590000185
C5：
Figure BDA0002649381590000186
C6：
Figure BDA0002649381590000187
C7：
Figure BDA0002649381590000188
C8：
Figure BDA0002649381590000189
C9：
Figure BDA0002649381590000191
C10：
Figure BDA0002649381590000192
C11：
Figure BDA0002649381590000193
of the above, constraints C1, C2, C3 are integer constraints that ensure that only one position is selected for computation per computation task m. Constraint C4 ensures that each local device and D2D device is assigned at least one task. Constraint C5 ensures that each computation task m completes within the maximum tolerated delay. Constraint C6, C7
Figure BDA0002649381590000194
Representing the remaining energy of the local device k,
Figure BDA0002649381590000195
representing residual energy of local device i, constraints C6, C7 guaranteeThe energy consumed by the computing tasks of the standby device k and the device i does not exceed the residual energy of the device. Constraint C8 ensures that the computing resources allocated by the MEC server to all local users cannot exceed the total amount of computing resources of the server, i.e., the total amount of computing resources of the MEC server. The above equations (2), (6) and (9) are constraints C3, C9 and C10.
For the meaning of maximizing the original objective function of the local equipment and maximizing the number of processing tasks of the D2D equipment, the invention makes a similar assumption scene I as follows, and assumes that only one local equipment and two D2D equipment matched with the local equipment and the D2D equipment are arranged in the system. The local device generates three computing tasks a, b, c, which consume 3, 4, 5 of processing power, 1 of transmission power consumption for the three tasks, and 2 of local device remaining power, 6 and 7 of two D2D devices E, F. The processing power of the MEC server is ignored.
Under the above conditions, the local device cannot process 3 computation tasks, but satisfies the transmission power consumption of 3 tasks. The local device will now transmit the computing task to D2D devices E, F. At this point a decision is encountered as to which D2D device the 3 computation tasks are offloaded.
The general decision making method is as follows: and F, randomly distributing the computing task c to F, so that the residual energy of the equipment E is 6, for the computing task a being 3, for the computing task b being 4, only one task a or b can be distributed, so that the residual energy distributed to F is 2, and for the computing task E, the residual energy distributed to a is 3. Only two tasks can be performed in this case.
Post-optimization decision (last column in table below): the computing tasks a and b are allocated to the device F, and a + b is 7, which just satisfies the remaining energy of F and can be allocated. The computing task c is assigned to device E, c 5<6, so it can be assigned. Under this strategy, the system can complete three computational tasks.
The policy matrix for the above problem is:
a 1(E) 1(E) 0 1(F)
b 1(F) 0 1(E) 1(F)
c 0 1(F) 1(F) 1(E)
∑π 2 2 2 3
the last column in the policy matrix of the above example is the optimal allocation scheme, so according to the above example, the sub-problem of the present invention is to find the D2D partially optimal offloading policy scheme.
Similar to the scenario assumed above, our optimization goal is to find an optimal offloading strategy to maximize the number of computing tasks that can be performed by the local and D2D devices, so as to meet the optimization goal of maximizing the computing power of the D2D-MEC system proposed by the present invention. The remaining computing tasks that are not allocated are then uploaded to the MEC server for execution.
(3.1) task allocation strategy for maximizing computing power of D2D
From the foregoing analysis, in order to maximize the computing power of the system and improve the utilization rate of the wireless resources, the tasks are preferentially allocated to the D2D device for execution when the task offloading decision is made, so that the maximization of the computing power of the D2D is achieved first. For this reason, the part decomposes the problem P1, extracts the D2D computational power maximization modeling problem, and since the D2D equipment does not relate to the bandwidth allocation and computational resource allocation problems of the MEC server in task unloading decision, the D2D computational power maximization problem is modeled as a problem P2, and the aim is to solve the problem of pi (m, k) xD,m,k,iThe calculation task of (2) is to find the maximum value of the sum thereof, indicating that the more calculation tasks are allocated to D2D, the better the target value.
P2:
Figure BDA0002649381590000211
Conditions are as follows: c12:
Figure BDA0002649381590000212
C13：
Figure BDA0002649381590000213
C1，C2，C3，C4，C6
c12 is obtained by deforming C7.
