CN115665802A - Calculation unloading and resource allocation method based on Lyapunov optimization - Google Patents

Calculation unloading and resource allocation method based on Lyapunov optimization Download PDF

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CN115665802A
CN115665802A CN202211347119.7A CN202211347119A CN115665802A CN 115665802 A CN115665802 A CN 115665802A CN 202211347119 A CN202211347119 A CN 202211347119A CN 115665802 A CN115665802 A CN 115665802A
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vehicle
mobile terminal
task
mounted mobile
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章谦骅
单杭冠
张朝阳
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Zhejiang University ZJU
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Abstract

The invention discloses a calculation unloading and resource allocation method based on Lyapunov optimization, which is applied to a mobile edge calculation task unloading system. The method determines the weighted sum of the total time delay, the total energy consumption and the total task migration overhead of the mobile edge computing task unloading system as the system overhead, and models the system overhead. Then, the problem of minimizing the total system overhead is solved by using a Lyapunov optimization theory, an unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and the calculation rate of the mobile edge calculation server to the task are calculated by using an iterative method, the optimal system overhead is obtained, and further the total system overhead is reduced.

Description

Calculation unloading and resource allocation method based on Lyapunov optimization
Technical Field
The invention belongs to the technical field of mobile edge computing, and particularly relates to a computing unloading and resource allocation method based on Lyapunov optimization.
Background
The 5G provides a highly flexible and extensible network technology, so that everything can be connected with each other, namely everything interconnection is supported. With the continuous development and perfection of the internet of things and wireless communication technology, various novel mobile applications are popular, so that the number of mobile terminals is increased explosively, and a large amount of mobile resources are consumed. As a key technology of 5G, the mobile edge computing server can be regarded as a new architecture, and compared with mobile cloud computing, the mobile edge computing server provides lower time delay and better computing flexibility for task offloading. The mobile terminal task can be sunk to be deployed on the mobile edge computing server for processing, so that the computing time delay and energy consumption are reduced, and the service quality and the user experience quality can be effectively improved.
In the prior art, task migration overhead generated by a vehicle-mounted mobile terminal is difficult to take into account. In a complex mobility scene, the problem analysis is performed based on a one-dimensional random uniform motion or a two-dimensional random uniform motion scene of a user, and a real scene user is generally a moving scene of a two-dimensional non-uniform random motion. In the current research of unloading the edge calculation task, aiming at the condition of a multi-mobile-terminal multi-mobile-edge calculation server, the research of minimizing average processing time delay and processing energy consumption is more perfect, but the additional overhead brought by the dynamic cross-area of the mobile terminal is not considered, so that the calculation deviation is larger.
Disclosure of Invention
The invention aims to solve the problems in the background art and provides a calculation unloading and resource allocation method based on Lyapunov optimization.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention provides a calculation unloading and resource allocation method based on Lyapunov optimization, which is applied to a mobile edge calculation task unloading system, wherein the mobile edge calculation task unloading system comprises M vehicle-mounted mobile terminals and N mobile edge calculation servers, and the calculation unloading and resource allocation method based on the Lyapunov optimization comprises the following steps:
calculating the weighted sum of the total time delay, the total energy consumption and the total task migration cost of the task unloading system by using the mobile edge as the system cost, and establishing an optimization model as follows:
Figure BDA0003917627290000021
wherein the content of the first and second substances,
Figure BDA0003917627290000022
Figure BDA0003917627290000023
Figure BDA0003917627290000024
wherein E is m (t) represents total energy consumption, q m (T) represents the total task migration overhead, T m (t) represents total delay, C (t) represents overhead,
Figure BDA0003917627290000025
an overhead weighting factor indicating the occurrence of region migration,
Figure BDA0003917627290000026
a weight factor that represents the total time delay,
Figure BDA0003917627290000027
weight factor representing the total consumed energy, E total Indicating the total amount of power of the vehicle-mounted mobile terminal, E cur (t) represents a current remaining capacity of the in-vehicle mobile terminal,
Figure BDA0003917627290000028
the percentage of the current residual capacity of the vehicle-mounted mobile terminal is represented, C1 represents that the calculation rate of the vehicle-mounted mobile terminal to the task cannot be larger than the maximum calculation rate per se
Figure BDA0003917627290000029
C2 represents that the calculation rate of the mobile edge calculation server to the task cannot be larger than the maximum calculation rate of the mobile edge calculation server
Figure BDA00039176272900000210
C3 represents that the calculation rate of all tasks in the area of the mobile edge calculation server cannot be larger than the maximum calculation rate of the mobile edge calculation server
Figure BDA00039176272900000211
C4 represents that the total consumed energy consumption cannot be larger than the current residual electric quantity of the vehicle-mounted mobile terminal, and C5 represents that the total time delay cannot be larger than the maximum tolerant time delay T of the task max And C6 represents that the transmitting power of the vehicle-mounted mobile terminal cannot be larger than the maximum transmitting power of the vehicle-mounted mobile terminal
Figure BDA00039176272900000212
C7 represents a value range of the unloading decision, C8 represents a value range of a weight factor of the total delay, and T ∈ T = {1,2.
Introducing a delay penalty function phi (t) into the optimization model, and simplifying the optimization model into:
П 2 :
Figure BDA0003917627290000031
s.t.C2,C3,C7,C8
according to time segments 2 Splitting to obtain the subproblems of the optimization model:
П 3 :
Figure BDA0003917627290000032
s.t.C2,C3,C7,C8
establishing a virtual queue and a penalty function for energy consumption according to the Lyapunov theory, calculating the drift upper boundary of the Lyapunov, and converting the subproblems of the optimization model into:
Π 4 :
Figure BDA0003917627290000033
s.t.C2,C3,C7,C8
wherein Q is m (t) represents the energy consumption backlog at time t, and V is a constant control parameter representing the tradeoff between system overhead and virtual queues.
According to II 4 And constructing an unloading decision, a calculation rate of the vehicle-mounted mobile terminal to the task and a mathematical expression of the transmitting power of the vehicle-mounted mobile terminal.
And randomly generating an unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and an initial solution of the calculation rate of the mobile edge calculation server to the task, then performing iterative calculation by using an iterative algorithm, updating the system overhead after each iteration until the value of the system overhead is converged, and outputting the final system overhead as the optimal system overhead.
