A solution method for optimal time allocation in multi-user mobile edge computing scenarios

Abstract

The present invention proposes a method for solving the optimal time allocation in a multi-user mobile edge computing scenario, considering the scenario of collaboration between multiple users and a single edge computing server. Its communication transmission mode adopts TDMA, and the finite code length theorem and the extreme value theorem are used to respectively model the reliability of the communication transmission process and the server computing process, and construct an overall error probability minimization problem with the allocation time as the optimization variable. By calculating the second-order derivative of the optimization problem, the convexity of the proposed optimization problem is proved, and the optimal solution of the problem is characterized by contradiction and KKT conditions, and the intrinsic relationship between the optimal solutions is obtained. Based on this, the original problem is converted into an optimization problem for single variable solution, and a closed-form expression for the proposed problem regarding the optimal time allocation is obtained. This method significantly improves the computational efficiency of the optimal time allocation and reduces the decision-making difficulty of the edge computing network. It has extremely high scalability and a wide range of practical application scenarios.

Description

Technical Field

[0001] The present invention belongs to the field of mobile edge computing, and in particular relates to a method for solving optimal time allocation in a multi-user mobile edge computing scenario. Background Art

[0002] The introduction and application of mobile edge computing have played a significant role in enabling highly reliable, low-latency communications, enabling faster data transmission and more efficient computation in diverse scenarios, such as smart meters in urban living areas and the coordinated operation of multiple machines in industrial production areas. However, current mobile edge computing still lacks sufficient application in multi-user scenarios, particularly those where a single edge computing server provides services to multiple users. Therefore, research on multi-user, single-server mobile edge computing scenarios remains a critical issue, and maximizing reliability in these scenarios is of great significance.

[0003] Thanks to the research of Polyanskiy et al. on the finite code length theorem, the decoding error probability during wireless communication transmission can be well modeled. However, Polyanskiy et al. only analyzed the decoding error probability during point-to-point wireless communication transmission, and end-to-end reliability research is still lacking. In traditional mobile edge computing research, the server computing process is generally assumed to be correct (with the continuous upgrading of hardware, the errors introduced by hardware can be ignored), making it difficult to complete reliability modeling of the server computing process. With the analysis of the tail distribution of the queue using the extreme value theorem proposed by Bennis et al., the reliability modeling of the server computing process has been completed, but research on the time dimension of this process is still lacking. Although the above research has completed the reliability modeling of these two processes, end-to-end reliability research is still lacking, especially the optimal time allocation scheme and efficient solution method for multi-user mobile edge computing scenarios. Summary of the Invention

[0004] Facing the future high-reliability and low-latency mobile edge computing scenarios, the current lack of research on multi-user single edge computing servers, especially the efficient solution method for end-to-end optimal time allocation, is the focus of this patent. Therefore, this invention provides an efficient solution method for optimal time allocation in multi-user mobile edge computing scenarios, aiming to improve the reliability of multi-user mobile edge computing scenarios, and proposes an efficient solution method for optimal time allocation to improve the efficiency of multi-user time allocation.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A method for solving optimal time allocation in a multi-user mobile edge computing scenario includes the following steps:

[0007] Step 1: Model a multi-user, single-server mobile edge computing network. Use TDMA for communication transmission. Characterize the independent transmission time of each user and the entire communication transmission time. Use the finite code length theorem and the extreme value theorem to characterize the reliability of the communication transmission process and the server computing process, respectively.

[0008] Step 2: Based on the fact that all users transmit the collected data to the edge computing server and all of them are successfully decoded, the overall error probability in the communication transmission and server calculation process is obtained, and an optimization problem is constructed to minimize the overall error probability with the allocation time as the optimization variable;

[0009] Step 3: Calculate the second-order derivative of the optimization problem, prove the convexity of the proposed optimization problem, and characterize the optimal solution of the optimization problem using contradiction and KKT conditions, thereby obtaining the intrinsic relationship between the optimal solutions;

[0010] Step 4: Convert the original problem into a single variable optimization problem and obtain the closed-form expression of the original problem regarding the optimal time allocation.

