CN118741609A - Time slot allocation solving method and system for multi-user MEC network dynamic frame structure - Google Patents
Time slot allocation solving method and system for multi-user MEC network dynamic frame structure Download PDFInfo
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Abstract
The invention provides a time slot allocation solving method and a system of a multi-user MEC network dynamic frame structure, comprising the following steps: modeling decoding error probability in a communication transmission process based on an industrial Internet of things scene, and characterizing delay violation probability; constructing end-to-end error probability in a single frame based on decoding error probability and delay violation probability in a communication transmission process, and obtaining average end-to-end error probability under a multi-frame task based on the error probability; constructing an optimization problem of minimizing the end-to-end average error probability by taking the time length as an optimization variable; converting the channel domain from the time domain to the channel domain to obtain the equivalent optimization problem; the Lagrangian dual method is utilized to obtain the dual problem of the optimization problem under the channel domain, and the dual problem is decomposed into the sub-problems with the same number and the same length as the channel number; and solving the time slot allocation under the dynamic frame structure by analyzing the characteristics of the optimal solution of the dipole problem. The invention effectively improves the reliability of the mobile edge computing network.
Description
Technical Field
The invention belongs to the field of edge calculation, and particularly relates to a time slot allocation solving method and a time slot allocation solving system for a dynamic frame structure of a multi-user MEC network.
Background
The method and the device for calculating the mobile edge greatly improve the reliability of time-sensitive application in wireless communication transmission, and particularly realize reliable and efficient data transmission and calculation in the field of industrial Internet of things, such as the scenario of multi-machine collaborative operation. However, the current mobile edge computing network still does not fully consider the multi-user scene, especially the dynamic frame structure design and the time slot allocation solving method under the multi-user scene. Therefore, the research on dynamic frame structure design and time slot allocation for improving the reliability of multi-user mobile edge computing networks is still a critical problem.
Thanks to the research of Polyanskiy et al on the finite code length theorem, the decoding error probability in the wireless communication transmission process can be well modeled, however Polyanskiy et al only analyze the decoding error probability in the peer-to-peer wireless communication transmission process, and the research on the reliability from end to end is still lacking. With the continuous improvement of the hardware performance, the probability of calculation errors is often negligible, but the delay violation probability that the current task cannot be completed on time due to insufficient time still exists. Bennis et al propose that analysis of the tail distribution of the queue using the extremum theorem compensates for this deficiency and completes modeling of the queue delay violation probability. Although the above work has completed the reliability modeling of the peer-to-peer wireless communication and the server computing process, the modeling of the end-to-end average reliability of the edge computing network and the time slot allocation method of the dynamic frame structure are still lacking, in particular to a dynamic frame structure design and time slot allocation solving method for improving the reliability of the multi-user mobile edge computing network.
Disclosure of Invention
In the future, the modeling of the end-to-end average reliability is aimed at, especially the time slot allocation method under the dynamic frame structure, which is aimed at the edge computing scene with high reliability and low time delay. Therefore, the invention provides a dynamic frame structure design and time slot allocation solving method for improving the reliability of a multi-user mobile edge computing network, aiming at improving the reliability of the multi-user edge computing network.
In order to solve the technical problems, the invention provides the following technical scheme:
The method for solving the time slot allocation of the dynamic frame structure of the multi-user MEC network comprises the following steps:
step 1: based on an industrial Internet of things scene, dividing the whole process of sending the time delay sensitivity task collected by the sensor to the edge computing server into N frames, modeling decoding error probability of each frame communication transmission process, and characterizing delay violation probability;
Step 2: constructing end-to-end error probability in a single frame based on the decoding error probability and the delay violation probability in the communication transmission process in the step 1, and obtaining the average end-to-end error probability under the multi-frame task based on the error probability; constructing an optimization problem of minimizing the end-to-end average error probability by taking the time length as an optimization variable;
Step 3: based on the constructed optimization problem with minimized end-to-end average error probability, converting the optimization problem from a time domain to a channel domain to obtain an equivalent optimization problem; the Lagrangian dual method is utilized to obtain the dual problem of the optimization problem under the channel domain, and the dual problem is decomposed into the sub-problems with the same number and the same length of the channel number;
Step 4: and deriving the optimal value of the Lagrange multiplier of each sub-problem by solving the first derivative of the objective function of the dual problem with respect to the allocation time length, and obtaining a time slot allocation solution under a dynamic frame structure according to the optimal value of the Lagrange multiplier of each sub-problem.
