CN115551014A - Task unloading scheduling method in air-ground cooperative unmanned aerial vehicle edge computing network - Google Patents
Task unloading scheduling method in air-ground cooperative unmanned aerial vehicle edge computing network Download PDFInfo
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Abstract
The invention provides a task unloading scheduling method in an air-ground cooperative unmanned aerial vehicle edge computing network. The method comprises the following steps: 1. and generating a task description set, and constructing a problem model P1 of task unloading scheduling, computing resource allocation and the optimal position of the unmanned aerial vehicle in the edge computing network of the unmanned aerial vehicle. 2. Giving the CPU calculation frequency, the unmanned aerial vehicle position and the unloading data quantity of the initial unmanned aerial vehicle, constructing a problem model P2, and solving a task unloading decision and a task scheduling sequence by adopting a greedy strategy. 3. And (3) constructing a problem model P3, and solving the position of the unmanned aerial vehicle by adopting a continuous convex approximation method. 4. And solving the task transmission power and the unmanned aerial vehicle CPU calculation frequency by adopting a convex optimization method. 5. A target value E is calculated. 6. And (5) repeating the step 2 to the step 5, solving a new target value E ', comparing E with E ', if | E-E ' | < epsilon, exiting, and otherwise, repeating the step 6. By the method, the execution energy consumption of the task in the air-ground cooperative unmanned aerial vehicle edge computing network can be effectively reduced.
Description
Technical Field
The invention belongs to the technical field of wireless networks, and relates to a task unloading scheduling and computing resource allocation method in an air-ground cooperative unmanned aerial vehicle edge computing network.
Background
Unmanned Aerial Vehicles (UAVs) have been widely used in various fields in recent years due to their characteristics of low cost, convenient operation and control, flexibility and the like. Unmanned aerial vehicle's mobility is strong, the removal is nimble, can deploy fast in the network is as the node, accessible dynamic adjustment guarantees communication service in emergent scene.
In a Mobile Edge Computing (MEC) application scenario, normal network communication services will be affected when a base station equipment failure is encountered or signals cannot be communicated due to terrain factors, etc. If the addition of the unmanned aerial vehicle to the MEC network for assistance (hereinafter referred to as an unmanned aerial vehicle MEC network) is considered, the robustness and the flexible deployment capability of the system can be improved. Compared to traditional ground MEC networks, drone-assisted MEC networks have several significant advantages. First, they can be flexibly deployed in most scenarios. In complex terrains such as the open air, desert, etc., a terrestrial MEC network may be inconvenient and reliable to establish, and an unmanned aerial vehicle can solve the deployment problem well through the maneuvering flexibility of the unmanned aerial vehicle. Secondly, after the unmanned aerial vehicle is added into the MEC network, because of the line of sight (LOS) connection between the unmanned aerial vehicle and a ground node or other unmanned aerial vehicles, the system can obtain reliable communication service with high data rate and large coverage area by using less transmitting power. According to the characteristics of the unmanned aerial vehicle, the unmanned aerial vehicle can serve as an aerial base station to provide services for ground users, or serve as a communication relay node to forward service information between the ground base station and the users. However, the unmanned aerial vehicle has a narrow fuselage and limited onboard battery capacity. As a network communication node, except for normal navigation propulsion control, energy consumption is needed by communication signal transmission and emission, an airborne arithmetic unit to execute calculation tasks and the like, so that reasonable distribution is needed to be carried out on power consumption of the unmanned aerial vehicle according to the characteristics and requirements of the executed tasks, and the energy efficiency and the endurance time of the unmanned aerial vehicle are improved.
In view of the above consideration, the invention provides a task unloading scheduling method in an air-ground cooperative unmanned aerial vehicle edge computing network.
Disclosure of Invention
The invention aims to solve the technical problem of providing a task unloading scheduling method in an air-ground cooperative unmanned aerial vehicle edge computing network. By performing joint optimization on task unloading decisions, task scheduling, resource allocation and the optimal position of the unmanned aerial vehicle, the aim is to minimize energy consumption.
The technical solution of the invention is as follows:
a task unloading scheduling method in an air-ground cooperative unmanned aerial vehicle edge computing network is characterized by firstly constructing an unmanned aerial vehicle assisted mobile edge computing system which consists of K = {1,2,. Rightang, K,.., N } terminal devices, an unmanned aerial vehicle carrying an edge server and G = {1,2,. Rightang, K,. Rightang, J } ground edge servers (base stations), wherein all the terminal devices are provided with single antennas and can transmit tasks to the unmanned aerial vehicle; the unmanned aerial vehicle can receive a plurality of tasks simultaneously, the cache is large enough, but only a single-core CPU is arranged, and all the tasks are processed in sequence according to the sequence transmitted to the unmanned aerial vehicle. The cache of the ground edge server is large enough and all tasks are transmitted to the ground edge server in the scheduling order. Each terminal device has only 1 task at the current moment, the computing capacity of the terminal devices is very limited, the ground edge servers are far away from each other, direct communication cannot be carried out, all the tasks of which K belongs to K are not locally computed, and each task can be unloaded to an unmanned aerial vehicle for execution or can be unloaded to the ground edge servers for execution through the unmanned aerial vehicle as a relay. Offload decision variable X = { X 1 ，...，X i ，...，X N In which X is i ＝{β i，0 ，β i，1 ，...，β i，j ，...β i，J Denotes the task unloading decision of the terminal device K ∈ K, where β i，0 ，β i，j ∈{0，1}，β i，0 =1 represents that the task of the terminal device i ∈ K is unloaded to the unmanned aerial vehicle for execution, β i，j And =1 represents that the task of the terminal device i ∈ K is unloaded to the ground edge server j ∈ G for execution.
The invention provides a task unloading scheduling method in an air-ground cooperative unmanned aerial vehicle edge computing network, which comprises the following specific steps:
1. the method comprises the following steps of constructing a problem model for the linear dependent task unloading of the edge computing network of the unmanned aerial vehicle, and comprises the following steps:
the Task of the terminal device i belonging to K is expressed as a binary group Task i ＝(L i ，C i ) Wherein the Task i Comprises two parts, L i Program data representing tasks, the unit being bits; c i Indicating the number of CPU cycles required to process a task in cycles/bits.
Representing a position Q of a drone using a 3D Cartesian coordinate system UAV ＝{x uav ，y uav ，H}，x uav Denotes the abscissa, y, of the drone uav The vertical coordinate of the unmanned aerial vehicle is shown, and H is the height of the unmanned aerial vehicle and is fixed to 100m. The position of the ground terminal device is represented as
Wherein
Respectively represent the abscissa and ordinate of the ith ground terminal device. The location of the ground edge server is represented as
Wherein
Respectively representing the abscissa and the ordinate of the jth ground edge server.