The P2 objective is an integer linear programming problem, and to solve the objective value such that the number of computational tasks assigned by D2D is maximized, the computational tasks are first assigned according to the energy retained on the device. The solution of the target is obtained through an algorithm 1, wherein the algorithm 1 firstly arranges the task set M in a descending order according to the byte size and then arranges the task set M according to the residual energy consumption set OESize of (D2D) to D2D device set IkIn ascending order, then put the larger computing task into the D2D device with less remaining energy first, and put the smaller computing task second, while marking each meterThe calculation task is specifically placed in which D2D device, so that the residual energy of the D2D device can be maximally utilized to place a larger number of calculation tasks to achieve the goal of P2. After finding in which D2D device each computing task is placed, tasks and devices can be labeled to find the optimal D2D offload policy set pi.
And finally, unloading the computing tasks which are remained after the computing tasks executed by the D2D equipment reach the maximum value to an MEC server for execution, and solving the target P3.
Algorithm 1: D2D task allocation algorithm that maximizes computational power.
Figure BDA0002649381590000214
Figure BDA0002649381590000221
Figure BDA0002649381590000231
For a single local device, the invention is multi-device, so that a maximum number of offloads of the overall task is required, for m of them*Summing is performed for multiple local devices.
(3.2) bandwidth allocation and computing resource allocation policy of MEC server
Set of remaining computing tasks M*＝{m1,m2,m3,...,miThese tasks are performed at the local device or MEC server. The goal P3 is the set of policies that maximizes the number of computing tasks performed by this portion.
P3:
Figure BDA0002649381590000232
Conditions are as follows:
C14：
Figure BDA0002649381590000233
C15：
Figure BDA0002649381590000234
C16：
Figure BDA0002649381590000235
C17：
Figure BDA0002649381590000236
c14 is the maximum tolerated time for the sum of the MEC server computation and transmission delays to meet the task, assuming that single device based multitasking is performed in parallel on the server. C15 is that the transmission power allocated to D2D and the transmission power of the MEC server satisfy the local device's own maximum transmission power constraint. C16 is the remaining energy of the device that must be satisfied for the server to transfer the task.
The above function is a linear programming problem, two boundary values of the programming problem are considered, and therefore a corresponding unloading strategy solution can be obtained.
The following two boundary value conditions are considered:
(1) when the MEC server does not allocate bandwidth resources and computational resources to the local device, the computational tasks generated by the local device are all performed locally or by the D2D device, i.e.
Figure BDA0002649381590000241
In this case, according to the constraint conditions:
xs,m,k＝0，xl,m,k＝1 (16)
(2) when all resources of the entire D2D-MEC system are fully allocated, the MEC server various resources are filled. At this time, the number of system processing tasks reaches the maximum, namely bandwidth resources, computing resources and transmission power are completely distributed.
Figure BDA0002649381590000242
In this case, according to the constraint conditions:
xs,m,k＝1，xl,m,k＝0 (18)
the computing resources and bandwidth resources of the MEC server are fixed, and if some tasks cannot be completed in the scheduling, the tasks can only be completed by waiting for next sub-optimal scheduling in the task queue.
Through the analysis, the invention provides a task allocation algorithm for maximizing the computing capacity of the D2D-MEC system, and the specific description is shown as algorithm 2.
And 2, algorithm: task allocation algorithm for maximizing computing power of D2D-MEC system
1 inputting various parameter values;
2 initialization policy set
Figure BDA0002649381590000251
3 if D2D device non-empty pocket
4, solving the maximum task number contained in a single task by using an algorithm 1;
5 summing the computing tasks distributed by D2D to all local devices in the system
Figure BDA0002649381590000252
6 end if }; first, algorithm 1 is used to find the maximum number of computing tasks assigned by D2D.