Preferably, the total delay is expressed as follows:
Figure BDA0003917627290000034
T m (t)≤T max ≤τ
wherein the content of the first and second substances,
Figure BDA0003917627290000035
Figure BDA0003917627290000036
Figure BDA0003917627290000037
Figure BDA0003917627290000041
H m.n (t)＝h m,n (t)g 0 (d 0 /d m,n ) θ
wherein the content of the first and second substances,
Figure BDA0003917627290000042
represents the execution time delay of the in-vehicle mobile terminal,
Figure BDA0003917627290000043
representing the execution latency of the mobile edge compute server,
Figure BDA0003917627290000044
represents the transmission delay, T, of the vehicle-mounted mobile terminal for unloading the task to the mobile edge computing server max Representing the maximum tolerant time delay of each task, tau represents the working time slot of each mobile edge computing server, and the time slot tau is a time segment of the moment t, s m (t) denotes the unload decision at time t, and s m (t) =0 denotes that all tasks are performed at the in-vehicle mobile terminal, s m (t) =1 denotes that the task is completely unloaded to the mobile edge computing server for execution, 0 < s m (t) < 1 indicates that a part of tasks are executed in the vehicle-mounted mobile terminal and another part of tasks are executed in the mobile edge computing server, lambda m (t) represents the calculation task amount generated by downloading the mobile terminal at the moment t, and the unit is bit, c m The CPU period required by the vehicle-mounted mobile terminal to calculate each bit of data is represented, and the unit is cycle/bit, f m (t) represents the calculated rate of the task at time t of the in-vehicle mobile terminal,
Figure BDA0003917627290000045
representing the computation rate of the mobile edge computation server on the task, r m,n (t) represents the task transmission rate at time t,
Figure BDA0003917627290000046
representing the transmission power of the mobile terminal loaded at time t, I representing the average interference in each zone, σ 2 Representing the channel background noise, ω the channel bandwidth, H m,n (t) denotes channel gain, g 0 Represents a constant of path loss, and theta represents a road stiffness loss exponent，d 0 Denotes a reference distance, d m,n Indicates the distance from the vehicle-mounted mobile terminal to the mobile edge calculation server in the area, h m,n (t) represents a small-scale Rayleigh fading factor between the vehicle-mounted mobile terminal and the mobile edge computing server in the area where the vehicle-mounted mobile terminal is located,
Figure BDA0003917627290000047
indicating the connection state of the vehicle-mounted mobile terminal and the mobile edge computing server in the area, and when the connection state is
Figure BDA0003917627290000048
When the coverage of the mobile edge calculation server in the area of the vehicle-mounted mobile terminal is represented, the vehicle-mounted mobile terminal is in
Figure BDA0003917627290000049
Indicating that the vehicle-mounted mobile terminal is not under the coverage of the mobile edge computing server in the area.
Preferably, the total overhead is expressed as follows:
Figure BDA00039176272900000410
wherein the content of the first and second substances,
when the area of the vehicle-mounted mobile terminal is migrated, the following requirements are met:
q m (t)＝ε
when the vehicle-mounted mobile terminal does not have the region migration, the following requirements are met:
q m (t)＝0
wherein epsilon represents the overhead generated by the region migration of the vehicle-mounted mobile terminal,
Figure BDA0003917627290000051
showing the connection state of the vehicle-mounted mobile terminal and the mobile edge computing server in the area at the moment t,
Figure BDA0003917627290000052
vehicle-mounted mobile terminal for representing t-1 momentA connection status with a mobile edge computing server within the area.
Preferably, a virtual queue and a penalty function are established for energy consumption according to the Lyapunov theory, the drifting upper boundary of the Lyapunov is calculated, and the sub-problem of the optimization model is converted into an II 4 The method comprises the following steps:
because the energy consumption backlog quantity of the vehicle-mounted mobile terminal is influenced by the current residual electric quantity which depends on the total energy consumption at the last moment, the virtual queue Q is established according to the Lyapunov theory m (t) represents the backlog of energy consumption at time t:
Q m (t+1)＝max{Q m (t)+E cur (t)-E m (t),0}
wherein Q m (t + 1) represents the energy consumption backlog at time t + 1;
according to the lyapunov theory, the quadratic lyapunov function at time t is expressed as:
Figure BDA0003917627290000053
wherein L (t) represents a virtual queue Q m (t) a scalar of the total backlog;
the difference between the scalar quantity of the total backlog of the virtual queue at time t +1 and the scalar quantity of the total backlog of the virtual queue at time t is called Lyapunov drift DeltaL (t), and is expressed as:
ΔL(t)＝L(t+1)-L(t)
substituting lyapunov drift into drift theorem, and expressing as:
Figure BDA0003917627290000054
wherein V is a constant control parameter representing a tradeoff between system overhead and virtual queues;
substituting the drift theorem into the derivation of the energy consumption backlog:
Figure BDA0003917627290000055
therefore, the temperature of the molten metal is controlled,
Figure BDA0003917627290000056
and the number of the first and second electrodes,
Figure BDA0003917627290000057
wherein E is max The maximum energy consumption required by the vehicle-mounted mobile terminal to execute the task under the single time slot is represented;
B(t)≤B
and the number of the first and second electrodes,
Figure BDA0003917627290000061
the obtained drift theorem satisfies:
Figure BDA0003917627290000062
since B is constant, the formula (1) can be converted into pi 4 。
Preferably according to II 4 And constructing a mathematical expression of an unloading decision, a calculation rate of the vehicle-mounted mobile terminal to the task and the transmitting power of the vehicle-mounted mobile terminal, wherein the mathematical expression comprises the following steps:
∏ 4 the solution of (ii) can be regarded as two parts, namely, the combined solution of the current residual capacity of the vehicle-mounted mobile terminal, the total consumption energy consumption and the system overhead is established, and a current residual capacity model pi of the vehicle-mounted mobile terminal is established 4.1 ：
∏ 4.1 :
Figure BDA0003917627290000063
Current residual capacity E of vehicle-mounted mobile terminal cur (t) satisfies:
Figure BDA0003917627290000064
wherein the content of the first and second substances,
Figure BDA0003917627290000065
represents the average of the required maximum energy consumption of all tasks, and
Figure BDA0003917627290000066
optimal solution of current remaining capacity of the vehicle-mounted mobile terminal
Figure BDA0003917627290000067
Comprises the following steps:
Figure BDA0003917627290000068
establishing a total consumption energy consumption and system overhead model pi 4.2 ：
∏ 4.2 :
Figure BDA0003917627290000069
s.t.C2,C3,C7,C8
Calculating an unloading decision: defining the calculation rate of the vehicle-mounted mobile terminal to the task, the calculation rate of the mobile edge calculation server to the task and the emission power of the vehicle-mounted mobile terminal to be known, solving an unloading decision under a single time slot tau, and connecting II 4.2 Rewritten as n 4.2.1 ：
∏ 4.2.1 :
Figure BDA0003917627290000071
s.t.
Figure BDA0003917627290000072
Figure BDA0003917627290000073
II 4.2.1 For functional representation:
Figure BDA0003917627290000074
wherein λ is m (τ) represents the amount of computational tasks that would be generated by loading a mobile terminal in time slot τ, f m (τ) represents the calculated rate of tasks at the time slot τ for the loaded mobile terminal, r m,n (τ) represents the task transmission rate at slot τ,
Figure BDA0003917627290000075
representing the computation rate of the mobile edge computing server for the task at time slot tau,
Figure BDA0003917627290000076
representing the transmit power of the downloaded mobile terminal in time slot tau,
Figure BDA0003917627290000077
representing a monotonic function whose monotonicity depends on V-Q m (t) and
Figure BDA0003917627290000078
positive and negative, unload decision s m The value range of (t) can be determined by pi 4.2.1 The constraint of (2) obtains:
Figure BDA0003917627290000079
from this, an offloading strategy S can be derived m (t)：
Figure BDA00039176272900000710
Calculating the calculation rate of the vehicle-mounted mobile terminal to the task: defining an offloading decision,The calculation rate of the mobile edge calculation server to the task and the transmission power of the vehicle-mounted mobile terminal are known, the calculation rate of the vehicle-mounted mobile terminal to the task is solved in a single time slot, and pi is obtained 4.2 Rewritten as n 4.2.2 ：
Π 4.2.2 ：
Figure BDA00039176272900000711
s.t.(1-s m (τ))λ m (τ)c m /f m (t)≤T max
Figure BDA00039176272900000712
Figure BDA00039176272900000713
Wherein, E min The minimum energy consumption required by the vehicle-mounted mobile terminal to execute the task in a single time slot is represented.