The unloading scheduling sequence queue of all tasks is S = { L, S 1 ，S 2 ，...，S k ，...，S j Where L = { L = } 1 ，l 2 ，...，l k ，...，l NL Denotes the computation order of NL tasks offloaded to computation on the drone, where l k Represents a kth task performed on the drone;
representing NS offloaded to computation on ground edge server j ∈ G j The unloading order of individual tasks, wherein s j，k Represents the kth task offloaded to the ground edge server j ∈ G, where
CPU frequency F = { F) to which calculation task is allocated and unloaded onto unmanned aerial vehicle 1 ，f 2 ，...，f k ，...，f NL In which f k Task representation k Calculating the frequency by the distributed CPUCPU when the unmanned aerial vehicle executes; so the uplink transmission power of the task
Wherein
Task representation k An uplink transmission power transmitted to the drone; so that the downlink transmission power of the task
Wherein
Task representation k Downlink transmission power transmitted to the ground edge server by the unmanned aerial vehicle;
s1-1 construction of communication model
Task of S1-1-1 terminal equipment i belonging to K i Uplink free space path loss model channel gains offloaded to drones are shown in (1)
Wherein alpha is 0 Indicating that for a transmission power of 1W, the received power at a reference distance of 1m,
representing the uplink distance from the terminal device i e K to the drone.
The channel gain of the downlink free space path loss model of the S1-1-2 task unloaded to the ground edge server j ∈ G through the unmanned aerial vehicle is shown in (2)
Wherein
Representing the downlink distance of the drone to the ground edge server j e G.
Task of S1-1-3 terminal equipment i belonging to K i Uplink transmission data rate offloaded to drone is shown in (3)
Wherein B is UL Indicates the bandwidth of the uplink channel and,
task representing terminal equipment i belonging to K i Transmission power, σ, offloaded to drone 2 Representing the noise spectral density.
Task of S1-1-4 terminal equipment i belonging to K i Downlink transmission data rates offloaded by drones to ground edge servers j ∈ G are shown in (4)
Wherein B is DL Which represents the bandwidth of the downlink channel(s),
task for representing terminal equipment i belongs to K i And unloading the transmission power of j ∈ G to the ground edge server by the unmanned aerial vehicle.
S1-2 time delay analysis
Task of S1-2-1 terminal equipment i belonging to K i The uplink transmission time for transmitting to the unmanned aerial vehicle is shown as (5)
Task for S1-2-2 terminal equipment i belonging to K i The calculated time at the unmanned plane is shown as (6)
Wherein
Task representing allocation of unmanned aerial vehicle to terminal device i ∈ K k In cycles/s. Task of S1-2-3 terminal equipment i belonging to K i The downlink transmission time transmitted to the ground edge server j epsilon G by the unmanned aerial vehicle is shown as (7)
Task for S1-2-4 terminal equipment i belonging to K i The computation time at the ground edge server is shown in (8)
Wherein
Representing the CPU frequency (in cycles/s) of the ground edge server j ∈ G.
Task of S1-2-5 terminal equipment i belonging to K i The calculated completion time of unloading to the drone is shown in (9)
Task of S1-2-6 terminal equipment i belonging to K i The completion time calculated by the unmanned aerial vehicle unloading onto the ground edge server j ∈ G is shown in (10)
Wherein
Transmission completion time for the task of device i e K to be offloaded to ground edge server j e eta by unmanned aerial vehicle, as shown in (11)
S1-2-7 so that the final completion time of the task is shown as (12)
S1-3 energy consumption analysis
Task of S1-3-1 terminal equipment i belonging to K i The uplink transmission energy consumption for transmitting to the unmanned aerial vehicle is shown as (11)
Task for S1-3-2 terminal equipment i belonging to K i The calculated energy consumption on the unmanned aerial vehicle is shown as (14)
Where k represents the effective capacitance coefficient of the drone, depending on the chip architecture of the CPU.
S1-3-3 terminal equipment i belongs to KTask i The energy consumption of downlink transmission transmitted to the ground edge server by the unmanned aerial vehicle is shown as (15)
The hovering energy consumption consumed by the unmanned aerial vehicle after S1-3-4 completes all tasks is calculated as shown in (16)
E hover ＝P h T (16)
Wherein P is h Indicating the hovering power of the drone in watts (W).
S1-3-5 Total energy consumption for the ground terminal equipment and the unmanned aerial vehicle for completing all tasks is shown as (17)
Wherein eta 1 Representing transmission coefficient of energy, η 2 Representing the calculated energy consumption coefficient.
S1-4 problem description
Performing joint optimization on task unloading decision, task scheduling, resource allocation and optimal positions of the unmanned aerial vehicles, wherein the aim is to minimize the total energy consumption of all ground terminals and the unmanned aerial vehicles, and the problem is described as follows:
Q UAV ＝{x uav ，y uav ，H}，x uav ∈[0，1000]，y uav ∈[0，1000] (18i)
the equation (18 a) is an objective function, wherein χ = { Q = UAV ，P UL ，P DL And F, X, S represent optimization variables.
Equation (18 b) represents that the drone CPU computation frequency is greater than zero and does not exceed the maximum CPU computation frequency.
Equation (18 c) indicates that the uplink transmission power of the task is greater than zero and does not exceed the maximum transmission power.
Equation (18 d) indicates that the downlink transmission power of the task is greater than zero and does not exceed the maximum transmission power.
Equation (18 e) represents the offloading tasks and corresponding scheduling order of the drones and the ground edge server.
Equation (18 f) indicates that the completion time for all tasks does not exceed the maximum time limit.
Equation (18 h) indicates that the task must be offloaded and can only be executed on a single edge server.
Equation (18 h) indicates that the task can only be completely unloaded or not.
Equation (18 i) indicates that the drone can only be within a specified range.
The problem model P1 proposed by the present invention is a nonlinear mixed integer optimization problem. By analyzing the problem model P1, we can find the following three features. First, the unmanned aerial vehicle location directly or indirectly affects the allocation of computing resources and overall computing energy consumption, and the offloading scheduling decisions of tasks, computing resources and communication resource allocation are closely related to the unmanned aerial vehicle location. Second, the optimal position of the drone cannot be determined until the offload scheduling decision, computing resource and communication resource allocation is generated, and therefore it is affected by the offload scheduling decision, computing resource and communication resource allocation results. Thirdly, the allocation of computing resources and communication resources can only be accurately calculated if the unloading scheduling decision of the position and task of the unmanned aerial vehicle is optimal.
In order to solve the problem model P1, based on the idea of multi-objective hierarchical optimization, the P1 is converted into three sub-problems to be subjected to successive iterative solution, and each sub-problem is to solve the sub-problem optimization problem under the condition of ensuring the optimality of other two sub-problems. The method regards the unloading scheduling decision as a first sub-problem, and solves the problem by adopting a greedy algorithm; the optimal position problem of the unmanned aerial vehicle is regarded as a second sub-problem, and a solution is carried out by adopting an SCA method; taking the problem of computing resource and communication resource allocation as a third sub-problem, and solving by adopting a convex optimization method; the purpose is to minimize the sum of the energy consumption of all ground terminals and drones.
Because the problem is decomposed into three subproblems, each subproblem can only obtain the solution of the current subproblem under the condition that the variables optimized by other subproblems are determined, and thus the global solution cannot be directly obtained. By successively iterating the three subproblems, the global solution is converged, and when the error solved by the current iteration and the next iteration is smaller than a specified threshold value, the global solution can be considered to be obtained.