[0011] Furthermore, in step 1, an edge computing server is fixed at any position in a circular area with a radius of R, and serves K edge user nodes, and these K users obey Gaussian distribution and are randomly placed around the edge computing server.

[0012] K users can be defined as a set and expressed as:

[0013]

[0014] Among them, K represents the maximum number of users. These K users first collect a set of delay-sensitive data and send it wirelessly to the edge computing server. After all the data are sent, the edge computing server starts to collaboratively calculate the data. This whole process requires the overall delay constraint T max Next completed.

[0015] Furthermore, in step 1, for the communication transmission process, each user has its own independent transmission time, which is expressed as t k , then the entire communication transmission time is expressed as For the server computing process, its computing time is expressed as t c , then the time taken for the whole process is In this multi-user mobile edge computing scenario, the downlink data transmitted back by the edge computing server is a decision signal, which is much smaller than the size of the uplink transmission data. Therefore, the impact of downlink data transmission on the entire process is no longer considered.

[0016] Furthermore, in step 1, the decoding error probability corresponding to each user during the communication transmission process can be expressed as:

[0017]

[0018] in, is a Gaussian function, γ k is the signal-to-noise ratio received by the edge server from the kth user decoding corresponding data, r k is the corresponding coding rate, and its corresponding transmission time is related to r k =τ k T s / t k , where τ k is the size of the transmitted data packet, T s is the length of a symbol, n k is the corresponding transmission code length, and its corresponding transmission time is related to n k =t k / T s , V k is the channel dispersion, is the channel transmission capacity.

[0019] Furthermore, in step 1, for the server calculation process, the corresponding delay violation error probability can be expressed as:

[0020]

[0021] Among them, F W (d th ) is about d th The cumulative distribution function, d th The time threshold set for the extreme value theorem, c tot is the total workload, f is the computing frequency of the edge computing server, σ is the range parameter, ξ is the shape parameter, and G(·) is the GPD distribution.

[0022] Furthermore, in step 2, the entire communication transmission process is successful only when the data transmitted by all users is successfully decoded. The corresponding decoding error probability is:

[0023]

[0024] Similarly, the entire process is successful if and only if both the communication transmission process and the server calculation process are successful. The overall error probability can be expressed as:

[0025]

[0026] Among them, ε ΔExpressed as the overall error probability after approximation.

[0027] Furthermore, in step 2, the optimization problem of minimizing the overall error probability with the allocation time as the optimization variable is constructed as follows:

[0028]

[0029]

[0030]

[0031] ε2≤ε th (d)

[0032] Among them, (b) is the overall delay constraint, (c) and (d) limit the decoding error probability and delay violation error probability of each user's transmission data to not exceed the given threshold ε th ; The corresponding optimization variables are the transmission time allocated to each user and the computing time of the edge computing server.

[0033] Furthermore, in step 3, the objective function (a) of the optimization problem of minimizing the overall error probability with the allocation time as the optimization variable can be expressed as the Hessian matrix of the optimization variable:

[0034]

[0035] Since the transmission of each user is independent of each other and the server calculation, the above Hessian matrix has all elements except the elements on the diagonal line as 0, that is, the above Hessian matrix is a diagonal matrix, which can be expressed as:

[0036]

[0037] t k and t C Taking the second derivative we get Therefore, the above Hessian matrix is semi-positive definite, and since constraints (b), (c), and (d) are all linear or affine, the optimization problem (OP) is a convex optimization problem;

[0038] The direct relationship between the obtained optimal solution is analyzed. For the obtained optimal solution {t1,…,t K ,t C}, it can be easily obtained by contradiction, the optimal solution must satisfy In addition, part of the Lagrangian dual problem of the original problem can be expressed as follows:

[0039]