II 4.2.2 Expressed in functional form:
Figure BDA0003917627290000081
wherein s is m (τ) indicates the offload decision at time slot τ, function
Figure BDA0003917627290000082
Is a quadratic function of the opening direction of the function and V-Q m The positive and negative of (t) are related when V-Q m (t) is positive with opening upward when V-Q m (t) is negative, open downwards, calculating f from the constraint m (t) the following:
Figure BDA0003917627290000083
calculating the task by the vehicle-mounted mobile terminalRate f m (t)：
Figure BDA0003917627290000084
Calculating the transmitting power of the vehicle-mounted mobile terminal: defining unloading decision, calculating speed of the vehicle-mounted mobile terminal to the task and calculating speed of the mobile edge calculating server to the task to be known, solving transmitting power of the vehicle-mounted mobile terminal in a single time slot, and calculating pi 4.2 Rewritten as pi 4.2.3 ：
Figure BDA0003917627290000085
II 4.2.3 Expressed in functional form:
Figure BDA0003917627290000086
constructing helper functions
Figure BDA0003917627290000091
Analysis of
Figure BDA0003917627290000092
Monotonicity of the function:
Figure BDA0003917627290000093
and the number of the first and second electrodes,
Figure BDA0003917627290000094
the first derivative is taken of the helper function:
Figure BDA0003917627290000095
order:
Figure BDA0003917627290000096
to pair
Figure BDA0003917627290000097
And (5) obtaining a derivative:
Figure BDA0003917627290000098
when in use
Figure BDA0003917627290000099
When the temperature of the water is higher than the set temperature,
Figure BDA00039176272900000910
when in use
Figure BDA00039176272900000911
When the temperature of the water is higher than the set temperature,
Figure BDA00039176272900000912
at this time
Figure BDA00039176272900000913
Is a monotonic function whose monotonicity is V-Q m (t) determining. For the
Figure BDA00039176272900000914
Is solved for, due to the constraints contained therein
Figure BDA00039176272900000915
Is difficult to solve directly, and therefore a taxonomic discussion is required, as follows:
according to the total time delay T in the formula (2) max To obtain a constraint condition of
Figure BDA00039176272900000916
The lower bound of (1):
Figure BDA00039176272900000917
then, the solution is carried out according to the second constraint condition in the formula (2) when
Figure BDA00039176272900000918
When the temperature of the water is higher than the set temperature,
Figure BDA0003917627290000101
then the second constraint in equation (2) is also obtained as:
Figure BDA0003917627290000102
transmitting power of the in-vehicle mobile terminal
Figure BDA0003917627290000103
Figure BDA0003917627290000104
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003917627290000105
two values of the transmitting power of the vehicle-mounted mobile terminal are respectively:
Figure BDA0003917627290000106
Figure BDA0003917627290000107
calculating the calculation rate of the mobile edge calculation server to the task: defining an optimal unloading decision, a calculation rate of the vehicle-mounted mobile terminal to the task and vehicle-mounted movementThe transmitting power of the terminal is known, the calculation rate of the mobile edge calculation server to the task is solved under the condition of single time slot, and pi is used 4.2 Rewritten as pi 4.2.4 ：
Π 4.2.4 :
Figure BDA0003917627290000111
s.t.
Figure BDA0003917627290000112
Figure BDA0003917627290000113
II 4.2.4 Expressed in functional form:
Figure BDA0003917627290000114
function(s)
Figure BDA0003917627290000115
Is a monotonic function, and is monotonic with V-Q m (t) is related.
According to II 4.2.4 Solving the constraint conditions of
Figure BDA0003917627290000116
The value range of (A):
Figure BDA0003917627290000117
computing the computing rate of the server to the task
Figure BDA0003917627290000118
Figure BDA0003917627290000119
Compared with the prior art, the invention has the beneficial effects that:
the method determines the weighted sum of the total time delay, the total energy consumption and the total task migration overhead of the mobile edge computing task unloading system as the system overhead, and models the system overhead. Then, the problem of minimizing the total system overhead is solved by using a Lyapunov optimization theory, an unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and the calculation rate of the mobile edge calculation server to the task are calculated by using an iterative method, the optimal system overhead is obtained, and further the total system overhead is reduced.
Drawings
FIG. 1 is a block diagram of a Lyapunov optimization-based computing offload and resource allocation method of the present invention;
FIG. 2 is a flow chart of a calculation offloading and resource allocation method based on Lyapunov optimization according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
It will be understood that when an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description of the present application herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.
As shown in fig. 1-2, a calculation offloading and resource allocation method based on lyapunov optimization is applied to a mobile edge calculation task offloading system, where the mobile edge calculation task offloading system includes M vehicle-mounted mobile terminals and N mobile edge calculation servers, and the calculation offloading and resource allocation method based on lyapunov optimization includes:
it should be noted that, as shown in fig. 1, there is one moving edge computing server in each area, and there are multiple vehicle-mounted mobile terminals, and because of limited computing capability of the vehicle-mounted mobile terminals, each vehicle-mounted mobile terminal can offload all or part of its task to the moving edge computing server in its area for remote execution. Besides, the positions of the vehicle-mounted mobile terminals are randomly distributed and are in a continuously moving state, the edge computing server is in a static state, and the position of the vehicle-mounted mobile terminal is static at each time slot.