2. The first sub-problem is solved:
the first subproblem of S2-1 is expressed as: under the conditions of the position of the unmanned aerial vehicle, the transmission power and the CPU calculation frequency, a task unloading decision and task scheduling are solved, and a problem model can be expressed as P2:
S.t.(18e)，(18f)，(18g)，(18h) (19b)
where (19 a) is an objective function and (19 b) is a constraint, { X, S } is an optimization variable, where X denotes an unload decision of a task and S denotes an unload scheduling order queue of the task.
S2-2, based on a greedy strategy with minimum priority of the number of cycles required by the CPU to process the tasks, the unloading decision of the tasks and the scheduling sequence of the tasks are solved, and the method specifically comprises the following steps:
i) Calculating the number of cycles required by the processing of the CPU corresponding to each task, and arranging all the tasks in a descending order according to the number of cycles required by the processing of the tasks to obtain a task sequence V = { V } i |v i ＝L i C i ，v i E.g., K) and record the original subscript R = { R } for the task 1 ，...，r i ，...，r N }，r i ∈{1，...，N}。
ii) setting the initial index value of the array V to h =1, and setting the current energy consumption initial value excluding hovering energy consumption to E now =0, the initial value of the current task number of the unmanned aerial vehicle is NL =0, and the initial value of the current task number of the ground edge server j ∈ G is NS j ＝0。
iii) Computation task v h Respectively putting an unmanned aerial vehicle unloading queue L and a ground edge server j belonging to a G unloading queue S j Post system energy consumption
And
comparison E UAV，now And
size of (1), if
Then the task V h Putting the unmanned aerial vehicle into an unloading queue L,
h = h +1, nl = nl +1, step iii) is repeatedly performed; otherwise, step iv) is entered after exit.
iv) computational task v h Respectively putting an unmanned aerial vehicle unloading queue L and a ground edge server j belonging to a G unloading queue S j Post system energy consumption
And
comparison E UAV，now And
size of (1), if
Then the task V h Unloading queue S placed in ground edge server k E G k ，
h＝h+1，NS k ＝NS k +1, iteratively performing step iv); otherwise, the step v) is entered after exiting.
v) if h is less than or equal to N, entering step iii), otherwise entering step vi).
vi) classifying all tasks in the unmanned aerial vehicle unloading queue L, and adding the tasks with the unloading transmission time smaller than the unmanned aerial vehicle calculation time into the array P by comparing the task unloading transmission time with the unmanned aerial vehicle calculation time L ，
Will P L All the tasks are arranged in an ascending order according to the unloading transmission time; adding the tasks with the unloading transmission time being more than or equal to the calculation time of the unmanned aerial vehicle into an array Q L ，
Will Q L In the method, all tasks are arranged in descending order according to the calculation time of the unmanned aerial vehicle, and the array Q is obtained L Added to array P L Later get a new task scheduling order L = [ P = [) L ，Q L ]Go to step vii).
vii) offloading queue S to ground edge server j Classifying all the tasks, comparing the task unloading downlink transmission time with the ground edge server calculation time, and adding the tasks with the unloading downlink transmission time less than the ground edge server calculation time into an array
Will be provided with
All tasks in the system are arranged in an ascending order according to the unloading downlink transmission time; adding the task of which the unloading downlink transmission time is more than or equal to the calculation time of the ground edge server into an array
Will be provided with
All the tasks are arranged according to the descending order of the calculation time of the ground edge server, and the arrays are arranged
To an array
Later deriving new task schedulesSequence of
And ending the step and outputting S.
3. The second sub-problem is solved:
the second subproblem of S3-1 is expressed as: under the condition of giving unloading decision, scheduling sequence, uplink and downlink transmission power of a task and CPU (central processing unit) calculation frequency of the unmanned aerial vehicle, the optimal position of the unmanned aerial vehicle is solved, and a problem model can be represented as P3:
S.t.(18i) (20b)
wherein (20 a) is an objective function, Q UAV Are the optimization variables.
Since the drone position optimizes variables and will not be moving upon determination, assuming offload scheduling queue S, ground terminals, and drone transmit power determination.
And
is about Q UAV Is not a convex function, however
And
are respectively about
And
is convex function of, so will
And
are respectively paired
And
and (3) performing first-order Taylor expansion to obtain corresponding Taylor expansion formulas shown as (21) and (22):
wherein
k is the current number of iterations.
Obtaining corresponding uplink transmission energy consumption
And downlink transmission energy consumption
As shown in (23) and (24):
will be provided with
And
substituting P3, the problem model P3 transforms into a problem model P4:
S.t.(18i) (25b)
wherein (25 a) is an objective function, Q UAV Are the optimization variables.
S3-2, solving the position of the unmanned aerial vehicle based on an SCA algorithm, and specifically comprising the following steps:
i) Initialization Q UAV (0)＝(500，500，100)，k＝0，α＝0.5，ρ＝0.01，θ(0)＝1，θ(k)∈(0，1]。
ii) solving for the objective formula P4 yields the minimum E total (k) And corresponding unmanned plane position, note
iii) Updating
θ(k+1)＝θ(k)(1-α)。
iv) calculating the target value Total energy consumption E based on the formula (17) total (k + 1), if | | | E total (k+1)-E total (k) If | is greater than ρ, k = k +1, jumping to step ii), otherwise, ending iteration and outputting the optimal position Q of the unmanned aerial vehicle UAV (k+1)。
4. Solving a third sub-problem:
the third subproblem of S4-1 is expressed as: under the condition of giving unloading decision, scheduling sequence and position of the unmanned aerial vehicle of the task, solving uplink and downlink transmission power of the task and CPU calculation frequency when calculating on the unmanned aerial vehicle, wherein a problem model can be represented as P5:
S.t.(18b)，(18c)，(18d) (26b)
equation (26 c) indicates that all tasks on the drone can be executed only after transmission to the drone.
Equation (26 d) indicates that all tasks on the drone, except the first task, must wait until the last off-load task is completed before being executed.
Equation (26 e) indicates that all tasks on the ground edge server can be transmitted to the ground edge server for execution only after being transmitted to the drone.
Equation (26 f) indicates that all tasks on the ground edge server, except the first task, must wait until the last offload task is transferred before being transferred to the ground edge server for execution.
S4-1-1 introduces variable substitution, so that
ω＝σ 2 /α 0 ，ε＝1/B UL ，τ＝1/B DL . Transforming problem model P5 to problem model P6, as follows:
S.t.(26c)，(26d)，(26e)，(26f) (27b)
wherein
And
to optimize variables, where j ∈ G,
s4-1-2, obtaining an unloading scheduling decision according to the first sub-problem, determining the unloading scheduling decision S of the task and the completion time of the task executed on the unmanned aerial vehicle
Transmission completion time for task transmission to ground edge server
Completion time of task execution on edge server
And flight energy consumption E of unmanned aerial vehicle hover And the target equation is the sum of convex functions, so the solution can be based on convex optimization.