7 if
Figure BDA0002649381590000253
{// D2D Equipment is full of assigned computing tasks and there is a remainder of computing tasks, which are assigned to MEC Server
8 solving for P2, use case 2;
9 obtaining optimal distribution
Figure BDA0002649381590000254
10 update strategy set pi*(m,k)；
11 end if }; v/after the calculation task is distributed to the MEC, the strategy value of the task is modified
12, outputting: pi*(m,k)，
Figure BDA0002649381590000255
The algorithm 2 is that the computing tasks generated by the local devices are firstly distributed to the D2D devices, the optimal computing device is found, then the rest computing tasks are uploaded to the MEC server to be executed, the distribution strategy of each computing task is updated in real time, the computing capacity in the D2D-MEC system is maximized, and the core goal of maximizing the number of processing tasks is achieved under the condition that various constraints are met.

Claims (10)

1. A task offloading method for maximizing computing power of a D2D-MEC system, the D2D-MEC system comprising an MEC server, a plurality of local devices and a plurality of D2D devices, each local device generating a plurality of computing tasks; the method is characterized in that: the method comprises the following steps:
s1: building a system model and a task allocation model to establish an execution position of each calculation task on each local device;
s2: constructing a local computing model, a wireless channel model, a D2D unloading model and an MEC server unloading model to obtain the execution delay and energy consumption of each computing task in the system;
s3: establishing an objective function P1 for solving the maximum computing capacity of the system;
s4: the objective function P1 is decomposed: firstly, solving the problem of maximizing the number of tasks executed on D2D equipment matched with a single local equipment, namely P2, obtaining the maximum number of computing tasks on all local equipment placed on the D2D equipment, and meanwhile, solving task unloading strategies of the computing tasks according to the part of tasks; secondly, for the rest tasks which cannot be executed on the D2D device, the local device unloads the tasks to the MEC server for execution, and the target P3 is solved.
2. The method of task offloading with maximized computing power for D2D-MEC system of claim 1, wherein: in step S1, the system model is:
the local devices are represented by the set K {1, 2.,. K }, the computing tasks on each local device are represented by the set M {1, 2.,. M }, and the D2D devices that each local device can match are represented by the set Ik＝{i1,i2,i3,...,inRepresents; the remaining energy consumption of each D2D device is integrated into
Figure FDA0002649381580000011
Using three-dimensional vectors for a single computational task
Figure FDA0002649381580000012
Represents;
wherein, bm，kWhich represents the size of the computing task,
Figure FDA0002649381580000013
representing the number of CPU cycles required to compute a task,
Figure FDA0002649381580000014
representing the maximum computation tolerance time of the computation task.
3. The method of task offloading with maximized computing power for D2D-MEC system of claim 2, wherein: in step S1, the task allocation model is:
in the D2D-MEC system, each computation task execution of each local device is divided into three positions, namely the local device, the D2D device or the MEC server; the parameter pi is used as a task allocation policy to first decide where to perform each computational task:
Figure FDA0002649381580000021
Figure FDA0002649381580000022
wherein pi (m, k) ═ 0 represents that the computation task m fails to execute; pi (m, k) ═ 1 represents that the calculation task m is successfully calculated; pi (m, k) ═ xl,m,kMeaning that the computing task m is executed in the local device, pi (m, k) ═ xD,m,k,iIndicating that the computing task m is executed in the D2D device through the D2D link, pi (m, k) ═ xS,m,kIndicating that the computing task m is executed in the MEC server.
4. The method of task offloading with maximized computing power for D2D-MEC system of claim 3, wherein: in step S2, the local computation model is:
if the computation task m is executed in the local device k, pi (m, k) ═ xl,m,kThen the time it takes local device k to perform the task locally is:
Figure FDA0002649381580000023
in the formula (f)kRepresents the computational resources of the local device k;
in addition, the energy consumption of the local device k for processing and executing the task is as follows:
Figure FDA0002649381580000024
wherein, the effective capacitance parameter is related to the chip structure of the device.