Step S1, calculating the weighted sum of the total time delay, the total energy consumption and the total task migration overhead of a task unloading system by using a mobile edge as the system overhead, and establishing an optimization model as follows:
Figure BDA0003917627290000131
wherein the content of the first and second substances,
Figure BDA0003917627290000132
Figure BDA0003917627290000133
Figure BDA0003917627290000134
wherein E is m (t) represents total energy consumption, q m (T) represents the total task migration overhead, T m (t) represents total delay, C (t) represents overhead,
Figure BDA0003917627290000135
an overhead weighting factor indicating the occurrence of region migration,
Figure BDA0003917627290000136
a weight factor representing the total time delay,
Figure BDA0003917627290000137
weight factor representing the total consumed energy, E total Indicating the total amount of power of the vehicle-mounted mobile terminal, E cur (t) represents a current remaining capacity of the in-vehicle mobile terminal,
Figure BDA0003917627290000138
the percentage of the current residual capacity of the vehicle-mounted mobile terminal is represented, C1 represents that the calculation rate of the vehicle-mounted mobile terminal to the task cannot be larger than the maximum calculation rate per se
Figure BDA0003917627290000139
C2 represents that the calculation rate of the mobile edge calculation server to the task cannot be larger than the maximum calculation rate of the mobile edge calculation server
Figure BDA00039176272900001310
C3 represents that the calculation rate of all tasks in the area of the mobile edge calculation server cannot be larger than the maximum calculation rate of the mobile edge calculation server
Figure BDA00039176272900001311
C4 represents that the total consumed energy consumption cannot be larger than the current residual electric quantity of the vehicle-mounted mobile terminal, and C5 represents that the total time delay cannot be larger than the maximum tolerance time delay T of the task max And C6 represents that the transmitting power of the vehicle-mounted mobile terminal cannot be larger than the maximum transmitting power of the vehicle-mounted mobile terminal
Figure BDA00039176272900001312
C7 represents a value range of the unloading decision, C8 represents a value range of a weight factor of the total delay, and T ∈ T = {1,2.
Specifically, a set of vehicle-mounted Mobile terminals M = {1,2,. M., M }, a set of Mobile Edge Computing (MEC) servers N = {1,2,. N., N }, different times T ∈ T = {1,2,..., T }, the working time slot of each Mobile Edge Computing server is τ, and the time slot τ is a time slice of the time T.
Each task of the in-vehicle mobile terminal is represented by a quintuple { lambda [ ] m (t),c m ,T max ,A m (t),B m (t) }, in which, A m (t) the position of the vehicle-mounted mobile terminal at time t is represented by a coordinate (alpha) m (t),β m (t)) represents; b is m (t) represents the moving direction a of the in-vehicle mobile terminal m (t) and moving speed v m (t) of (d). And the vehicle-mounted mobile terminal t is at the time A m The abscissa and ordinate of (t) can be expressed as:
Figure BDA0003917627290000149
tasks of the vehicle-mounted mobile terminal are independent.
Because the downlink data volume is very small compared with the uplink data volume (namely, the data volume fed back after the mobile edge computing server finishes processing the task is smaller than the data volume transmitted to the mobile edge computing server), the time delay of the computing result returned by the mobile edge computing server to the vehicle-mounted mobile terminal can be ignored.
The total delay is expressed as follows:
Figure BDA0003917627290000141
T m (t)≤T max ≤τ
wherein the content of the first and second substances,
Figure BDA0003917627290000142
Figure BDA0003917627290000143
Figure BDA0003917627290000144
Figure BDA0003917627290000145
H m.n (t)＝h m,n (t)g 0 (d 0 /d m,n ) θ
wherein the content of the first and second substances,
Figure BDA0003917627290000146
represents the execution time delay of the in-vehicle mobile terminal,
Figure BDA0003917627290000147
representing the execution latency of the mobile edge compute server,
Figure BDA0003917627290000148
represents the transmission delay, T, of the vehicle-mounted mobile terminal for unloading the task to the mobile edge computing server max Representing the maximum tolerant time delay of each task, tau represents the working time slot of each mobile edge computing server, and the time slot tau is a time segment of the moment t, s m (t) denotes the unload decision at time t, and s m (t) =0 denotes that all tasks are performed at the in-vehicle mobile terminal, s m (t) =1 denotes that the task is completely unloaded to the mobile edge computing server for execution, 0 < s m (t) < 1 indicates that a part of tasks are executed in the vehicle-mounted mobile terminal and another part of tasks are executed in the mobile edge computing server, lambda m (t) represents the calculation task amount generated by downloading the mobile terminal at the moment t, and the unit is bit, c m The CPU period required by the vehicle-mounted mobile terminal to calculate each bit of data is represented, and the unit is cycle/bit, f m (t) represents the calculated rate of the tasks at the time t of the vehicle-mounted mobile terminal,
Figure BDA0003917627290000151
representing the computation rate of the mobile edge computation server on the task, r m,n (t) represents the task transmission rate at time t,
Figure BDA0003917627290000152
denotes the transmission power of the mobile terminal loaded at time t, I denotes the average interference in the respective region, σ 2 Representing the channel background noise, ω the channel bandwidth, H m,n (t) denotes channel gain, g 0 Represents the path loss constant, theta represents the road power loss exponent, d 0 Denotes a reference distance, d m,n Indicating the distance h from the vehicle-mounted mobile terminal to the mobile edge calculation server in the area m,n (t) represents a small-scale Rayleigh fading factor between the vehicle-mounted mobile terminal and the mobile edge calculation server in the area where the vehicle-mounted mobile terminal is located,
Figure BDA0003917627290000153
indicating the connection state of the vehicle-mounted mobile terminal and the mobile edge computing server in the area, and when the connection state is
Figure BDA0003917627290000154
Indicating that the vehicle-mounted mobile terminal is under the coverage of the mobile edge computing server in the area where the vehicle-mounted mobile terminal is located
Figure BDA0003917627290000155
Indicating that the vehicle-mounted mobile terminal is not under the coverage of the mobile edge computing server in the area.
The total consumed energy is expressed as follows:
Figure BDA0003917627290000156
wherein the content of the first and second substances,
Figure BDA0003917627290000157
Figure BDA0003917627290000158
Figure BDA0003917627290000159
wherein the content of the first and second substances,
Figure BDA00039176272900001510
represents the execution energy consumption of the in-vehicle mobile terminal,
Figure BDA00039176272900001511
represents the transmission energy consumption of the vehicle-mounted mobile terminal for unloading the task to the mobile edge computing server,
Figure BDA00039176272900001512
the power of the vehicle-mounted mobile terminal for executing the task is represented, and k represents a power traction coefficient.
The total overhead is expressed as follows:
Figure BDA00039176272900001513
wherein the content of the first and second substances,
when the area of the vehicle-mounted mobile terminal is migrated, the following requirements are met:
q m (t)＝ε
when the vehicle-mounted mobile terminal does not have the region migration, the following requirements are met:
q m (t)＝0
wherein epsilon represents the overhead generated by the region migration of the vehicle-mounted mobile terminal,
Figure BDA00039176272900001514
showing the connection state of the vehicle-mounted mobile terminal and the mobile edge computing server in the area at the moment t,
Figure BDA0003917627290000161
representing the calculation of the moving edge of the vehicle-mounted mobile terminal and the area at the t-1 momentThe connection status of the server.
S2, introducing a delay penalty function phi (t) into the optimization model, and simplifying the optimization model into:
П 2 :
Figure BDA0003917627290000162
s.t.C2,C3,C7,C8
and phi (t) = + (plus) varies when the execution energy consumption of the vehicle-mounted mobile terminal exceeds the current residual electric quantity of the vehicle-mounted mobile terminal at the moment t or the execution delay of the vehicle-mounted mobile terminal exceeds the maximum tolerance delay of the task, and phi (t) =0 when the execution energy consumption of the vehicle-mounted mobile terminal does not exceed the current residual electric quantity of the vehicle-mounted mobile terminal at the moment t or the execution delay of the vehicle-mounted mobile terminal does not exceed the maximum tolerance delay of the task.