S4-1-3 introduction of Lagrange multiplier
Wherein
And
wherein j belongs to G, and constructing a Lagrangian function and a dual problem of the problem model P6, wherein the Lagrangian function of the problem model P6 is as follows:
the dual function of the problem model P6 is defined as
The dual problem is that
S4-2, solving transmission power of the task and unmanned aerial vehicle CPU calculation frequency based on convex optimization, and the steps are as follows:
i) And calculating a target value of the current given task unloading decision, a task scheduling sequence, the uplink and downlink transmission power of the task and the calculation frequency of the unmanned aerial vehicle CPU according to the problem model P5, and recording the target value as Val _ old.
ii) solving the unconstrained convex function (27 a) by Newton's method. The solution obtained is
The solutions F are respectively substituted into the formulas (26 c), (26 d), (26 e) and (26 f) to obtain solutions F L ，
Each of which satisfies the equations (26 c), (26 d), (26 e) and (26 f), respectively, then Γ L ，
Is the optimal solution for the target formula and proceeds to step vi), otherwise to step iii).
iii) Lagrange function (28 a) pair
And
the partial derivatives are obtained by calculating Lagrangian multipliers as shown in (29), (30), (31) and (32)
And
as shown in (33), (34), (35) and (36).
iv) solving the solution gamma L ，
Classifying the solutions satisfying the beam conditions (26 c), (26 d), (26 e), and (26 f) into classes
Classifying solutions that do not satisfy the beam conditions (26 c), (26 d), (26 e), and (26 f) as
Will be assembled
And
the number of the elements in (A) is respectively 2NL, nopt and
will be provided with
And
the corresponding Lagrange multipliers are obtained by substituting (29), (30), (31) and (32) respectively
And
while
And
corresponding Lagrange multiplier
And
the values are all 0, and the problem model P6 becomes
And
problem model P7 as a variable:
S.t.(28b) (37b)
v) solving for P7 again by Newton method to obtain optimal
Bonding of
And
obtaining a corresponding optimal solution gamma L ，
Step vi) is entered.
vi) solving the solution F L ，
Substituting (38), (39) and (40) to obtain
And substituted into the question P5 to obtain the latest target value, denoted as Val _ new, and the routine proceeds to step vii).
vii) comparing the difference value between Val _ new and Val _ old, if the difference value is less than the threshold value rho, namely | Val _ new-Val _ old | < epsilon, finishing the iteration and outputting
Otherwise jump to i).
5. And (4) substituting the problem P1 to obtain a latest target value according to the task unloading scheduling decision obtained in the step (2), the step (3) and the step (4), the position of the unmanned aerial vehicle, the uplink and downlink transmission rates of the corresponding task and the CPU calculation frequency of the task on the unmanned aerial vehicle, wherein the value is recorded as E _ new.
6. And calculating a difference value between the current iteration target value E _ new and the previous iteration target value E _ old, wherein the initial value of E _ old is 0, if the difference value is smaller than a threshold epsilon, namely | E _ new-E _ old | is smaller than epsilon, the iteration is ended, the optimal unmanned aerial vehicle position, unloading decision, scheduling sequence and resource allocation scheme are obtained, and if not, E _ old = E _ new, the step 2 is skipped.
Advantageous effects
The invention provides a task unloading scheduling method in an air-ground cooperative unmanned aerial vehicle edge computing network. Effectively obtain energy consumption's optimal value to reduce unmanned aerial vehicle and ground terminal's energy consumption.
Drawings
FIG. 1 is a schematic view of a scene model of the present invention;
FIG. 2 is a flowchart of a task offloading scheduling method in an air-ground cooperative unmanned aerial vehicle edge computing network according to the present invention;
FIG. 3 is a flowchart illustrating a task offload scheduling decision optimization solution based on a greedy strategy according to the present invention;
FIG. 4 is a flow chart of the solution of the position optimization of the unmanned aerial vehicle based on SCA according to the present invention;
FIG. 5 is a flow chart of the solution of convex optimization-based resource allocation optimization according to the present invention;
Detailed Description
The invention will be described in further detail below with reference to the following figures and specific examples:
example 1:
l1 in this embodiment, fig. 1 shows a schematic view of an unmanned aerial vehicle edge computing scene model, which includes an unmanned aerial vehicle equipped with edge servers, J ground edge servers, and J =4; n ground terminal devices, N =10, each terminal device has 1 Task, and each Task is Task k ＝(L k ，C k ). Processing Task k Unit data amount is L k Task of processing k The CPU period required by unit bit data is C k . The maximum transmission power of the terminal equipment is
The maximum CPU frequency of the unmanned aerial vehicle is F UAV =1GHz, the CPU frequency of all ground edge servers is
Maximum transmission power of
Setting the uplink transmission bandwidth as B UL =0.45MHz, and downlink transmission bandwidth is B DL =1MHz, noise power σ 2 =100 dBm, received power α at a reference distance of 1m at a transmission power of 1w 0 = 50dB. Energy consumption coefficient eta of task transmission 1 =100, energy consumption coefficient eta of task calculation 2 =100 unmanned aerial vehicle flight power of hovering P h =100w, the effective capacitance coefficient of the drone k =10 -28 The iteration precision ρ =0.01, and the iteration precision ∈ =0.01.
L1-1 initialization, three-dimensional coordinates of each terminal device
And
as shown in Table 1, the unit m, task k L of k And C k As shown in Table 2, the data to be processed of each task is its program data L k The unit Mbits; number of CPU cycles C required to process unit bit task k The unit cycles/bit. Initializing three-dimensional coordinates of a base station
And
as shown in table 3, the unit m. Therefore, the uplink transmission power of the task is initialized to be 0.1w at the maximum value, and the downlink transmission power is initializedAnd the maximum value is 1w, and the task initial CPU calculation frequency calculated on the unmanned aerial vehicle is 1GHz. The initial drone three-dimensional coordinates are [500, 500, 100 ]]。
TABLE 1 three-dimensional coordinate table of terminal equipment
TABLE 2 task Attribute Table
| Task 1 | Task 2 | Task 3 | Task 4 | Task 5 | Task 6 | Task 7 | Task 8 | Task 9 | Task 10 | |
| L k | 2.15 | 2.88 | 3.21 | 2.61 | 2.81 | 2.20 | 2.95 | 2.58 | 2.03 | 3.77 |
| C k | 261 | 242 | 211 | 282 | 225 | 251 | 280 | 280 | 230 | 286 |
TABLE 3 three-dimensional coordinate table of base station
And L2, solving the unloading decision and task scheduling sequence of the task according to a greedy algorithm:
and the L2-1 converts the problem model P1 into a problem model P2 under the condition of giving the position of the unmanned aerial vehicle, the CPU calculation frequency and the uplink and downlink transmission power, and solves the problem model P2 by using a greedy strategy algorithm.
And L2-1-1 obtains all task descending queues V according to the comparison of the number of cycles required by the processing of each task and records the original positions R of the tasks.
L2-1-2 initializes the number NL =0 of the unmanned aerial vehicle queue tasks and the number NS of the queue tasks of each ground edge server 1 ＝0，NS 2 ＝0，NS 3 ＝0，NS 4 =0, and the currently processed task designator h =1.
L2-1-3 if task v h The total energy consumption after being unloaded to the unmanned aerial vehicle is smaller than the total energy consumption calculated after being unloaded to other positions, h is less than or equal to N, the task is distributed to the unmanned aerial vehicle,
NL = NL +1, h = h +1, and this step is repeated; otherwise, the next step is carried out.
