CN110099384B - Multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation - Google Patents
Multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation Download PDFInfo
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Abstract
The invention discloses a multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation, which comprises the following steps: step 1, task analysis: analyzing the task completion time delay and determining the task completion benefit; step 2, problem formation: forming an optimization problem by taking the overall efficiency of the maximized task completion as a target; step 3, ensuring a steady state: the stability of the task backlog queue is ensured to simplify the problem; step 4, channel allocation: determining optimal channel allocation by a given task unloading allocation strategy; step 5, task scheduling: determining optimal task scheduling by a given channel resource allocation strategy; step 6, joint optimization: and combining the steps 4 and 5 to obtain optimal channel allocation and task scheduling. The invention fully considers the service diversity, carries out priority division on the tasks, improves the user side income to the maximum extent and realizes the multi-user multi-MEC task unloading resource scheduling.
Description
Technical Field
The invention relates to a multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation, and belongs to the technical field of network resource allocation.
Background
The Mobile Edge Computing (MEC) technology belongs to a distributed Computing, and puts data processing, application program running and even implementation of some functional services on nodes at the Edge of a network. The mobile edge cloud is composed of one or more edge servers, namely servers equipped with computing storage functions on the traditional base station, and the traditional base station is updated to be the mobile edge computing base station. Because the MEC base station is close to the user terminal, the mobile terminal can be helped to process tasks, the task processing time delay is reduced, and the energy consumption of the mobile terminal is reduced. Different from Cloud Computing (Cloud Computing), edge Computing puts down functions such as data processing and the like from a network center to a network edge node, processes data nearby, does not need to upload a large amount of data to a remote core management platform, and can reduce time for data to come to and go from a Cloud end and network bandwidth cost.
The complete edge calculation unloading process is divided into the following three parts: 1) the mobile terminal sends a task unloading request to an MEC service area (including some necessary information of task calculation amount); 2) unloading the task to an MEC server for processing; 3) the MEC server transmits an offload response (including a task processing result, etc.) to the mobile terminal. Time is divided into frames, where the frames are divided into control subframes and calculation offload subframes. In the control sub-frame, control information is exchanged between the MEC server and the mobile terminal to determine an offload schedule. In the calculation of the offload sub-frame, the workload is first sent to the MEC server, which returns the result to the mobile terminal after completing the processing workload. For an edge cloud consisting of a plurality of MEC servers, whether to offload tasks and to which MEC server the tasks are offloaded for processing is still an open question of how to ensure that all mobile terminals and the edge cloud servers can be allocated and efficiently adapt to changes in energy and user requirements.
The task amount of a user, the computing capacity of an MEC server, the computing capacity of a mobile terminal and the occupation condition of channel resources are comprehensively considered, a multi-user multi-MEC task unloading resource scheduling model is established by taking the task completion benefit maximization as a target, and great practical significance is brought to multi-user multi-MEC task unloading resource scheduling based on edge-end cooperation.
Disclosure of Invention
The invention aims to provide a multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation so as to realize optimal multi-user multi-MEC task unloading resource scheduling.
In order to achieve the purpose, the invention adopts the technical scheme that:
a multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation comprises the following steps:
step 3, ensuring a steady state: the stability of the task backlog queue is ensured to simplify the problem;
step 4, channel allocation: determining optimal channel allocation by a given task unloading allocation strategy;
step 5, task scheduling: determining optimal task scheduling by a given channel resource allocation strategy;
Step 6, joint optimization: and combining the steps 4 and 5 to obtain optimal channel allocation and task scheduling.
In the step 1, the benefit is determined by two factors: expected profit values generated by the attributes of the tasks and time delay loss generated in the task processing process; the specific steps of the step 1 are as follows:
step 11, considering that in K times, all users have I tasks that need to be executed locally or unloaded to the MEC for processing at time t, where a set J of the MEC is {1, 2, 3Denotes the ith task, I ═ 1, 2, 3, …, I; describing task m by using task model i Size: d i (t) (bit), i.e. task m i The packet size of (d); task m i The workload to be processed is D i (t)X i (CPU cycles) wherein X i Represents the CPU cycle required for processing 1bit data volume; setting the spectrum bandwidth possessed by MEC j to be B j (t) has N j (t) subcarriers, each subcarrier having a bandwidth ofAccording to the Shannon formula, the task m on the subcarrier n i Has a data transmission rate of
Task m i Total data transmission rate of
Wherein N is j (t) denotes a subcarrierWave number, pi i,n (t) is a channel allocation indicator when pi i,n When (t) is equal to 1, the subcarrier n is assigned to the task m i Unloading is carried out; when pi i,n When (t) is 0, this indicates that subcarrier n is not allocated to task m i Unloading is carried out; p is a radical of formula i Representing task m i The transmitting power of the terminal; h is n,j Denotes the channel gain of the user subcarrier n, sets the mobility of the user not high during the task unloading, so h n,j =127+logd i,j ,d i,j Representing a task m i The distance between the user terminal and MEC j; sigma 2 Is the channel noise power; task m i The transfer delay offloaded to MEC j is
Step 12, when the user leaves the task in the local processing, the time delay only comprises the task processing time; consider a mobile user terminal u i Has a CPU processing capacity ofThe local execution latency is
Step 13, the time delay for unloading the task to the MEC server is composed of the following three parts: a. b, when a large number of tasks need to be unloaded to the edge cloud for processing, the loads of the MEC servers are exceeded, and the tasks may need to be queued in each MEC server, namely queuing waiting time, c, and task processing time;
wherein the unloading transmission time isA queue waiting time ofSetting the CPU processing capability of MEC j toTask m i Is treated for a time ofThus, task m i The total latency to offload to the execution at MEC server j is
Step 14, for any MEC server, the task arrival process is modeled as a Bernoulli process, and the task arrival rate of the MEC server j is set to be lambda j (ii) a The number of tasks waiting in the queue is assumed to be the queue state: q j (t) {0, 1, 2, 3. }, queue Q of MEC j j (t) the update formula is
Q j (t+1)=Q j (t)-V j (t)+A j (t)
Wherein, V j (t) represents the processing speed of the task at MEC j, i.e. V is processed and completed within a time of length 1 at time t j (t) tasks; a. the j (t) indicates whether the task arrives at time t, A j (t) is an element of {0, 1 }; thus, there is Pr { A j (t)=1}=λ j And Pr { A j (t)=0}=1-λ j (ii) a Based on the litter's law, considering that the execution delay including the queuing delay and the processing delay is proportional to the average queue length of the task buffer in K time points, the average queue length is expressed as follows:
step 15, set u i Representing a task m i At the expected profit, L (T), formulated according to its priority i ) Representing a task m i At time T i Internally completing the paid delay loss;
c is a proportionality coefficient and is determined according to the sensitivity of a system to time delay, and the larger C is, the larger the time delay loss caused by the time delay is; rho i In order to lose the tolerance of time delay, when the time delay is less than the tolerance, the time delay does not influence the satisfaction of a user, namely the income of the user is not lost, and when the time delay is more than rho i The delay affects the user satisfaction and correspondingly causes delay loss.