Further, the industrial internet of things scenario in the step 1 is:
The radius of the industrial Internet of things area is R, the position of a server is calculated by randomly fixing edges, and K sensors are placed around industrial equipment and used for collecting operation data of the industrial equipment;
In the communication transmission part, the sensor sends data to the edge computing server in a frequency division multiple access mode.
Further, the decoding error probability of each frame communication transmission process in the step 1 is:
wherein, For the decoding error probability between the kth sensor to the server in the nth frame,Representing the signal-to-noise ratio between the kth sensor to the server within the nth frame,For the coding rate between the kth sensor to the server in the nth frame,Channel transmission capacity between the kth sensor to the server in the nth frame; Indicating a code length assigned to a communication time in an nth frame, Represents a Q function,Representing the channel dispersion from the kth sensor to the server in the nth frame,As an intermediate variable, the number of the variables,To be aboutProbability functions of (2);
for the server calculation process, the nth frame queue delay violation probability Expressed as:
wherein, As a cumulative distribution function with respect to the time threshold d,To complete the time required for the nth frame task,As a parameter of the range,Is a shape parameter, G is a GPD distribution,The phase time length is calculated for the nth frame server, max () is a maximum taking function.
Further, the end-to-end error probability in the single frame in the step 2 is expressed as:
wherein, For the end-to-end error probability within the structure of the nth frame,The communication error probability of the nth frame;
The average error probability from end to end of the multi-frame task is expressed as:
wherein, K represents the maximum number of sensors for the average error probability from the lower end to the end of the multi-frame task; n represents the nth frame.
Further, the optimization problem of minimizing the end-to-end average error probability with the time length as the optimization variable in the step 2The method comprises the following steps:
wherein, In order to be a constraint condition,The average of the total time spent for the phase is calculated for the nth frame communication transmission phase and the server,The communication transmission phase time length is the nth frame; for a given maximum length of time for the nth frame, Which means that the given average time is given,Representing a given maximum end-to-end error probability,The entire task in the time domain is allocated to a set of times of the communication phase,The entire task in the time domain is assigned to a set of times of the calculation phase,Is a set of frames.
Further, in the step 3, the time domain is converted into the channel domain, so as to obtain an equivalent optimization problemThe method comprises the following steps:
wherein, The expected value of the end-to-end error probability in the whole service period; Is the first The average time actually consumed by the communication stage and the calculation stage under the individual channels; to at the first Time allocated to the communication phase under the individual channels; to at the first Time allocated to the calculation phase under the individual channels; At the kth sensor Decoding error probability under each channel; to at the first The probability of a computed error under the individual channels,Is the firstGiven the maximum length of time under the individual channels,The entire task in the channel domain is allocated to a set of times of the communication phase,The entire task in the channel domain is assigned to a set of times of the computation phase,Is a set of channels.
Further, in the step 3, the dual equation is obtained by using the lagrangian dual method as follows:
wherein, Is a constraintThe corresponding pair of questions for the lagrangian multiplier of (2) are:
wherein, Represented asCorresponding pair problems;
The optimization problem P1 is decomposed into L sub-problems, expressed as:
wherein, And the feasible region of the optimization variables is expressed as:
wherein, Is the firstDual equations under the individual channels; in order to be a channel of a radio, Is the firstChannel values under the individual channels; Is the first End-to-end error probability under the individual channels; A feasible region for communication transmission time; calculating a feasible region of time for the server; maximum data in the data packets transmitted by the K sensors; For the duration of each symbol; Is a threshold for SNR; As a set of channel gains, Serving a threshold of end-to-end error probability for each frame; to at the first The time actually spent in the individual channels; the threshold value given by the calculation phase is calculated, For a given channel gain threshold.