L2-1-4 if task v h The total energy consumption after being unloaded to the ground edge server 1 is smaller than the total energy consumption calculated after being unloaded to other positions, h is less than or equal to N, the task is distributed to the ground edge server 1,
NS 1 ＝NS 1 +1,h= h +1, and repeat this step; otherwise, the next step is carried out.
L2-1-5 if task v h The total energy consumption calculated after being unloaded to the ground edge server 2 is smaller than the total energy consumption calculated after being unloaded to other positions, h is less than or equal to N, the task is distributed to the ground edge server 2,
NS 2 ＝NS 2 +1,h= h +1, and repeat this step; otherwise, the next step is carried out.
L2-1-6 if task v h The total energy consumption calculated after being unloaded to the ground edge server 3 is smaller than the total energy consumption calculated after being unloaded to other positions, h is less than or equal to N, the task is distributed to the ground edge server 3,
NS 3 ＝NS 3 +1,h = h +1, and repeating this step; otherwise go intoGo to the next step.
L2-1-7 if task v h The total energy consumption calculated after being unloaded to the ground edge server 4 is smaller than the total energy consumption calculated after being unloaded to other positions, h is less than or equal to N, the task is distributed to the ground edge server 4,
NS 4 ＝NS 4 +1,h = h +1, and repeating this step; otherwise, the next step is carried out.
And if the task identifier h currently processed by the L2-1-8 is not more than N, returning to the step L2-1-3, otherwise, entering the next step.
L2-1-9 sequences the tasks in the unmanned aerial vehicle queue, and puts the tasks with the unloading transmission time less than the unmanned aerial vehicle calculation time into a queue P L Otherwise, put the task into queue Q L A 1 is to P L All the tasks in the system are arranged according to the ascending order of unloading transmission time, and Q is obtained L All the tasks are arranged in a descending order according to the calculation time of the unmanned aerial vehicle to obtain a scheduling queue L = [ P ] of the tasks calculated on the unmanned aerial vehicle finally L ，Q L ]。
L2-1-10 sequences the tasks in the queue of the edge server 1, and puts the tasks with the unloading downlink transmission time less than the calculation time of the ground edge server into the queue
Otherwise, the task is put into the queue
Will be provided with
All the tasks are arranged according to the ascending order of the unloading downlink transmission time
All the tasks are arranged according to the descending order of the calculation time of the ground edge server to obtain a scheduling queue of the calculation tasks on the unmanned aerial vehicle
L2-1-11 sequences the tasks in the queue of the edge server 2, and puts the tasks with the unloading downlink transmission time less than the calculation time of the ground edge server into the queue
Otherwise, the task is put into the queue
Will be provided with
All the tasks are arranged according to the ascending order of the unloading downlink transmission time
All the tasks are arranged according to the descending order of the calculation time of the ground edge server to obtain a scheduling queue of the calculation tasks on the unmanned aerial vehicle
L2-1-12 sequences the tasks in the edge server 3 queue, and puts the tasks whose unloading downlink transmission time is less than the calculation time of the ground edge server into the queue
Otherwise, the task is put into the queue
Will be provided with
All the tasks are arranged according to the ascending order of the unloading downlink transmission time
All the tasks are arranged according to the descending order of the calculation time of the ground edge server to obtain a scheduling queue for calculating the tasks on the unmanned aerial vehicle finally
L2-1-13 sequences the tasks in the edge server 4 queue, and puts the tasks whose unloading downlink transmission time is less than the calculation time of the ground edge server into the queue
Otherwise, the task is put into the queue
Will be provided with
All the tasks are arranged according to the ascending order of the unloading downlink transmission time
All the tasks are arranged according to the descending order of the calculation time of the ground edge server to obtain a scheduling queue of the calculation tasks on the unmanned aerial vehicle
Finally, the decision and scheduling order by task offloading is shown in table 4.
TABLE 4 task offload decision and scheduling order Table
| 1 | 2 | 3 | |
| L | Task 10 | ||
| S 1 | Task 4 | Task 7 | |
| S 2 | Task 2 | Task 3 | |
| S 3 | Task 8 | Task 5 | Task 1 |
| S 4 | Task 6 | Task 9 |
L3, solving the optimal position of the unmanned aerial vehicle according to an SCA algorithm:
and the L3-1 converts the problem model P1 into a problem model P3 under the conditions of giving initial CPU calculation frequency, uplink and downlink transmission power, and the unloading decision and task scheduling sequence of the tasks obtained according to the L2, and solves the problem model P3 by using an SCA algorithm.
L3-1-1 initialization of Q UAV (0)＝(500，500，100)，k＝0，α＝0.5，ρ＝0.01，θ(0)＝1。
L3-1-2 solves the objective formula P4 to obtain the minimum E total (k) And corresponding unmanned plane position, note
L3-1-3 update
θ(k+1)＝θ(k)(1-α)。
L3-1-4 calculates the target value Total energy consumption E based on the formula (17) total (k + 1) if | | | E total (k+1)-E total (k) If | is greater than ρ, k = k +1 and proceeds to step L3-1-2, otherwise, the step is ended and Q is output UAV ＝[516.93，470.63，100.00]The correspondence between the number of iterations and the position of the drone is shown in table 5, with the unit being m.
Table 5 unmanned plane position-iteration times table
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| x UAV | 500.00 | 509.31 | 513.82 | 515.56 | 516.33 | 516.67 | 516.81 | 516.90 | 516.93 |
| y UAV | 500.00 | 485.86 | 478.23 | 474.30 | 472.35 | 471.41 | 470.95 | 470.73 | 470.63 |
| z UAV | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 |
L4, solving the uplink and downlink transmission power of the task and the CPU calculation frequency calculated on the unmanned aerial vehicle according to the convex optimization-based algorithm:
and the L4-1 calculates a target value of the current given task unloading decision, a task scheduling sequence, the maximum transmission power of the uplink and downlink transmission of the task and the maximum CPU calculation frequency of the unmanned aerial vehicle according to the problem model P5, and records the target value as Val _ old.
L4-2 solves the convex function (27 a) by Newton's method, and the solution obtained
As shown in table 6.
TABLE 6 solution of gamma L ，
Watch (CN)
L4-3 solving the gamma L ，
Classifying the solutions satisfying the constraints (26 c), (26 d), (26 e) and (26 f) into classes
Classifying solutions that do not satisfy the constraints (26 c), (26 d), (26 e), and (26 f) as
And substituting the solutions into (33), (34), (35) and (36) to obtain corresponding Lagrange multipliers
And
as shown in table 7 and table 8.
TABLE 7 Lagrangian multiplier
And
watch (CN)
TABLE 8 Lagrangian multiplier
And
watch (A)
The L4-4 substituted Lagrange multiplier adopts Newton method again to solve P7, obtains the optimal solution, obtains the corresponding transmission rate substitution (38), (39) and (40), obtains the transmission power
And calculating frequency by unmanned aerial vehicle
As shown in table 9, the current target value Val _ new =349.060 was obtained from the problem model P5.
TABLE 9 Transmission Power
And calculating frequency by unmanned aerial vehicle
Watch (CN)
And L4-5 calculates the difference value between Val _ new and Val _ old, | Val _ new-Val _ old | < ρ, the iteration is ended, otherwise, L4-1 is skipped.