5. The method of task offloading with maximized computing power for D2D-MEC system of claim 3, wherein: in the step S2, in the D2D offload model and the MEC server offload model, an orthogonal frequency division multiple access method is used for channel access; the wireless channel model comprises a D2D wireless channel model and an MEC server wireless channel model:
(2-1) D2D Wireless channel model
The MEC server allocates a bandwidth B quota between each local device k and the D2D device over the D2D linkDFor each local device k, the data rate is:
Figure FDA0002649381580000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002649381580000032
transmission Power offloaded for D2D between local device k and device i, HD,k,iWhich represents the gain of the channel and is,
Figure FDA0002649381580000033
representing the transmission distance between a local device k and a device i, beta representing a path loss parameter, and N representing a gain white Gaussian noise;
(2-2) MEC Server Wireless channel model
For MEC server offload mode, the MEC server allocates sub-bandwidth to local device k
Figure FDA0002649381580000034
And computing resources, then the local device k allocates its tasks to the MEC server at the data rate:
Figure FDA0002649381580000035
in the formula (I), the compound is shown in the specification,
Figure FDA0002649381580000036
is the uplink transmission power, H, between the local device k and the serverS,kRepresenting the channel gain between the local device k and the server,
Figure FDA0002649381580000037
represents the transmission distance between the local device k and the server, BS,kRepresents the bandwidth allocated to the local device k by the MEC service, and bandwidth BS,kThe conditions are satisfied:
Figure FDA0002649381580000038
in the formula (I), the compound is shown in the specification,
Figure FDA0002649381580000039
representing the total bandwidth available to the MEC server.
6. The method of task offloading with maximized computing power for D2D-MEC system of claim 3, wherein: in step S2, the D2D unloading model is:
for a task that is not executing in the local device, it is first offloaded to the neighboring D2D device, and the execution time of each D2D device is:
Figure FDA0002649381580000041
in the formula (f)iRepresenting the computing resources that D2D device i can provide;
corresponding energy consumption consumed by D2D device i:
Figure FDA0002649381580000042
uplink transmission delay between local device k and D2D device i:
Figure FDA0002649381580000043
the corresponding transmission energy consumption is as follows:
Figure FDA0002649381580000044
the new set of a single local device k and its matching D2D devices is:
Yi,k＝{i1,i2,...,in,k}
wherein the new set of computing resources of each D2D device is:
Figure FDA0002649381580000045
wherein the remaining energy consumption set of each D2D device is:
Figure FDA0002649381580000046
the conditions are satisfied for the computational tasks offloaded onto D2D device i:
Figure FDA0002649381580000047
the above conditions indicate that the overall energy consumption of a single D2D device to perform a task cannot exceed the remaining energy of the device.
7. The method of task offloading with maximized computing power for D2D-MEC system of claim 3, wherein: in step S2, the MEC server uninstall model is:
if the computing task data is large enough, the maximum tolerant delay is small, or the local device in the system does not have an additional D2D device, unloading the residual tasks m of the local device k to the MEC server; then the MEC server calculates the delay as:
Figure FDA0002649381580000051
in the formula (f)S,kComputing resources allocated to the local device k for the MEC server;
the transmission delay of the local device k when unloading the task to the MEC server is as follows:
Figure FDA0002649381580000052
the corresponding energy consumption is as follows:
Figure FDA0002649381580000053
8. the method of task offloading with maximized computing power for D2D-MEC system of claim 3, wherein: in step S3, the number of tasks processed by the system is represented by the computing power of the system, the problem of maximizing the computing power of the entire system is modeled as an objective function P1, and an optimal offloading policy, an optimal bandwidth allocation policy, and a computing resource allocation policy are solved while ensuring various constraints:
Figure FDA0002649381580000054
conditions are as follows:
C1：
Figure FDA0002649381580000055
C2：
Figure FDA0002649381580000056
C3：
Figure FDA0002649381580000057
C4：
Figure FDA0002649381580000061
C5：
Figure FDA0002649381580000062
C6：
Figure FDA0002649381580000063
C7：
Figure FDA0002649381580000064
C8：
Figure FDA0002649381580000065
C9：
Figure FDA0002649381580000066
C10：
Figure FDA0002649381580000067
C11：
Figure FDA0002649381580000068
among the constraints mentioned above, constraints C1, C2, and C3 are integer constraints that ensure that only one position is selected for computation per computation task m; constraint C4 ensures that each local device and D2D device is assigned at least one task; constraint C5 ensures that each computation task m completes within the maximum tolerated delay; constraint C6, C7
Figure FDA0002649381580000069
Representing the remaining energy of the local device k,
Figure FDA00026493815800000610
representing the residual energy of local device i, constraints C6, C7 guarantee device k andthe energy consumed by the computing task of the equipment i does not exceed the residual energy of the equipment; constraint C8 ensures that the computing resources allocated by the MEC server to all local users cannot exceed the total amount of computing resources of the server, i.e., the total amount of computing resources of the MEC server.