Further, in the step 4, for any given channel, whenIs determined by solvingWith respect toAndThe first order derivative of (1) results in a solution to the optimization problem P2, comprising:
the first part is to determine the optimum : First, randomly give; Determining the currentThe communication time length and the calculation time length under the values; updatingUntil convergence, to obtain the optimum；
The second part is to determine the most time allocation for each frame under the dynamic frame structure: optimizing channel state under current frameObtaining optimal communication time length and calculation time length;
Substituting back according to the obtained optimal solution With respect toAndEnd-to-end average error probability obtained by the first derivative of (a).
In another aspect, the present invention provides a slot allocation solution system for a dynamic frame structure of a multi-user MEC network, comprising the steps of:
module one: the method is used for dividing the whole process of sending the time delay sensitivity tasks collected by the sensor to the edge computing server into N frames based on an industrial Internet of things scene, modeling the decoding error probability of the communication transmission process and characterizing the delay violation probability;
And a second module: the method is used for constructing the end-to-end error probability in a single frame based on the decoding error probability and the delay violation probability in the communication transmission process, and obtaining the average end-to-end error probability under the multi-frame task based on the error probability; constructing an optimization problem of minimizing the end-to-end average error probability by taking the time length as an optimization variable;
And a third module: the method is used for converting the optimization problem from a time domain to a channel domain based on the constructed optimization problem with minimized end-to-end average error probability to obtain an equivalent optimization problem; the Lagrangian dual method is utilized to obtain the dual problem of the optimization problem under the channel domain, and the dual problem is decomposed into the sub-problems with the same number and the same length of the channel number;
And a fourth module: the method is used for deriving the optimal value of the Lagrangian multiplier of each sub-problem by solving the first derivative of the objective function of the dual-problem sub-problem about the allocation time length, and obtaining a time slot allocation solution under a dynamic frame structure according to the optimal value of the Lagrangian multiplier of each sub-problem.
Compared with the prior art, the invention has the following beneficial effects:
Compared with the traditional fixed frame structure, the time slot allocation method design of the dynamic frame structure under the multi-user MEC network can greatly improve the reliability of the network, and the fewer the number of sensors, the more obvious the reliability is increased.
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In order to more clearly illustrate the invention or the technical solutions of the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the invention, and other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic illustration of an edge computing network model comprising a plurality of sensors, a single edge computing server, according to the present invention;
fig. 2 is a schematic frame structure of a multi-user edge computing network according to the present invention;
FIG. 3 is a flow chart of a dynamic frame structure design and time slot allocation solution method for improving reliability of a multi-user mobile edge computing network according to the present invention;
fig. 4 is a performance illustration of a dynamic frame structure design and time slot allocation solution method for improving reliability of a multi-user mobile edge computing network according to the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
The embodiment provides a time slot allocation solving method of a multi-user MEC network dynamic frame structure, which comprises the following steps:
step 1: based on an industrial Internet of things scene, dividing the whole process of sending the time delay sensitivity task collected by the sensor to the edge computing server into N frames, modeling decoding error probability of each frame communication transmission process, and characterizing delay violation probability;
Step 2: constructing end-to-end error probability in a single frame based on the decoding error probability and the delay violation probability in the communication transmission process in the step 1, and obtaining the average end-to-end error probability under the multi-frame task based on the error probability; constructing an optimization problem of minimizing the end-to-end average error probability by taking the time length as an optimization variable;
Step 3: based on the constructed optimization problem with minimized end-to-end average error probability, converting the optimization problem from a time domain to a channel domain to obtain an equivalent optimization problem; the Lagrangian dual method is utilized to obtain the dual problem of the optimization problem under the channel domain, and the dual problem is decomposed into the sub-problems with the same number and the same length of the channel number;
Step 4: and deriving the optimal value of the Lagrange multiplier of each sub-problem by solving the first derivative of the objective function of the dual problem with respect to the allocation time length, and obtaining a time slot allocation solution under a dynamic frame structure according to the optimal value of the Lagrange multiplier of each sub-problem.