And substituting the L5 into a formula (18 a) to calculate the energy consumption of the system according to the obtained task unloading decision, the task scheduling sequence, the position of the unmanned aerial vehicle, the uplink and downlink transmission power and the unmanned aerial vehicle calculation resource allocation, wherein the target value is recorded as E _ new =349.060.
L5-1 compares E _ new with E _ old, if the difference value of the target value after the optimization in the steps L2, L3 and L4 is less than the threshold value, | E _ new-E _ old | < epsilon, the iteration is ended, otherwise, L2 is skipped.
After a plurality of iterative optimizations, the final target value is 349.058. The obtained unmanned aerial vehicle position, all task unloading decisions and task scheduling sequences, uplink and downlink transmission power and the CPU calculation frequency of the tasks on the unmanned aerial vehicle are shown in tables 10, 11 and 12.
Table 10 unmanned aerial vehicle position table
| UAV location | |
| x UAV | 514.64 |
| y UAV | 471.58 |
| z UAV | 100.00 |
TABLE 11 offload decision and scheduling order Table
| 1 | 2 | 3 | |
| L | Task 10 | ||
| S 1 | Task 8 | Task 5 | Task 1 |
| S 2 | Task 6 | Task 9 | |
| S 3 | Task 4 | Task 7 | |
| S 4 | Task 2 | Task 3 |
Table 12 uplink and downlink transmission power and CPU calculation frequency table of task on the drone
Claims (1)
1. The task unloading scheduling method in the air-ground cooperative unmanned aerial vehicle edge computing network comprises the following steps:
step 1: and constructing a problem model P1 of tasks in the air-ground cooperative unmanned aerial vehicle edge computing network.
And 2, step: giving CPU calculation frequency F of unmanned aerial vehicle and uplink transmission power P of task UL Downlink transmission power P DL And position Q of the drone UAV A problem model P2 is constructed. And solving the problem P2 by adopting a greedy strategy to obtain a task unloading decision X with an optimal task and a task scheduling sequence S.
And 3, step 3: solving a task unloading decision X, a task scheduling sequence S and initial data according to the step 2, constructing a problem model P3, and solving the optimal unmanned aerial vehicle position Q under the current strategy by using a continuous convex approximation method UAV 。
And 4, step 4: respectively obtaining the optimal task unloading according to the step 2 and the step 3Decision X, task scheduling sequence S and unmanned aerial vehicle position Q UAV Constructing a problem model P5, and solving the task uplink transmission power P by using a convex optimization method UL Downlink transmission power P DL And a drone computing resource allocation scheme F.
And 5: and calculating the energy consumption of the system according to the obtained task unloading decision, the task scheduling sequence, the unmanned aerial vehicle position, the uplink transmission power, the downlink transmission power and the calculation resource allocation scheme, wherein the target value is marked as E _ new.
Step 6: and (4) repeating the step 2, the step 3, the step 4 and the step 5 to calculate the difference value between the target values E _ new and E _ old for 2 times before and after, if the difference value is smaller than the threshold value, namely | E _ new-E _ old | < epsilon, the loop iteration is ended, otherwise E _ old = E _ new, and repeating the step 6.
Step 1, constructing a problem model of unmanned aerial vehicle edge computing network linear dependence task unloading, and comprising the following steps:
the Task of the terminal device i belonging to K is expressed as a binary group Task i ＝(L i ,C i ) Wherein the Task i Comprises two parts, L i Program data representing tasks, the unit being bits; c i Indicating the number of CPU cycles required to process a task in cycles/bits.
Representing a position Q of a drone using a 3D Cartesian coordinate system UAV ＝{x uav ,y uav ,H}，x uav Abscissa, y, representing unmanned aerial vehicle uav The vertical coordinate of the unmanned aerial vehicle is shown, and H is the height of the unmanned aerial vehicle and is fixed to 100m. The position of the ground terminal device is represented as
Wherein
Respectively represent the abscissa and ordinate of the ith ground terminal device. The location of the ground edge server is represented as
Wherein
Respectively representing the abscissa and the ordinate of the jth ground edge server.
The offload schedule order queue for all tasks is S = { L, S. the 1 ,S 2 ,…,S k ,…,S j Where L = { L = } 1 ,l 2 ,…,l k ,…,l NL Denotes the computation order of NL tasks computed off-board the drone, where l k Represents a kth task performed on the drone;
representing NS offloaded to computation on ground edge server j ∈ G j The unloading order of individual tasks, wherein s j,k Represents the kth task offloaded to the ground edge server j ∈ G, where
CPU frequency F = { F) assigned to calculation task unloaded to unmanned aerial vehicle 1 ,f 2 ,…,f k ,…,f NL In which f k Task for presentation k Calculating the frequency of the distributed CPUCPU when the unmanned aerial vehicle executes; so the uplink transmission power of the task
Wherein
Task representation k An uplink transmission power transmitted to the drone; so that the downlink transmission power of the task
Wherein
Task representation k Downlink transmission power transmitted to a ground edge server by an unmanned aerial vehicle;
s1-1 construction of communication model
Task of S1-1-1 terminal equipment i belonging to K i Uplink free space path loss model channel gains offloaded to drones are shown in (1)
Wherein alpha is 0 Indicating that for a transmission power of 1W, the received power at a reference distance of 1m,
representing the uplink distance from the terminal device i e K to the drone.
The channel gain of the downlink free space path loss model of the S1-1-2 task unloaded to the ground edge server j ∈ G through the unmanned aerial vehicle is shown in (2)
Wherein
Representing the downlink distance of the drone to the ground edge server j e G.
Task of S1-1-3 terminal equipment i belonging to K i Uplink transmission data rate offloaded to drone is shown as (3)
Wherein B is UL Indicates the bandwidth of the uplink channel and,
task representing terminal equipment i belonging to K i Transmission power, σ, offloaded to drone 2 Representing the noise spectral density.
Task of S1-1-4 terminal equipment i belonging to K i Downlink transmission data rates offloaded by drone to ground edge servers j ∈ G are shown in (4)
Wherein B is DL Which represents the bandwidth of the downlink channel(s),
task representing terminal equipment i belonging to K i And unloading the transmission power of j ∈ G to the ground edge server by the unmanned aerial vehicle.
S1-2 time delay analysis
Task of S1-2-1 terminal equipment i belonging to K i The uplink transmission time for transmitting to the unmanned aerial vehicle is shown as (5)
Task for S1-2-2 terminal equipment i belonging to K i The calculated time at the unmanned plane is shown as (6)
Wherein
Task representing allocation of unmanned aerial vehicle to terminal device i ∈ K k In cycles/s.
S1-2-3 terminal deviceTask for preparing i belonging to K i The downlink transmission time transmitted to the ground edge server j E G by the unmanned aerial vehicle is shown as (7)
Task for S1-2-4 terminal equipment i belonging to K i The computation time at the ground edge server is shown in (8)
Wherein
Representing the CPU frequency (in cycles/s) of the ground edge server j ∈ G.