[0040] Among them, μ and λ 1,kIts dual variables are all positive numbers, and μ is the constraint The Lagrangian dual coefficient, λ 1,k is the constraint (ε 1,k ≤ε th )’s Lagrange dual coefficient, according to the KKT condition, the optimal solution of the dual problem The following necessary and sufficient conditions must be met:

[0041]

[0042] in, It represents the optimal error value of the current link, that is, ε 1,k The optimal value of μ * represents the optimal value of μ, Expressed as λ 1,k The optimal value of

[0043] Optimal solution by eliminating dual variables The following relationship can be obtained

[0044]

[0045] Due to ε 1,k For about t k is monotonically decreasing, then the above chain is true if and only if holds true, where k refers to the user's index and K refers to the maximum number of users;

[0046] Based on this, we can obtain the intrinsic relationship between the optimal variables in the original problem, namely the following two equations:

[0047] 1)

[0048] Furthermore, in step 4, based on the intrinsic relationship between the optimal variables of the original problem obtained above, the relationship between the optimal time allocated to all users can be further expressed as:

[0049]

[0050] when When is determined, the optimal time allocated to other times can also be determined, so the problem (OP) can be converted into a problem of solving the variable t1, which can be expressed as:

[0051]

[0052]

[0053]

[0054] ε2≤ε th(iv)

[0055] t k =t k (t1) (v)

[0056] Furthermore, in step 4, the objective function in problem (P1) decreases monotonically with respect to variable t1, and its optimal value is can be obtained quickly, then other optimal values can be obtained by the following closed-form expressions:

[0057]

[0058] The optimal time allocation in the multi-user mobile edge computing scenario is obtained based on the solution of the above closed-form expression.

[0059] Compared with the prior art, the present invention has at least the following beneficial effects:

[0060] The present invention provides an efficient solution method for optimal time allocation in a multi-user mobile edge computing scenario, which meets the high reliability guarantee in the multi-user mobile edge computing scenario, ensures the efficiency of the optimal time allocation solution, and reduces the decision-making difficulty of the edge computing network. It has extremely high scalability and broad practical application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0062] Figure 1 A schematic diagram of a multi-user mobile edge computing scenario proposed by the present invention;

[0063] Figure 2 This is a flowchart of an efficient solution method for optimal time allocation in a multi-user mobile edge computing scenario proposed by the present invention;

[0064] Figure 3 : Performance diagram of the proposed efficient solution method for optimal time allocation; DETAILED DESCRIPTION

[0065] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0066] It should be noted that the experimental methods described in the following embodiments are conventional methods unless otherwise specified, and the reagents and materials are commercially available unless otherwise specified; in the description of the present invention, the terms "horizontal", "longitudinal", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention.

[0067] Furthermore, terms such as "horizontal," "vertical," and "overhanging" do not necessarily imply that a component must be absolutely horizontal or overhanging, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but rather that it can be slightly tilted.

[0068] It should also be noted that, in the description of this application, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in this application based on the specific circumstances.

[0069] Figure 1 This invention proposes an efficient solution method for optimal time allocation in a multi-user mobile edge computing scenario. The proposed multi-user mobile edge computing scenario includes K (K ≥ 2) users and an edge computing server. Each user collects data τ k The proposed multi-user mobile edge computing scenario has a radius of R = 150m, a transmission power of 20dBm for each user, a bandwidth of 5MHz, and a path loss problem of PL = 17.0 + 40.0log 10 (d k ), the duration of each symbol is set to T s =0.025ms. The shape parameter and scale parameter in the server calculation process are set to ξ = -0.0214 and σ = 3.4955×10 6 , the server's CPU frequency is set to f = 3GHz, the number of CPU revolutions required per bit of data is 15000 cycles, and the threshold value of the server queue setting is d th=5.7ms. The given maximum error probability and time limit are ε th =0.01, T max = 25ms. Considering that the efficiency of solving this problem will increase with the increase of the number of users, the present invention proposes an efficient optimal time allocation solution method, the algorithm flow is as follows Figure 2 As shown:

[0070] Preferably, the K users in step 1 can be defined as a set and expressed as:

[0071]

[0072] Here, K represents the maximum number of users. These K users first collect a set of delay-sensitive data and send it wirelessly to the edge computing server. After all the data is sent, the edge computing server starts to collaboratively calculate the data. This whole process requires the overall delay constraint T max For the communication transmission process, since TDMA transmission mode is adopted, each user has its own independent transmission time, which is expressed as t k , then the entire communication transmission time is expressed as For the server computing process, its computing time is expressed as t c , then the time taken for the whole process is In this multi-user mobile edge computing scenario, the downlink data transmitted back by the edge computing server is a decision signal, which is much smaller than the size of the uplink transmission data. Therefore, the impact of downlink data transmission on the entire process is no longer considered.

[0073] For the communication transmission process, its reliability is mainly affected by the allocated time. According to the finite code length theorem, the decoding error probability corresponding to each user in the communication transmission process can be expressed as:

[0074]

[0075] in, is a Gaussian function, γ k is the signal-to-noise ratio received by the edge server from the kth user decoding corresponding data, r k is the corresponding coding rate, and its corresponding transmission time is related to r k =τ k T s / t k (τ k is the size of the transmitted data packet, T s is the length of a symbol), n k is the corresponding transmission code length, and its corresponding transmission time is related to n k =tk / T s , V k is the channel dispersion, is the channel transmission capacity. For the server calculation process, the corresponding delay violation error probability can be expressed as:

[0076]

[0077] Among them, F W (d th ) is about d th The cumulative distribution function, d th The time threshold set for the extreme value theorem, c tot is the total workload, f is the computing frequency of the edge computing server, σ is the range parameter, ξ is the shape parameter, and G(·) is the GPD distribution.

[0078] Preferably, the entire communication transmission process is successful if and only if the data transmitted by all users is successfully decoded in step 2, and the corresponding decoding error probability is:

[0079]

[0080] Similarly, the entire process is successful if and only if both the communication transmission process and the server calculation process are successful. The overall error probability can be expressed as:

[0081]

[0082] In order to achieve the requirements of high reliability and low latency in the multi-user mobile edge computing scenario, that is, to minimize the overall error probability within a given time range, the corresponding optimization problem can be expressed as:

[0083]

[0084]

[0085]

[0086] ε2≤ε th (d)

[0087] Where (b) is the overall delay constraint, and (c) and (d) limit the probability of decoding error and delay violation error of each user's transmitted data to not exceed a given threshold. The corresponding optimization variables are the transmission time allocated to each user and the computation time of the edge computing server.

[0088] Preferably, the objective function (a) of the optimization problem described in step 3 with respect to the Hessian matrix of the optimization variables can be expressed as:

[0089]

[0090] Since the transmission of each user is independent of each other and the server calculation, the above Hessian matrix has all elements except the elements on the diagonal line as 0, that is, the above Hessian matrix is a diagonal matrix, which can be expressed as:

[0091]

[0092] t k and t C Taking the second derivative we get Therefore, the above Hessian matrix is semi-positive definite. And since constraints (b), (c), and (d) are all linear or affine, the optimization problem (OP) is a convex optimization problem.

[0093] When the number of users increases, even for convex optimization problems, the solution speed will still become very slow. Therefore, the direct relationship between the obtained optimal solution is analyzed. For the obtained optimal solution {t1,…,t K ,t C}, it can be easily obtained by contradiction, the optimal solution must satisfy In addition, part of the Lagrangian dual problem of the original problem can be expressed as follows:

[0094]

[0095] Among them, μ and λ 1,k Its dual variables are all positive numbers, and μ is the constraint The Lagrangian dual coefficient, λ 1,k is the constraint (ε 1,k -ε th )’s Lagrange dual coefficient, according to the KKT condition, the optimal solution of the dual problem The following necessary and sufficient conditions must be met:

[0096]

[0097] in, It represents the optimal error value of the current link, that is, ε 1,k The optimal value of μ * represents the optimal value of μ, Expressed as λ 1,k The optimal value of

[0098] By eliminating the dual variable The following relationship can be obtained

[0099]

[0100] Due to ε1,k For about t k is monotonically decreasing, then the above chain is true if and only if holds true, where k refers to the user's index and K refers to the maximum number of users.