Fig. 1 shows a scenario of industrial internet of things proposed by the present invention: in this embodiment, multiple users refer to multiple sensors, each sensor and the single edge computing server form an independent communication link, the radius r=150 m of the proposed multi-user mobile edge computing scene is 20 dBm, the bandwidth is 5 MHz, and the path loss model isThe duration of each symbol is set toMs. The given maximum error probability is. In order to model and optimize the effective unsecure transmission throughput, its frame structure is shown in fig. 2. The invention provides a dynamic frame structure time slot allocation solving method for improving the reliability of a multi-user mobile edge computing network, wherein the algorithm flow is shown in figure 3;
The K sensors described in step 1 are defined as a combination, expressed as follows:
Where K represents the maximum number of sensors in the group. The K sensors are used for monitoring industrial equipment and sending the collected time delay sensitive tasks to an edge computing server, and the total time of the whole tasks is expressed as . The whole process is divided into N frames, and the time length of the nth frame isN is denoted as an index of frames, which N frames can be defined as a set, denoted as:
Each frame structure consists of two parts of content: the communication transmission stage and the server calculation stage are expressed as the corresponding time length for the nth frame AndThe following relationship is satisfied:
Maximum length of time at the nth frame;
in the industrial internet of things scenario, the downlink transmission data of the edge computing network is often a logic signal, so the downlink transmission process is not performed.
For a communication transmission procedure, the decoding error probability thereof can be expressed as:
wherein, For the decoding error probability between the kth sensor to the server in the nth frame,Representing the signal-to-noise ratio between the kth sensor to the server within the nth frame,For the coding rate between the kth sensor to the server in the nth frame,Channel transmission capacity between the kth sensor to the server in the nth frame; Indicating a code length assigned to a communication time in an nth frame, Represents a Q function,Representing the channel dispersion from the kth sensor to the server in the nth frame,As an intermediate variable, the number of the variables,To be aboutProbability functions of (2);
for the server calculation process, the nth frame queue delay violation probability Expressed as:
wherein, As a cumulative distribution function with respect to the time threshold d,To complete the time required for the nth frame task,As a parameter of the range,Is a shape parameter, G is GPD distribution (generalized Paret distribution),The phase time length is calculated for the nth frame server, max () is a maximum taking function.
The task execution in the current frame is considered to be reliable only when the data decoding of all links is successful and the server calculates on time as described in step 2. Thus, the end-to-end error probability within a single frame structure can be expressed as:
wherein, For the end-to-end error probability within the structure of the nth frame,The communication error probability of the nth frame;
Since this patent considers the analysis of the average reliability under a multi-frame structure, the end-to-end average error probability can be expressed as:
wherein, K represents the maximum number of sensors for the average error probability from the lower end to the end of the multi-frame task; n represents the nth frame.
In order to minimize the end-to-end average error probability, i.e. maximize the end-to-end average reliability, the corresponding optimization problem can be expressed as:
wherein, The average of the total time spent for the phase is calculated for the nth frame communication transmission phase and the server,The communication transmission phase time length is the nth frame; for a given maximum length of time for the nth frame, Which means that the given average time is given,Representing a given maximum end-to-end error probability,The entire task in the time domain is allocated to a set of times of the communication phase,The entire task in the time domain is assigned to a set of times of the calculation phase.
The average value representing the total time spent should not exceed the average value for a given total time,Meaning that the total duration should not exceed a given threshold, The decoding error probability and the delay violation error probability are limited not to exceed the threshold.