Task for S1-2-5 terminal equipment i belonging to K i The calculated completion time for unloading to the drone is shown in (9)
Task for S1-2-6 terminal equipment i belonging to K i The completion time calculated by the unmanned aerial vehicle unloading onto the ground edge server j ∈ G is shown in (10)
Wherein
Transmission completion time for the task of device i e K to be offloaded to ground edge server j e eta by unmanned aerial vehicle, as shown in (11)
S1-2-7 so that the final completion time of the task is shown as (12)
S1-3 energy consumption analysis
Task for S1-3-1 terminal equipment i belonging to K i The uplink transmission energy consumption for transmitting to the unmanned aerial vehicle is shown as (11)
Task of S1-3-2 terminal equipment i belonging to K i The calculated energy consumption on the unmanned aerial vehicle is shown as (14)
Where k represents the effective capacitance coefficient of the drone, depending on the chip architecture of the CPU.
Task of S1-3-3 terminal equipment i belonging to K i The energy consumption of downlink transmission transmitted to the ground edge server by the unmanned aerial vehicle is shown as (15)
The hovering energy consumption required to be consumed by the unmanned aerial vehicle after the unmanned aerial vehicle finishes all tasks is calculated as shown in (16)
E hover ＝P h T (16)
Wherein P is h Indicating the hovering power of the drone in watts (W).
S1-3-5 Total energy consumption of ground terminal equipment and unmanned aerial vehicle for completing all tasks is shown as (17)
Wherein eta 1 Representing transmission coefficient of energy, η 2 Representing the calculated coefficient of energy consumption.
S1-4 problem description
Performing joint optimization on task unloading decision, task scheduling, resource allocation and the optimal position of the unmanned aerial vehicle, wherein the aim is to minimize the total energy consumption of all ground terminals and the unmanned aerial vehicle, and the problem is described as follows:
Q UAV ＝{x uav ，y uav ，H}，x uav ∈[0，1000]，y uav ∈[0，1000] (18i)
equation (18 a) is an objective function, where χ = { Q = { (Q) } UAV ,P UL ,P DL And F, X, S represent optimization variables.
Equation (18 b) represents that the drone CPU computation frequency is greater than zero and does not exceed the maximum CPU computation frequency.
Equation (18 c) indicates that the uplink transmission power of the task is greater than zero and does not exceed the maximum transmission power.
Equation (18 d) indicates that the downlink transmission power of the task is greater than zero and does not exceed the maximum transmission power.
Equation (18 e) represents the offloading tasks and corresponding scheduling order for the drone and the ground edge server.
Equation (18 f) indicates that the completion time for all tasks does not exceed the maximum time limit.
Equation (18 h) indicates that the task must be offloaded and can only be executed on a single edge server.
Equation (18 h) indicates that the task can only be completely unloaded or not.
Equation (18 i) indicates that the drone can only be within a specified range.
The problem model P1 proposed by the present invention is a nonlinear mixed integer optimization problem. By analyzing the problem model P1, we can find the following three features. Firstly, the unmanned aerial vehicle position directly or indirectly influences the allocation of computing resources and the overall computing energy consumption, and the unloading scheduling decision of tasks, the allocation of computing resources and communication resources are closely related to the unmanned aerial vehicle position. Second, the optimal position of the drone cannot be determined until the offload scheduling decision, computing resource and communication resource allocation is generated, and therefore it is affected by the offload scheduling decision, computing resource and communication resource allocation results. Thirdly, the allocation of computing resources and communication resources can only be accurately calculated if the unloading scheduling decision of the position and task of the unmanned aerial vehicle is optimal.
In order to solve the problem model P1, based on the idea of multi-objective hierarchical optimization, P1 is converted into three sub-problems to be subjected to successive iteration solution, and each sub-problem is to solve the sub-problem optimization problem under the condition of ensuring the optimality of other two sub-problems. The method regards the unloading scheduling decision as a first sub-problem, and solves the problem by adopting a greedy algorithm; the problem of the optimal position of the unmanned aerial vehicle is regarded as a second sub-problem, and a solution is carried out by adopting an SCA method; taking the problem of computing resource and communication resource allocation as a third sub-problem, and solving by adopting a convex optimization method; the purpose is to minimize the sum of the energy consumption of all ground terminals and drones.
Because the problem is decomposed into three subproblems, each subproblem can only obtain the solution of the current subproblem under the condition that the variables optimized by other subproblems are determined, and the global solution cannot be directly obtained. By successively iterating the three subproblems, the global solution is converged, and when the error solved by the current iteration and the later iteration is smaller than a specified threshold value, the global solution can be considered to be obtained.
Step 2, solving a first sub-problem:
the first subproblem of S2-1 is expressed as: under the conditions of the position of the unmanned aerial vehicle, the transmission power and the CPU calculation frequency, a task unloading decision and task scheduling are solved, and a problem model can be expressed as P2:
S.t.(18e)，(18f)，(18g)，(18h) (19b)
where (19 a) is an objective function and (19 b) is a constraint, { X, S } is an optimization variable, where X denotes an unload decision of a task and S denotes an unload scheduling order queue of the task.
S2-2, based on a greedy strategy with minimum priority of the number of cycles required by the CPU to process the tasks, the unloading decision of the tasks and the scheduling sequence of the tasks are solved, and the method specifically comprises the following steps:
i) Finding the CPU corresponding to each taskThe number of cycles required for processing is counted, all tasks are arranged in a descending order according to the number of cycles required for processing the tasks, and the task order V = { V } is obtained i |v i ＝L i C i ,v i E.g., K) and record the original subscript R = { R } for the task 1 ,...,r i ,...,r N }，r i ∈{1,...,N}。
ii) setting the initial index value of the array V to h =1, and setting the current energy consumption initial value excluding hovering energy consumption to E now =0, the initial value of the current task number of the unmanned aerial vehicle is NL =0, the initial value of the current task number of the ground edge server j belongs to G, and is NS j ＝0。
iii) Calculation task v h Respectively putting an unmanned aerial vehicle unloading queue L and a ground edge server j epsilon G unloading queue S j Post system energy consumption
And
comparison E UAV,now And
size of (1), if
Then the task V h Putting the unmanned aerial vehicle into an unloading queue L,
h = h +1, nl = nl +1, step iii) is repeatedly performed; otherwise, step iv) is entered after exit.
iv) computational task v h Respectively putting an unmanned aerial vehicle unloading queue L and a ground edge server j belonging to a G unloading queue S j Post system energy consumption
And
comparison E UAV,now And
size of (1), if
Then the task V h Unloading queue S for putting ground edge server k E G k ，
h＝h+1，NS k ＝NS k +1, iteratively performing step iv); otherwise, the step v) is entered after exiting.
v) if h is less than or equal to N, entering step iii), otherwise entering step vi).
vi) classifying all tasks in the unmanned aerial vehicle unloading queue L, and adding the tasks with the unloading transmission time smaller than the unmanned aerial vehicle calculation time into the array P by comparing the task unloading transmission time with the unmanned aerial vehicle calculation time L ，
Will P L All the tasks are arranged in an ascending order according to the unloading transmission time; adding the task with the unloading transmission time larger than or equal to the calculation time of the unmanned aerial vehicle into an array Q L ，
Will Q L In the method, all tasks are arranged according to the descending order of the unmanned aerial vehicle calculation time, and an array Q is obtained L To array P L Later get a new task scheduling order L = [ P = [) L ,Q L ]Go to step vii).
vii) offloading queues to ground edge servers S j All the tasks are classified, and the downlink transmission time and the ground edge are unloaded by comparing the tasksCalculating time of server, adding task whose unloading down transmission time is less than ground edge server calculation time into array
Will be provided with
All the tasks are arranged in an ascending order according to the unloading downlink transmission time; adding the task of which the unloading downlink transmission time is more than or equal to the calculation time of the ground edge server into an array
Will be provided with
All tasks are arranged according to the descending order of the calculation time of the ground edge server, and the arrays are arranged
To an array of
Later get a new task scheduling order
And ending the step and outputting S.