[0101] Based on this, we can obtain the intrinsic relationship between the optimal variables in the original problem, namely the following two equations: i)

[0102] Preferably, the relationship between the optimal time allocated to all users can be obtained based on the intrinsic relationship between the optimal variables obtained above in step 4, which can be further expressed as:

[0103]

[0104] when When is determined, the optimal time allocated to other times can also be determined. Therefore, the problem (OP) can be converted into a problem of solving the variable t1, which can be expressed as:

[0105]

[0106]

[0107]

[0108] ε2≤ε th (iv)

[0109] t k =t k (t1) (v)

[0110] And the objective function at this time is monotonically decreasing with respect to the variable t1, and its optimal value is can be obtained quickly, then other optimal values can be obtained by the following closed-form expressions:

[0111]

[0112] Therefore, the optimal time allocation in a multi-user mobile edge computing scenario can be obtained through the above efficient solution method.

[0113] in, Figure 3 The following simulations compare the optimal solution obtained using the proposed method and a convex optimization method. The solid line represents the optimal solution obtained using convex optimization, while the dotted lines of varying shapes represent the solutions obtained using the proposed method. As can be seen, the proposed method consistently achieves the optimal solution, and the solution is a single-variable one, improving overall efficiency.

[0114] The above embodiments are merely illustrative of the technical solutions of the present invention. The methods and devices of the present invention are not limited solely to those described in the above embodiments, but are subject to the scope defined by the claims. Any modifications, supplements, or equivalent substitutions made by persons skilled in the art based on these embodiments are within the scope of protection claimed in the claims.

Claims

1. A method for solving optimal time allocation in a multi-user mobile edge computing scenario, characterized in that: The following steps are involved: Step 1: Model a multi-user, single-server mobile edge computing network. Use TDMA for communication transmission. Characterize the independent transmission time of each user and the entire communication transmission time. Use the finite code length theorem and the extreme value theorem to characterize the reliability of the communication transmission process and the server computing process, respectively. The decoding error probability corresponding to each user during the communication transmission process can be expressed as: in, is a Gaussian function, For edge servers from k The signal-to-noise ratio received by each user when decoding the corresponding data, is the corresponding coding rate, and its corresponding transmission time is ,in is the size of the transmitted data packet, is the length of a symbol, nk is the corresponding transmission code length, and its corresponding transmission time is , is the channel dispersion, is the channel transmission capacity; For the server computing process, the corresponding delay violation error probability can be expressed as: in, For about The cumulative distribution function of The time threshold set for the extreme value theorem, is the total workload, is the computing frequency of the edge computing server, is the range parameter, is the shape parameter, is the GPD distribution; Step 2: Based on the fact that all users transmit the collected data to the edge computing server and all of them are successfully decoded, the overall error probability in the communication transmission and server calculation process is obtained, and an optimization problem is constructed to minimize the overall error probability with the allocation time as the optimization variable; Step 3: Calculate the second-order derivative of the optimization problem, prove the convexity of the proposed optimization problem, and characterize the optimal solution of the optimization problem using contradiction and KKT conditions, thereby obtaining the intrinsic relationship between the optimal solutions; Step 4: Convert the original problem into a single variable optimization problem and obtain the closed-form expression of the original problem regarding the optimal time allocation.

2. The method for solving the optimal time allocation in a multi-user mobile edge computing scenario according to claim 1 is characterized in that: In step 1, the radius is R In the circular area, the edge computing server is fixed at any location and serves K edge user nodes, and this K Users follow Gaussian distribution and are randomly placed around the edge computing server. K A user can be defined as a set and expressed as: in, K Expressed as the maximum number of users, this K Each user first collects a set of delay-sensitive data and sends it wirelessly to the edge computing server. After all the data is sent, the edge computing server starts to collaboratively calculate the data. This whole process requires the overall delay constraint. T max Next completed.