Step 3 first introduces a set of channel state combinations, expressed as:
wherein, Representing the joint probability density function of the channel,The resolution of these L combinations is represented, and the following relationship is satisfied between them:
and the above relationship is accurate when L approaches infinity. Thus, the optimization problem OP established in the time domain can be converted into an equivalent problem in the channel domain, and the equivalent problem is expressed as:
wherein, The expected value of the end-to-end error probability in the whole service period; Is the first The average time actually consumed by the communication stage and the calculation stage under the individual channels; to at the first Time allocated to the communication phase under the individual channels; to at the first Time allocated to the calculation phase under the individual channels; At the kth sensor Decoding error probability under each channel; to at the first The probability of a computed error under the individual channels,Is the firstGiven the maximum length of time under the individual channels,The entire task in the channel domain is allocated to a set of times of the communication phase,The entire task in the channel domain is assigned to a set of times of the computation phase,Is a set of channels.
At this time, the optimization problem P1 is an obvious dynamic programming problem, and the dual equation is obtained by using the lagrangian dual method:
wherein, Is a constrained Lagrangian multiplier, which corresponds to the pair of problems:
Due to Dual problemThe strong dual of (1) is still guaranteed, the optimization problem P1 can be decomposed into L sub-problems, denoted P2:
wherein, And the feasible region of the optimization variables can be expressed as:
To this end, the solution of the optimization problem OP may be converted into a solution of L sub-problems P2.
For any given channel, as described in step 4Determined, then the solution of the optimization problem P2 may be determined by solvingWith respect toAndThe first order derivative is obtained as follows:
In addition, another The following expression can be obtained:
Obviously, when After the determination, the time length of the communication phase can be directly obtained by comparing the expressions, but due to the complexity of the Q function, the time length of the communication phase cannot be directly determined and needs to be obtained through iteration. Therefore, the present embodiment proposes an iterative algorithm that mainly includes two major parts.
The first part is to determine the optimum: First, randomly give; Determining the current according to the obtained expressionThe communication time length and the calculation time length under the values; updatingUntil convergence. Thus, an optimum is obtained。
The second part is to determine the most time allocation for each frame in the dynamic frame structure. First, the channel state under the current frame is optimizedThe optimal communication time length and the optimal calculation time length can be obtained by bringing the communication time length into the expression.
And according to the obtained optimal solution, substituting the optimal solution into an end-to-end average error probability formula to obtain the end-to-end average error probability. So far, the time slot distribution result under the dynamic frame structure can be obtained by the multi-user mobile edge calculation.
As shown in fig. 4, the reliability of the dynamic frame structure under the time slot allocation method is always better than that of the static frame structure under the condition of different sensor numbers and different transmission distances, and the improvement of the reliability of the system by the dynamic frame is more obvious when the sensor numbers are smaller.
Example 2
The embodiment provides a time slot allocation solving system of a multi-user MEC network dynamic frame structure, which comprises the following steps:
module one: the method is used for dividing the whole process of sending the time delay sensitivity tasks collected by the sensor to the edge computing server into N frames based on an industrial Internet of things scene, modeling the decoding error probability of the communication transmission process and characterizing the delay violation probability;
And a second module: the method is used for constructing the end-to-end error probability in a single frame based on the decoding error probability and the delay violation probability in the communication transmission process, and obtaining the average end-to-end error probability under the multi-frame task based on the error probability; constructing an optimization problem of minimizing the end-to-end average error probability by taking the time length as an optimization variable;
And a third module: the method is used for converting the optimization problem from a time domain to a channel domain based on the constructed optimization problem with minimized end-to-end average error probability to obtain an equivalent optimization problem; the Lagrangian dual method is utilized to obtain the dual problem of the optimization problem under the channel domain, and the dual problem is decomposed into the sub-problems with the same number and the same length of the channel number;
And a fourth module: the method is used for deriving the optimal value of the Lagrangian multiplier of each sub-problem by solving the first derivative of the objective function of the dual-problem sub-problem about the allocation time length, and obtaining a time slot allocation solution under a dynamic frame structure according to the optimal value of the Lagrangian multiplier of each sub-problem.
It should be understood that parts of the specification not specifically set forth herein are all prior art.