Step S3, according to the time segments 2 Splitting to obtain the subproblems of the optimization model:
П 3 :
Figure BDA0003917627290000163
s.t.C2,C3,C7,C8
s4, establishing a virtual queue and a penalty function for energy consumption according to the Lyapunov theory, calculating the drifting upper boundary of the Lyapunov, and converting the subproblems of the optimization model into the following steps:
Π 4 :
Figure BDA0003917627290000164
s.t.C2,C3,C7,C8
wherein Q is m (t) represents the energy consumption backlog at time t, and V is a constant control parameter representing the tradeoff between system overhead and virtual queues.
Specifically, because the energy consumption backlog quantity of the vehicle-mounted mobile terminal is influenced by the current residual energy quantity, which depends on the total energy consumption at the last moment, the virtual queue Q is established according to the lyapunov theory m (t) represents the backlog of energy consumption at time t:
Q m (t+1)＝max{Q m (t)+E cur (t)-E m (t),0}
wherein Q is m (t + 1) represents the energy consumption backlog at time t + 1;
according to the lyapunov theory, the quadratic lyapunov function at time t is expressed as:
Figure BDA0003917627290000165
wherein L (t) represents a virtual queue Q m (t) a scalar of the total backlog;
the difference between the scalar quantity of the total backlog of the virtual queue at time t +1 and the scalar quantity of the total backlog of the virtual queue at time t is called Lyapunov drift DeltaL (t), and is expressed as:
ΔL(t)＝L(t+1)-L(t)
substituting lyapunov drift into the drift theorem, expressed as:
Figure BDA0003917627290000171
wherein V is a constant control parameter representing a tradeoff between system overhead and virtual queues;
substituting the drift theorem into the derivation of the energy consumption backlog:
Figure BDA0003917627290000172
therefore, the temperature of the molten metal is controlled,
Figure BDA0003917627290000173
and the number of the first and second electrodes,
Figure BDA0003917627290000174
wherein E is max The maximum energy consumption required by the vehicle-mounted mobile terminal to execute the task under the single time slot is represented;
B(t)≤B
and the number of the first and second groups is,
Figure BDA0003917627290000175
the obtained drift theorem satisfies:
Figure BDA0003917627290000176
since B is constant, equation (1) can be converted into pi 4 。
Step S5, according to pi 4 And constructing a mathematical expression of the unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task and the transmitting power of the vehicle-mounted mobile terminal.
In particular, pi 4 The solution can be regarded as two parts, namely the combined solution of the current residual capacity, the total consumption energy consumption and the system overhead of the vehicle-mounted mobile terminal, and the current residual capacity model pi of the vehicle-mounted mobile terminal is established 4.1 ：
П 4.1 :
Figure BDA0003917627290000177
Current residual capacity E of vehicle-mounted mobile terminal cur (t) satisfies:
Figure BDA0003917627290000181
wherein the content of the first and second substances,
Figure BDA0003917627290000182
represents the average of the required maximum energy consumption of all tasks, and
Figure BDA0003917627290000183
optimal solution of current remaining capacity of the vehicle-mounted mobile terminal
Figure BDA0003917627290000184
Comprises the following steps:
Figure BDA0003917627290000185
establishing a total consumption energy consumption and system overhead model pi 4.2 ：
∏ 4.2 :
Figure BDA0003917627290000186
s.t.C2,C3,C7,C8
Calculating an unloading decision: defining the calculation rate of the vehicle-mounted mobile terminal to the task, the calculation rate of the mobile edge calculation server to the task and the emission power of the vehicle-mounted mobile terminal to be known, solving an unloading decision under a single time slot tau, and connecting II 4.2 Rewritten as pi 4.2.1 ：
∏ 4.2.1 :
Figure BDA0003917627290000187
s.t.
Figure BDA0003917627290000188
Figure BDA0003917627290000189
II 4.2.1 For functional representation:
Figure BDA00039176272900001810
wherein λ is m (τ) represents the amount of computational tasks that would be generated by loading a mobile terminal in time slot τ, f m (τ) represents the calculated speed of the task by the loaded mobile terminal at time slot τRate, r m,n (τ) represents the task transmission rate at slot τ,
Figure BDA00039176272900001811
representing the computation rate of the mobile edge computing server for the task at time slot tau,
Figure BDA00039176272900001812
representing the transmit power of the downloaded mobile terminal in time slot tau,
Figure BDA00039176272900001813
representing a monotonic function whose monotonicity depends on V-Q m (t) and
Figure BDA00039176272900001814
positive and negative, unload decision s m The value range of (t) can be determined by pi 4.2.1 The constraint of (2) obtains:
Figure BDA00039176272900001815
from this, an offloading strategy S can be derived m (t)：
Figure BDA0003917627290000191
Calculating the calculation rate of the vehicle-mounted mobile terminal to the task: defining an unloading decision, calculating the task rate of the mobile edge calculation server and the transmitting power of the vehicle-mounted mobile terminal to be known, solving the task rate of the vehicle-mounted mobile terminal in a single time slot, and combining pi 4.2 Rewritten as n 4.2.2 ：
Π 4.2.2 ：
Figure BDA0003917627290000192
s.t.(1-s m (τ))λ m (τ)c m /f m (t)≤T max
Figure BDA0003917627290000193
Figure BDA0003917627290000194
Wherein E is min The minimum energy consumption required by the vehicle-mounted mobile terminal to execute the task under the single time slot is represented;
II 4.2.2 Expressed in functional form:
Figure BDA0003917627290000195
wherein s is m (τ) indicates the offload decision at time slot τ, function
Figure BDA0003917627290000196
Is a quadratic function of the relationship, and the opening direction of the function and V-Q m The positive and negative of (t) are related when V-Q m (t) is positive with opening upward when V-Q m (t) is negative, open downwards, calculating f from the constraint m (t) the following:
Figure BDA0003917627290000197
the vehicle-mounted mobile terminal calculates the task rate f m (t)：
Figure BDA0003917627290000198
Calculating the transmitting power of the vehicle-mounted mobile terminal: defining unloading decision, calculating speed of the vehicle-mounted mobile terminal to the task and calculating speed of the mobile edge calculating server to the task to be known, solving transmitting power of the vehicle-mounted mobile terminal in a single time slot, and combining II 4.2 Rewritten as pi 4.2.3 ：
Figure BDA0003917627290000201
II 4.2.3 Expressed in functional form:
Figure BDA0003917627290000202
constructing helper functions
Figure BDA0003917627290000203
Analysis of
Figure BDA0003917627290000204
Monotonicity of the function:
Figure BDA0003917627290000205
and the number of the first and second electrodes,
Figure BDA0003917627290000206
the first derivative is taken of the helper function:
Figure BDA0003917627290000207
order:
Figure BDA0003917627290000208
for is to
Figure BDA0003917627290000209
And (5) obtaining a derivative:
Figure BDA00039176272900002010
when in use
Figure BDA0003917627290000211
When the temperature of the water is higher than the set temperature,
Figure BDA0003917627290000212
when the temperature is higher than the set temperature
Figure BDA0003917627290000213
When the temperature of the water is higher than the set temperature,
Figure BDA0003917627290000214
at this time
Figure BDA0003917627290000215
Is a monotonic function whose monotonicity is V-Q m (t) determining. For the
Figure BDA0003917627290000216
Is solved for, due to the constraints contained therein
Figure BDA0003917627290000217
Is difficult to solve directly, and therefore a classification discussion is required, as follows:
according to the total time delay T in the formula (2) max To obtain a constraint condition of
Figure BDA0003917627290000218
The lower bound of (1):
Figure BDA0003917627290000219
then, the solution is carried out according to the second constraint condition in the formula (2) when
Figure BDA00039176272900002110
When the temperature of the water is higher than the set temperature,
Figure BDA00039176272900002111
then the second constraint in equation (2) is also obtained as:
Figure BDA00039176272900002112
transmitting power of the in-vehicle mobile terminal
Figure BDA00039176272900002113
Figure BDA0003917627290000221
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003917627290000222
respectively two values of the transmitting power of the vehicle-mounted mobile terminal:
Figure BDA0003917627290000223
Figure BDA0003917627290000224
calculating the calculation rate of the mobile edge calculation server to the task: defining an optimal unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task and the transmission power of the vehicle-mounted mobile terminal to be known, solving the calculation rate of the mobile edge calculation server to the task in a single time slot, and calculating the II 4.2 Rewritten as II 4.2.4 ：
Π 4.2.4 :
Figure BDA0003917627290000225
s.t.