3. The method for solving the optimal time allocation in a multi-user mobile edge computing scenario according to claim 1 is characterized in that: In step 1, for the communication transmission process, each user has its own independent transmission time, which is expressed as t k , then the entire communication transmission time is expressed as ; For the server calculation process, its calculation time is expressed as t c , then the time taken for the whole process is ,In this multi-user mobile edge computing scenario, the downlink data transmitted back by the edge computing server is a decision signal, which is much smaller than the size of the uplink transmission data, so the impact of downlink data transmission on the entire process is no longer considered.

4. The method for solving the optimal time allocation in a multi-user mobile edge computing scenario according to claim 1 is characterized in that: In step 2, the entire communication transmission process is successful only when all user transmitted data is successfully decoded. The corresponding decoding error probability is: Similarly, the entire process is successful if and only if both the communication transmission process and the server calculation process are successful. The overall error probability can be expressed as: in, Expressed as the overall error probability after approximation.

5. The method for solving the optimal time allocation in a multi-user mobile edge computing scenario according to claim 4 is characterized in that: In step 2, the optimization problem of minimizing the overall error probability with the allocation time as the optimization variable is constructed as follows: (a) (b) (c) (d) Among them, (b) is the overall delay constraint, (c) and (d) limit the decoding error probability and delay violation error probability of each user's transmission data to not exceed the given threshold ; The corresponding optimization variables are the transmission time allocated to each user and the computing time of the edge computing server.

6. The method for solving the optimal time allocation in a multi-user mobile edge computing scenario according to claim 5 is characterized in that: In step 3, the objective function (a) of the optimization problem of minimizing the overall error probability with the allocation time as the optimization variable can be expressed as the Hessian matrix of the optimization variable: Since the transmission of each user is independent of each other and the server calculation, the above Hessian matrix has all elements except the elements on the diagonal line as 0, that is, the above Hessian matrix is a diagonal matrix, which can be expressed as: respectively t k and t C Taking the second derivative we get , , so the above Hessian matrix is semi-positive definite, and since constraints (b), (c), and (d) are all linear or affine, the optimization problem (OP) is a convex optimization problem; Analyze the direct relationship between the optimal solution obtained. , it can be easily obtained by contradiction, the optimal solution must satisfy ; In addition, part of the Lagrangian dual problem of the original problem can be expressed as follows: in, and is its dual variable, and both are positive numbers, For the constraints ( ), For constraints The Lagrange dual coefficient of the KKT condition is the optimal solution of the dual problem. The following necessary and sufficient conditions must be met: in, Expressed as the optimal error probability value of the current link, that is, The optimal value of Indicated by The optimal value of Expressed as The optimal value of Optimal solution by eliminating dual variables , we can get the following relationship because For about t k is monotonically decreasing, then the above chain is true if and only if Established, of which k is the user's index, K Refers to the maximum number of users; Based on this, we can obtain the intrinsic relationship between the optimal variables in the original problem, namely the following two equations: 1） ；2） 。 7. The method for solving the optimal time allocation in a multi-user mobile edge computing scenario according to claim 6 is characterized in that: In step 4, based on the intrinsic relationship between the optimal variables of the original problem obtained above, the relationship between the optimal time allocated to all users can be further expressed as: when When the optimal time allocated to other variables is determined, the optimal time allocated to other variables can also be determined, so the problem (OP) can be converted into a variable t 1, which can be expressed as: 。 8. The method for solving the optimal time allocation in a multi-user mobile edge computing scenario according to claim 6 is characterized in that: In step 4, the objective function in problem (P1) is about the variable t 1 is monotonically decreasing, and its optimal value is can be obtained quickly, then other optimal values can be obtained by the following closed-form expressions: The optimal time allocation in the multi-user mobile edge computing scenario is obtained based on the solution of the above closed-form expression.

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