9. The method of task offloading with maximized computing power for a D2D-MEC system of claim 8, wherein: in the step S4, in order to maximize the computing capacity of the system and improve the utilization rate of the wireless resources, when performing task offloading decision, tasks are preferentially allocated to the D2D device for execution, and the maximization of the computing capacity of the D2D is first achieved; for this purpose, the objective function P1 is decomposed, and the D2D maximum computation capability modeling problem is extracted, so that the D2D maximum computation capability problem is modeled as the objective function P2:
P2:
Figure FDA0002649381580000071
conditions are as follows:
C12：
Figure FDA0002649381580000072
C13：
Figure FDA0002649381580000073
the goal of P2 is to be x (m, k) ═ xD,m,k,iThe calculation tasks of (2) are used for solving the maximum value of the sum, which means that the more calculation tasks are distributed to the D2D, the more the target value is, the better the target value is, the target value is an integer linear programming problem, and in order to solve the target value, the number of the calculation tasks distributed to the D2D reaches the maximum value, the calculation tasks are firstly distributed according to the energy reserved on the D2D equipment;
the solving algorithm of the target is as follows: firstly, the task sets M are arranged in descending order according to the size of bytes, and then the residual energy consumption sets O are arrangedESize of (D2D) to D2D device set IkThe ascending order is carried out, then the larger calculation task is firstly put into the D2D device with smaller residual energy, and then the larger calculation task is put into the deviceEntering small computing tasks while marking which D2D device each computing task is specifically placed in; therefore, the residual energy of the D2D equipment can be maximally utilized to put in a larger number of calculation tasks, and the goal of P2 is achieved;
after the D2D equipment in which each calculation task is placed is obtained, the tasks and the equipment can be marked, and an optimal D2D unloading strategy set pi is obtained;
finally, the computing task set M remained after the computing tasks executed by the D2D equipment reach the maximum value*＝{m1,m2,m3,...,miThe tasks are executed at the local device or the MEC server, and the target P3 is the policy set for the maximum number of executed computing tasks:
P3:
Figure FDA0002649381580000074
conditions are as follows:
C14：
Figure FDA0002649381580000081
C15：
Figure FDA0002649381580000082
C16：
Figure FDA0002649381580000083
C17：
Figure FDA0002649381580000084
c14 is the maximum tolerated time for the MEC server to compute and transmit the sum of the delays and meet the task, the single device based multitask execution on the server is assumed to be executed in parallel; c15 is that the transmission power allocated to D2D and the transmission power of the MEC server satisfy the local device's own maximum transmission power constraint; c16 is the remaining energy of the device that must be satisfied for the task to be delivered to the server;
the above function is a linear programming problem, two boundary values of the programming problem are considered, and therefore a corresponding unloading strategy solution can be obtained.
10. The method of task offloading with maximized computing power for a D2D-MEC system of claim 9, wherein: in step S4, the following two boundary value conditions are considered:
(1) when the MEC server does not allocate bandwidth resources and computational resources to the local device, the computational tasks generated by the local device are all performed locally or by the D2D device, i.e.
Figure FDA0002649381580000085
In this case, according to the constraint conditions:
xs,m,k＝0，xl,m,k＝1 (16)
(2) when all resources of the whole D2D-MEC system are fully allocated, the various resources of the MEC server are occupied, and at this time, the number of system processing tasks reaches the maximum, that is, when bandwidth resources, computing resources and transmission power are fully allocated:
Figure FDA0002649381580000091
in this case, according to the constraint conditions:
xs,m,k＝1，xl,m,k＝0 (18)
the computing resources and bandwidth resources of the MEC server are fixed, and if some tasks cannot be completed in the scheduling, the MEC server waits for the next suboptimal scheduling to be completed in the task queue.
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