Figure BDA0003917627290000226
Figure BDA0003917627290000227
II 4.2.4 Expressed in functional form:
Figure BDA0003917627290000228
function(s)
Figure BDA0003917627290000229
Is a monotonic function, and is monotonic with V-Q m (t) related;
according to II 4.2.4 Solving the constraint conditions of
Figure BDA00039176272900002210
The value range of (A):
Figure BDA0003917627290000231
computing the computing rate of the server to the task
Figure BDA0003917627290000232
Figure BDA0003917627290000233
And S6, randomly generating an unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and the initial solution of the calculation rate of the mobile edge calculation server to the task, then performing iterative calculation by using an iterative algorithm, updating the system overhead after each iteration until the value of the system overhead is converged, and outputting the final system overhead as the optimal system overhead.
Specifically, as shown in fig. 2, the iterative algorithm in this embodiment is implemented based on python, and the number M of the vehicle-mounted mobile terminals and the number of the mobile edge computing servers are input into the algorithmN, channel bandwidth omega, maximum rate of task calculation by vehicle-mounted mobile terminal
Figure BDA0003917627290000234
And maximum rate of computation of tasks by the mobile edge compute server
Figure BDA0003917627290000235
And parameters of a quintuple of the task, then randomly generating an unloading decision, a calculation rate of the vehicle-mounted mobile terminal to the task, a transmitting power of the vehicle-mounted mobile terminal and a calculation rate of the mobile edge calculation server to the task, solving corresponding system overhead, and taking secondary system overhead as initialization system overhead C old (t), the iterative algorithm iterates the unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and the calculation rate of the mobile edge calculation server to the task, and the updating of the system overhead C is completed each time of iteration new And (t), if the value of the direct system overhead is in convergence, finishing iteration to obtain the optimal system overhead, wherein the unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and the calculation rate of the mobile edge calculation server to the task are all optimal solutions.
The method determines the weighted sum of the total time delay, the total energy consumption and the total task migration overhead of the mobile edge computing task unloading system as the system overhead, and models the system overhead. Then, the problem of minimizing the total system overhead is solved by using a Lyapunov optimization theory, an unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and the calculation rate of the mobile edge calculation server to the task are calculated by using an iterative method, the optimal system overhead is obtained, and further the total system overhead is reduced.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express the more specific and detailed embodiments described in the present application, but not be construed as limiting the claims. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent application shall be subject to the appended claims.

Claims (6)

1. A calculation unloading and resource allocation method based on Lyapunov optimization is applied to a mobile edge calculation task unloading system and is characterized in that: the mobile edge computing task unloading system comprises M vehicle-mounted mobile terminals and N mobile edge computing servers, and the computing unloading and resource allocation method based on Lyapunov optimization comprises the following steps:
and (3) calculating the weighted sum of the total time delay, the total energy consumption and the total task migration overhead of the task unloading system by using the mobile edge as the system overhead, and establishing an optimization model as follows:
Figure FDA0003917627280000011
Figure FDA0003917627280000012
Figure FDA0003917627280000013
Figure FDA0003917627280000014
C4:E m (t)≤E cur (t)
C5:T m (t)≤T max ≤τ
Figure FDA0003917627280000015
C7:0≤s m (t)≤1
Figure FDA0003917627280000016
wherein the content of the first and second substances,
Figure FDA0003917627280000017
Figure FDA0003917627280000018
Figure FDA0003917627280000019
wherein E is m (t) represents total energy consumption, q m (T) represents the total task migration overhead, T m (t) represents total delay, C (t) represents overhead,
Figure FDA00039176272800000110
an overhead weighting factor indicating the occurrence of region migration,
Figure FDA00039176272800000111
a weight factor representing the total time delay,
Figure FDA00039176272800000112
weight factor representing the total consumed energy, E total Indicating the total amount of power of the vehicle-mounted mobile terminal, E cur (t) represents a current remaining capacity of the in-vehicle mobile terminal,
Figure FDA00039176272800000113
the percentage of the current residual capacity of the vehicle-mounted mobile terminal is represented, C1 represents that the calculation rate of the vehicle-mounted mobile terminal to the task cannot be larger than the maximum calculation rate per se
Figure FDA00039176272800000114
C2 represents that the calculation rate of the mobile edge calculation server to the task cannot be larger than the maximum calculation rate of the mobile edge calculation server
Figure FDA00039176272800000115
C3 represents that the calculation rate of the mobile edge calculation server for all tasks in the area cannot be larger than the maximum calculation rate of the mobile edge calculation server
Figure FDA0003917627280000021
C4 represents that the total consumed energy consumption cannot be larger than the current residual electric quantity of the vehicle-mounted mobile terminal, and C5 represents that the total time delay cannot be larger than the maximum tolerant time delay T of the task max And C6 represents that the transmitting power of the vehicle-mounted mobile terminal cannot be larger than the maximum transmitting power of the vehicle-mounted mobile terminal
Figure FDA0003917627280000022
C7 represents a value range of the unloading decision, C8 represents a value range of a weight factor of the total delay, and T ∈ T = {1,2., T } at different times;
introducing a delay penalty function phi (t) into the optimization model, and simplifying the optimization model into the following steps:
Figure FDA0003917627280000023
s.t.C2,C3,C7,C8
according to time segments 2 Splitting to obtain the subproblems of the optimization model:
Figure FDA0003917627280000024
s.t.C2,C3,C7,C8
establishing a virtual queue and a penalty function for energy consumption according to the Lyapunov theory, calculating the drift upper boundary of the Lyapunov, and converting the subproblems of the optimization model into:
Figure FDA0003917627280000025
s.t.C2,C3,C7,C8
wherein Q m (t) represents the energy consumption backlog at time t, and V is a constant control parameter representing the balance between the system overhead and the virtual queue;
according to II 4 Constructing an unloading decision, a calculation rate of the vehicle-mounted mobile terminal to the task and a mathematical expression of the transmitting power of the vehicle-mounted mobile terminal;
and randomly generating an unloading decision, the calculation rate of the vehicle-mounted mobile terminal to the task, the transmitting power of the vehicle-mounted mobile terminal and an initial solution of the calculation rate of the mobile edge calculation server to the task, then performing iterative calculation by using an iterative algorithm, updating the system overhead after each iteration until the value of the system overhead is converged, and outputting the final system overhead as the optimal system overhead.