It should be understood that the above description of the preferred embodiments is not intended to limit the scope of the invention, nor is it intended to be exhaustive of all embodiments. Those skilled in the art can make substitutions and alterations without departing from the scope of the invention as defined by the appended claims, which are intended to be embraced by the claims.
Claims (9)
1. The method for solving the time slot allocation of the dynamic frame structure of the multi-user MEC network is characterized by comprising the following steps:
step 1: based on an industrial Internet of things scene, dividing the whole process of sending the time delay sensitivity task collected by the sensor to the edge computing server into N frames, modeling decoding error probability of each frame communication transmission process, and characterizing delay violation probability;
Step 2: constructing end-to-end error probability in a single frame based on the decoding error probability and the delay violation probability in the communication transmission process in the step 1, and obtaining the average end-to-end error probability under the multi-frame task based on the error probability; constructing an optimization problem of minimizing the end-to-end average error probability by taking the time length as an optimization variable;
Step 3: based on the constructed optimization problem with minimized end-to-end average error probability, converting the optimization problem from a time domain to a channel domain to obtain an equivalent optimization problem; the Lagrangian dual method is utilized to obtain the dual problem of the optimization problem under the channel domain, and the dual problem is decomposed into the sub-problems with the same number and the same length of the channel number;
Step 4: and deriving the optimal value of the Lagrange multiplier of each sub-problem by solving the first derivative of the objective function of the dual problem with respect to the allocation time length, and obtaining a time slot allocation solution under a dynamic frame structure according to the optimal value of the Lagrange multiplier of each sub-problem.
2. The method for solving the time slot allocation of the dynamic frame structure of the multi-user MEC network according to claim 1, wherein the industrial internet of things scenario in the step 1 is:
The radius of the industrial Internet of things area is R, the position of a server is calculated by randomly fixing edges, and K sensors are placed around industrial equipment and used for collecting operation data of the industrial equipment;
In the communication transmission part, the sensor sends data to the edge computing server in a frequency division multiple access mode.
3. The method for solving the slot allocation of the dynamic frame structure of the multi-user MEC network according to claim 1, wherein the decoding error probability of each frame communication transmission process in step 1 is:
wherein, For the decoding error probability between the kth sensor to the server in the nth frame,Representing the signal-to-noise ratio between the kth sensor to the server within the nth frame,For the coding rate between the kth sensor to the server in the nth frame,Channel transmission capacity between the kth sensor to the server in the nth frame; Indicating a code length assigned to a communication time in an nth frame, Represents a Q function,Representing the channel dispersion from the kth sensor to the server in the nth frame,As an intermediate variable, the number of the variables,To be aboutProbability functions of (2);
for the server calculation process, the nth frame queue delay violation probability Expressed as:
wherein, As a cumulative distribution function with respect to the time threshold d,To complete the time required for the nth frame task,As a parameter of the range,Is a shape parameter, G is a GPD distribution,The phase time length is calculated for the nth frame server, max () is a maximum taking function.
4. The method for solving the slot allocation of the dynamic frame structure of the multi-user MEC network according to claim 3, wherein the end-to-end error probability in the single frame in the step 2 is expressed as:
wherein, For the end-to-end error probability within the structure of the nth frame,The communication error probability of the nth frame;
The average error probability from end to end of the multi-frame task is expressed as:
wherein, K represents the maximum number of sensors for the average error probability from the lower end to the end of the multi-frame task; n represents the nth frame.
5. The method according to claim 4, wherein the optimization problem of minimizing the end-to-end average error probability using the time length as the optimization variable in step 2The method comprises the following steps:
wherein, In order to be a constraint condition,The average of the total time spent for the phase is calculated for the nth frame communication transmission phase and the server,The communication transmission phase time length is the nth frame; for a given maximum length of time for the nth frame, Which means that the given average time is given,Representing a given maximum end-to-end error probability,The entire task in the time domain is allocated to a set of times of the communication phase,The entire task in the time domain is assigned to a set of times of the calculation phase,Is a set of frames.