Step 3, solving a second sub-problem:
the second subproblem of S3-1 is expressed as: under the condition of giving unloading decision, scheduling sequence, uplink and downlink transmission power of a task and CPU (central processing unit) calculation frequency of the unmanned aerial vehicle, the optimal position of the unmanned aerial vehicle is solved, and a problem model can be represented as P3:
S.t.(18i) (20b)
wherein (20 a) is an objective function, Q UAV Are the optimization variables.
Since the drone position optimizes variables and will not be moving upon determination, assuming offload scheduling queue S, ground terminals, and drone transmit power determination.
And
is about Q UAV Is not a convex function, but
And
are respectively about
And
is convex function of, so will
And
are respectively paired
And
and (3) performing first-order Taylor expansion to obtain corresponding Taylor expansion formulas as shown in (21) and (22):
wherein
k is the current number of iterations.
Obtaining corresponding uplink transmission energy consumption
And downlink transmission energy consumption
As shown in (23) and (24):
will be provided with
And
substituting P3, the problem model P3 transforms into a problem model P4:
S.t.(18i) (25b)
wherein (25 a) is an objective function, Q UAV Are the optimization variables.
S3-2, solving the position of the unmanned aerial vehicle based on an SCA algorithm, and specifically comprising the following steps:
i) Initialization Q UAV (0)＝(500,500,100)，k＝0，α＝0.5，ρ＝0.01，θ(0)＝1，θ(k)∈(0,1]。
ii) solving for the objective P4 yields the smallest E total (k) And corresponding unmanned plane position, note
iii) Updating
θ(k+1)＝θ(k)(1-α)。
iv) calculating the target value Total energy consumption E based on the formula (17) total (k + 1), if | | | E total (k+1)-E total (k)||>P, if k = k +1, jumping to the step ii), otherwise, ending iteration, and outputting the optimal position Q of the unmanned aerial vehicle UAV (k+1)。
Step 4, solving a third sub-problem:
the third subproblem of S4-1 is expressed as: under the condition of giving unloading decision, scheduling sequence and position of the unmanned aerial vehicle of the task, solving uplink and downlink transmission power of the task and CPU calculation frequency when calculating on the unmanned aerial vehicle, wherein a problem model can be represented as P5:
S.t.(18b),(18c),(18d) (26b)
equation (26 c) indicates that all tasks on the drone can be executed only after transmission to the drone.
Equation (26 d) indicates that all tasks on the drone, except the first task, must wait until the last off-load task is completed before being executed.
Equation (26 e) indicates that all tasks on the ground edge server can be transmitted to the ground edge server for execution only after transmission to the drone.
Equation (26 f) indicates that all tasks on the ground edge server except the first task must wait for the last unloading task to be transmitted to the ground edge server for execution.
S4-1-1 introduces variable substitution, so that
ω＝σ 2 /α 0 ，ε＝1/B UL ，τ＝1/B DL . Transforming problem model P5 to problem model P6, as follows:
S.t.(26c),(26d),(26e),(26f) (27b)
wherein
And
to optimize the variables, where j ∈ G,
s4-1-2, according to the first sub-problem, an unloading scheduling decision is obtained, and unloading of the task can be determinedScheduling decision S, completion time of task execution on unmanned aerial vehicle
Transmission completion time for task transmission to ground edge server
Completion time of task execution on edge server
And flight energy consumption E of unmanned aerial vehicle hover And the target formula is the sum of convex functions, so the solution can be based on convex optimization.
S4-1-3 introduction of Lagrange multiplier
Wherein
And
wherein j belongs to G, the Lagrangian function and the dual problem of the problem model P6 are constructed, and the Lagrangian function of the problem model P6 is as follows:
the dual function of the problem model P6 is defined as
The dual problem is that
S4-2, solving transmission power of the task and unmanned aerial vehicle CPU calculation frequency based on convex optimization, and the steps are as follows:
i) And calculating a target value of the current given task unloading decision, the task scheduling sequence, the uplink and downlink transmission power of the tasks and the calculation frequency of the unmanned aerial vehicle CPU according to the problem model P5, and recording the target value as Val _ old.
ii) solving the unconstrained convex function (27 a) by Newton's method. The solution obtained
The solutions are respectively substituted into the formulas (26 c), (26 d), (26 e) and (26 f), and the solution gamma is obtained L ，
Each of which satisfies the equations (26 c), (26 d), (26 e) and (26 f), respectively, then Γ L ，
Is the optimal solution for the target formula and proceeds to step vi), otherwise to step iii).
iii) Lagrange function (28 a) pair
And
the partial derivatives are calculated as shown in (29), (30), (31) and (32), and the Lagrangian multiplier is calculated
And
such as (33)) And (34), (35) and (36).
iv) solving the solution gamma L ，
Classifying the solutions satisfying the beam conditions (26 c), (26 d), (26 e), and (26 f) into classes
Classifying solutions that do not satisfy the beam conditions (26 c), (26 d), (26 e), and (26 f) as
Will be collected
And
the number of the elements in (A) is respectively 2NL, nopt and 2NS j And nopt. Will be provided with
And
the corresponding Lagrange multipliers are obtained by substituting (29), (30), (31) and (32) respectively
And
while
And
corresponding lagrange multiplier
And
the values are all 0, and the problem model P6 becomes
And
problem model P7 for variables:
S.t.(28b) (37b)
v) solving for P7 again by Newton method to obtain optimal
Bonding of
And
obtaining a corresponding optimal solution gamma L ，
Step vi) is entered.
vi) solving the solution F L ，
Substituting (38), (39) and (40) to obtain
And substituted into the question P5 to obtain the latest target value, which is denoted as Val _ new, and the process proceeds to step vii).
vii) comparing the difference between Val _ new and Val _ old, if the difference is less than the threshold ρ, i.e. | Val _ new-Val _ old |, i.e.<E, the iteration is ended and output
Otherwise jump to i).
And 5, substituting the problem P1 to obtain a latest target value according to the task unloading scheduling decision obtained in the steps 2, 3 and 4, the position of the unmanned aerial vehicle, the uplink and downlink transmission rates of the corresponding tasks and the CPU calculation frequency of the tasks on the unmanned aerial vehicle, and recording the value as E _ new.
And 6, calculating a difference value between the current iteration target value E _ new and the previous iteration target value E _ old, wherein the initial value of E _ old is 0, if the difference value is smaller than a threshold epsilon, namely | E _ new-E _ old | < epsilon, the iteration is ended, and the optimal unmanned aerial vehicle position, unloading decision, scheduling sequence and resource allocation scheme are obtained, otherwise E _ old = E _ new, and jumping to the step 2.
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