2. The method of lyapunov-optimization-based computational offload and resource allocation according to claim 1, wherein: the total delay is expressed as follows:
Figure FDA0003917627280000026
T m (t)≤T max ≤τ
wherein the content of the first and second substances,
Figure FDA0003917627280000031
Figure FDA0003917627280000032
Figure FDA0003917627280000033
Figure FDA0003917627280000034
H m.n (t)＝h m,n (t)g 0 (d 0 /d m,n ) θ
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003917627280000035
represents the execution time delay of the in-vehicle mobile terminal,
Figure FDA0003917627280000036
representing the execution latency of the mobile edge compute server,
Figure FDA0003917627280000037
represents the transmission delay, T, of the vehicle-mounted mobile terminal for unloading the task to the mobile edge computing server max Representing the maximum tolerant time delay of each task, representing the working time slot of each mobile edge computing server, wherein the time slot is a time slice of the moment t, s m (t) denotes the offloading decision at time t, and s m (t) =0 denotes that all tasks are performed at the in-vehicle mobile terminal, s m (t) =1 denotes that the task is completely unloaded to the mobile edge computing server for execution, 0 < s m (t) < 1 indicates that a part of tasks are executed in the vehicle-mounted mobile terminal and another part of tasks are executed in the mobile edge computing server, lambda m (t) generated by downloading the mobile terminal at time tCalculating the task amount and the unit is bit, c m The CPU period required by the vehicle-mounted mobile terminal to calculate each bit of data is represented, and the unit is cycle/bit, f m (t) represents the calculated rate of the task at time t of the in-vehicle mobile terminal,
Figure FDA0003917627280000038
representing the computation rate of the mobile edge computation server on the task, r m,n (t) represents the task transmission rate at time t,
Figure FDA0003917627280000039
representing the transmission power of the mobile terminal loaded at time t, I representing the average interference in each zone, σ 2 Representing the channel background noise, ω the channel bandwidth, H m,n (t) denotes channel gain, g 0 Represents the path loss constant, theta represents the road power loss exponent, d 0 Denotes a reference distance, d m,n Indicating the distance h from the vehicle-mounted mobile terminal to the mobile edge calculation server in the area m,n (t) represents a small-scale Rayleigh fading factor between the vehicle-mounted mobile terminal and the mobile edge calculation server in the area where the vehicle-mounted mobile terminal is located,
Figure FDA00039176272800000310
indicating the connection state of the vehicle-mounted mobile terminal and the mobile edge computing server in the area, and when the connection state is
Figure FDA00039176272800000311
When the coverage of the mobile edge calculation server in the area of the vehicle-mounted mobile terminal is represented, the vehicle-mounted mobile terminal is in
Figure FDA00039176272800000312
Indicating that the vehicle-mounted mobile terminal is not under the coverage of the mobile edge computing server in the area.
3. The method of lyapunov-optimization-based computational offload and resource allocation according to claim 2, wherein: the total consumed energy is expressed as follows:
Figure FDA0003917627280000041
wherein the content of the first and second substances,
Figure FDA0003917627280000042
Figure FDA0003917627280000043
Figure FDA0003917627280000044
wherein the content of the first and second substances,
Figure FDA0003917627280000045
represents the execution energy consumption of the in-vehicle mobile terminal,
Figure FDA0003917627280000046
represents the transmission energy consumption of the vehicle-mounted mobile terminal for unloading the task to the mobile edge computing server,
Figure FDA0003917627280000047
the power of the vehicle-mounted mobile terminal for executing the task is represented, and k represents a power traction coefficient.
4. The method of lyapunov-optimization-based computational offload and resource allocation according to claim 3, wherein: the total overhead is expressed as follows:
Figure FDA0003917627280000048
wherein the content of the first and second substances,
when the area of the vehicle-mounted mobile terminal is migrated, the following requirements are met:
q m (t)＝ε
when the area of the vehicle-mounted mobile terminal is not migrated, the following conditions are met:
q m (t)＝0
wherein epsilon represents the overhead generated by the region migration of the vehicle-mounted mobile terminal,
Figure FDA0003917627280000049
showing the connection state of the vehicle-mounted mobile terminal and the mobile edge computing server in the area at the moment t,
Figure FDA00039176272800000410
and the connection state of the vehicle-mounted mobile terminal and the mobile edge computing server in the area at the moment of t-1 is shown.