6. The method according to claim 5, wherein in the step 3, the time slot allocation solution of the dynamic frame structure of the multi-user MEC network is converted from the time domain to the channel domain, so as to obtain an equivalent optimization problemThe method comprises the following steps:
wherein, The expected value of the end-to-end error probability in the whole service period; Is the first The average time actually consumed by the communication stage and the calculation stage under the individual channels; to at the first Time allocated to the communication phase under the individual channels; to at the first Time allocated to the calculation phase under the individual channels; At the kth sensor Decoding error probability under each channel; to at the first The probability of a computed error under the individual channels,Is the firstGiven the maximum length of time under the individual channels,The entire task in the channel domain is allocated to a set of times of the communication phase,The entire task in the channel domain is assigned to a set of times of the computation phase,Is a set of channels.
7. The method for solving the time slot allocation of the dynamic frame structure of the multi-user MEC network according to claim 6, wherein the step 3 obtains the dual equation by using the lagrangian dual method as follows:
wherein, Is a constraintThe corresponding pair of questions for the lagrangian multiplier of (2) are:
wherein, Represented asCorresponding pair problems;
The optimization problem P1 is decomposed into L sub-problems, expressed as:
wherein, And the feasible region of the optimization variables is expressed as:
wherein, Is the firstDual equations under the individual channels; in order to be a channel of a radio, Is the firstChannel values under the individual channels; Is the first End-to-end error probability under the individual channels; A feasible region for communication transmission time; calculating a feasible region of time for the server; maximum data in the data packets transmitted by the K sensors; For the duration of each symbol; Is a threshold for SNR; As a set of channel gains, Serving a threshold of end-to-end error probability for each frame; to at the first The time actually spent in the individual channels; the threshold value given by the calculation phase is calculated, For a given channel gain threshold.
8. The method for solving the time slot allocation of the dynamic frame structure of the multi-user MEC network according to claim 7, wherein, in the step 4, for any given channel, whenIs determined by solvingWith respect toAndThe first order derivative of (1) results in a solution to the optimization problem P2, comprising:
the first part is to determine the optimum : First, randomly give; Determining the currentThe communication time length and the calculation time length under the values; updatingUntil convergence, to obtain the optimum；
The second part is to determine the most time allocation for each frame under the dynamic frame structure: optimizing channel state under current frameObtaining optimal communication time length and calculation time length;
Substituting back according to the obtained optimal solution With respect toAndEnd-to-end average error probability obtained by the first derivative of (a).
9. The time slot allocation solving system of the multi-user MEC network dynamic frame structure is characterized by comprising the following steps:
module one: the method is used for dividing the whole process of sending the time delay sensitivity tasks collected by the sensor to the edge computing server into N frames based on an industrial Internet of things scene, modeling the decoding error probability of the communication transmission process and characterizing the delay violation probability;
And a second module: the method is used for constructing the end-to-end error probability in a single frame based on the decoding error probability and the delay violation probability in the communication transmission process, and obtaining the average end-to-end error probability under the multi-frame task based on the error probability; constructing an optimization problem of minimizing the end-to-end average error probability by taking the time length as an optimization variable;
And a third module: the method is used for converting the optimization problem from a time domain to a channel domain based on the constructed optimization problem with minimized end-to-end average error probability to obtain an equivalent optimization problem; the Lagrangian dual method is utilized to obtain the dual problem of the optimization problem under the channel domain, and the dual problem is decomposed into the sub-problems with the same number and the same length of the channel number;
and a fourth module: the method is used for deriving the optimal value of the Lagrangian multiplier of each sub-problem by solving the first derivative of the objective function of the dual problem with respect to the allocation time length, and obtaining a time slot allocation solution under a dynamic frame structure according to the optimal value of the Lagrangian multiplier of each sub-problem;
The time slot allocation solution system of a multi-user MEC network dynamic frame structure is configured to perform the steps in the time slot allocation solution method of a multi-user MEC network dynamic frame structure of any one of claims 1-8.
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