5. The Lyapunov optimization-based computing offload and resource allocation method of claim 4, wherein: establishing a virtual queue and a penalty function according to the Lyapunov theory pair energy consumption, calculating the drift upper boundary of the Lyapunov, and converting the sub-problem of the optimization model into pi 4 The method comprises the following steps:
because the energy consumption backlog quantity of the vehicle-mounted mobile terminal is influenced by the current residual electric quantity which depends on the total energy consumption at the last moment, the virtual queue Q is established according to the Lyapunov theory m (t) represents the backlog of energy consumption at time t:
Q m (t+1)＝max{Q m (t)+E cur (t)-E m (t),0}
wherein Q is m (t + 1) represents the energy consumption backlog at time t + 1;
according to lyapunov theory, the quadratic lyapunov function at time t is expressed as:
Figure FDA0003917627280000051
wherein L (t) represents a virtual queue Q m (t) a scalar of the total backlog;
the difference between the scalar quantity of the total backlog of the virtual queue at time t +1 and the scalar quantity of the total backlog of the virtual queue at time t is called Lyapunov drift DeltaL (t), and is expressed as:
ΔL(t)＝L(t+1)-L(t)
substituting lyapunov drift into the drift theorem, expressed as:
Figure FDA0003917627280000052
wherein V is a constant control parameter representing a tradeoff between system overhead and virtual queues;
substituting the drift theorem into the derivation of the energy consumption backlog:
Figure FDA0003917627280000053
therefore, the temperature of the molten metal is controlled,
Figure FDA0003917627280000054
and the number of the first and second electrodes,
Figure FDA0003917627280000055
wherein, E max The maximum energy consumption required by the vehicle-mounted mobile terminal to execute the task under the single time slot is represented;
B(t)≤B
and the number of the first and second electrodes,
Figure FDA0003917627280000056
the obtained drift theorem satisfies:
Figure FDA0003917627280000057
since B is constant, the formula (1) can be converted into pi 4 。
6. The Lyapunov optimization-based computing offload and resource allocation method of claim 4, wherein: the base II 4 And constructing a mathematical expression of an unloading decision, a calculation rate of the vehicle-mounted mobile terminal to the task and the transmitting power of the vehicle-mounted mobile terminal, wherein the mathematical expression comprises the following steps:
Π 4 the solution of (ii) can be regarded as two parts, namely, the combined solution of the current residual capacity of the vehicle-mounted mobile terminal, the total consumption energy consumption and the system overhead is established, and a current residual capacity model pi of the vehicle-mounted mobile terminal is established 4.1 ：
Figure FDA0003917627280000061
Current residual capacity E of vehicle-mounted mobile terminal cur (t) satisfies:
Figure FDA0003917627280000062
wherein the content of the first and second substances,
Figure FDA0003917627280000063
represents the average of the required maximum energy consumption of all tasks, and
Figure FDA0003917627280000064
optimal solution of current remaining capacity of the vehicle-mounted mobile terminal
Figure FDA0003917627280000065
Comprises the following steps:
Figure FDA0003917627280000066
establishing a total consumption energy consumption and system overhead model pi 4.2 ：
Figure FDA0003917627280000067
s.t.C2,C3,C7,C8
Calculating an unloading decision: defining the calculation rate of the vehicle-mounted mobile terminal to the task, the calculation rate of the mobile edge calculation server to the task and the emission power of the vehicle-mounted mobile terminal to be known, solving an unloading decision under a single time slot tau, and connecting II 4.2 Rewritten as n 4.2.1 ：
Figure FDA0003917627280000068
Figure FDA0003917627280000069
Figure FDA00039176272800000610
II 4.2.1 For functional representation:
Figure FDA00039176272800000611
wherein λ is m (τ) represents the amount of computational tasks that would be generated by loading a mobile terminal in time slot τ, f m (τ) represents the calculated rate of tasks at the time slot τ for the loaded mobile terminal, r m,n (τ) represents the task transmission rate at time slot τ,
Figure FDA00039176272800000612
representing the computation rate of the mobile edge computing server for the task at time slot tau,
Figure FDA00039176272800000613
representing the transmit power of the downloaded mobile terminal in time slot tau,
Figure FDA0003917627280000071
representing a monotonic function whose monotonicity depends on V-Q m (t) and
Figure FDA0003917627280000072
positive and negative, unload decision s m The value range of (t) can be II 4.2.1 The constraint of (2) obtains:
Figure FDA0003917627280000073
from this, an offloading strategy S can be derived m (t)：
Figure FDA0003917627280000074
Calculating the calculation rate of the vehicle-mounted mobile terminal to the task: defining an unloading decision, calculating the task rate of the mobile edge calculation server and the transmitting power of the vehicle-mounted mobile terminal to be known, solving the task rate of the vehicle-mounted mobile terminal in a single time slot, and combining pi 4.2 Rewritten as pi 4.2.2 ：
Figure FDA0003917627280000075
s.t.(1-s m (τ))λ m (τ)c m /f m (t)≤T max
Figure FDA0003917627280000076
Figure FDA0003917627280000077
Wherein E is min The minimum energy consumption required by the vehicle-mounted mobile terminal to execute the task under the single time slot is represented;
II 4.2.2 Expressed in functional form:
Figure FDA0003917627280000078
wherein s is m (τ) indicates the offload decision at time slot τ, function
Figure FDA0003917627280000079
Is a quadratic function of the opening direction of the function and V-Q m The positive and negative of (t) are related when V-Q m (t) is positive with opening upward when V-Q m (t) is negative, open downwards, calculating f from the constraint m (t) the following:
Figure FDA00039176272800000710
the calculation rate f of the vehicle-mounted mobile terminal to the task m (t)：
Figure FDA0003917627280000081
Calculating the transmitting power of the vehicle-mounted mobile terminal: defining unloading decision, calculating speed of the vehicle-mounted mobile terminal to the task and calculating speed of the mobile edge calculating server to the task to be known, and solving vehicle-mounted mobile in single time slotTransmitting power of terminal, will 4.2 Rewritten as pi 4.2.3 ：
Figure FDA0003917627280000082
II with door 4.2.3 Expressed in functional form:
Figure FDA0003917627280000083
constructing helper functions
Figure FDA0003917627280000084
Analysis of
Figure FDA0003917627280000085
Monotonicity of the function:
Figure FDA0003917627280000086
and the number of the first and second electrodes,
Figure FDA0003917627280000087
the first derivative is taken of the helper function:
Figure FDA0003917627280000088
order:
Figure FDA0003917627280000091
to pair
Figure FDA0003917627280000092
And (5) obtaining a derivative:
Figure FDA0003917627280000093
when in use
Figure FDA0003917627280000094
When the utility model is used, the water is discharged,
Figure FDA0003917627280000095
when in use
Figure FDA0003917627280000096
When the temperature of the water is higher than the set temperature,
Figure FDA0003917627280000097
at this time
Figure FDA0003917627280000098
Is a monotonic function whose monotonicity is V-Q m (t) determining. For the
Figure FDA0003917627280000099
Is solved for, due to the constraints contained therein
Figure FDA00039176272800000910
Is difficult to solve directly, and therefore a classification discussion is required, as follows:
according to the total time delay T in the formula (2) max To obtain a constraint condition of
Figure FDA00039176272800000911
The lower bound of (1):
Figure FDA00039176272800000912
according to the formula (2)Is solved when the second constraint of (2) is satisfied
Figure FDA00039176272800000913
When the temperature of the water is higher than the set temperature,
Figure FDA00039176272800000914
then the second constraint in equation (2) is also obtained as:
Figure FDA00039176272800000915
transmitting power of the in-vehicle mobile terminal
Figure FDA00039176272800000916
Figure FDA0003917627280000101
Wherein the content of the first and second substances,
Figure FDA0003917627280000102
two values of the transmitting power of the vehicle-mounted mobile terminal are respectively:
Figure FDA0003917627280000103
Figure FDA0003917627280000104
calculating the calculation rate of the mobile edge calculation server to the task: defining an optimal unloading decision, calculating the task speed of the vehicle-mounted mobile terminal and the transmitting power of the vehicle-mounted mobile terminal to be known, and solving the mobile edge calculation server pair in a single time slotCalculating rate of task, general 4.2 Rewritten as II 4.2.4 ：
Figure FDA0003917627280000105
Figure FDA0003917627280000106
Figure FDA0003917627280000107
II with door 4.2.4 Expressed in functional form:
Figure FDA0003917627280000108
function(s)
Figure FDA0003917627280000109
Is a monotonic function, and is monotonic with V-Q m (t) related;
according to II 4.2.4 Solving the constraint conditions of
Figure FDA00039176272800001010
The value range of (A):
Figure FDA0003917627280000111
computing the computing rate of the server to the task
Figure FDA0003917627280000112
Figure FDA0003917627280000113
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* Cited by examiner, † Cited by third party
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CN117119444B (en) * 2023-10-25 2024-01-16 成都信息工程大学 Position privacy protection method based on mobile edge calculation

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