In the step 2, a user benefit value is introduced as an index for measuring the system performance, and an optimization problem is established with the aim of maximizing the user-side task completion total benefit within a period of time; the method comprises the following specific steps:
step 21, task m i The off-load to MEC processing yields the benefit of Wherein u is i Representing a task m i At the expected profit, L (T), formulated according to its priority i,j (t)) is task m i Latency penalty incurred by offloading to MEC processing;
Step 23, the symbols pi are distributed by joint optimization of the subcarriers i,n (t) task assigner s i,j (t) obtaining an optimization problem with the goal of maximizing the total profit for the user-side task completion over a period of time:
wherein C1 ensures that a task can only be selected to be processed locally or offloaded to a MEC server for execution; c2 ensuring s i,j (t) is a binary variable; c3 ensuring pi i,n (t) is a binary variable; c4 ensures that one subcarrier can be allocated to only one user at most; c5 ensuring that the base station allocates transmission power to users not exceeding the maximum transmission power, p, of the base station max Is the maximum transmit power of the base station; c6 ensuring that unload transfer energy does not exceed task m i Residual energy of the mobile terminal equipmentC7 ensuring that task execution latency satisfies maximum latency requirement Expected benefit u per task in the objective function due to optimization problem P1 i Is fixed and does not change with time t, and time delay lossThe loss function L (-) is a linear function, thus resulting in a simplified optimization problem P2:
in the step 3, the stability of the task backlog queues of each MEC server is ensured, the problem is simplified to solve the optimal task unloading resource scheduling strategy under the steady-state condition based on the lyapunov theory, and the specific steps are as follows:
step 31, setting the task arrival state of each queue as a bernoulli process, and making Θ (t) ═ Q 1 (t),Q 2 (t),...,Q j (t),...,Q J (t)) represents the queue state, Θ (t) being based on the task arrival rate λ j Evolving at a time slot t e {0, 1, 2. }; defining a quadratic lyapunov function:
ω j representing a weight set, wherein different weights can cause different queues to have different positions in a task scheduling strategy, and setting all omega j Are both 1; obviously, the Lyapunov function is non-negative if and only if all Θ's are j (t) is 0, L (Θ (t)) equals 0;
step 32, defining the mean of the differences of the quadratic lyapunov functions at a time as the lyapunov drift function Δ (Θ (t)) in order to predict the changes of the respective queue states:
wherein the content of the first and second substances,represents the mean of the differences of the quadratic lyapunov functions;
This drift is the expected change in the lyapunov function over a time instant;
step 33, at each time t, observing the current Θ (t) value and taking control action, according to the consistent Θ (t), greedy minimizing drift plus penalty function expectation:
step 34, determining a time delay sensitive parameter v 0 V is provided 0 1, the optimization problem P2 is reduced to:
in the step 4, under the condition that a task unloading allocation strategy is given, converting the optimization problem P3 into a channel resource allocation problem, and solving optimal channel allocation by using a KKT condition; the method comprises the following specific steps:
step 41, setting given task unloading distribution strategy S' i,j (t), the optimization problem P3 is a question of R i,j (t) convex problem, assuming there are l tasks to offload to MEC processing, i.e. S i,j The number of (t) ═ 1 is l, and the optimization objective function is converted into the following formula:
f(R ij (t),S′ ij (t)) is with respect to R ij (t);
step 42, since f (R) i,j (t),S′ i,j (t)) is a convex function and all constraints are linear functions, so the optimization problem is a convex optimization problem, from the KKT condition, one can obtain information about R i,j (t) optimal solution
Step 43, construct the lagrangian function of the optimization problem as follows:
wherein, mu i,j Is the undetermined coefficient of each constraint condition;
If R is i,j (t) and μ i,j The KKT condition is satisfied at any point, yielding:
by solving the above equation, the optimal R is obtained i,j (t):
From this, a fixed task offload distribution policy S 'can be derived' i,j (t) optimal solution:
in the step 5, a given channel resource allocation strategy is set, and the optimization problem P3 is converted into a 0-1 integer programming problem; the method comprises the following specific steps:
step 51, setting a given channel resource allocation strategy, and converting the optimization problem P3 into a 0-1 integer programming problem as follows:
step 52, at each time t, the task allocation strategy S (t) is solved by taking the total time delay of all task processing as a target, namely, the optimal MEC server corresponding to each task is solved, and each task is unloaded to the optimal MEC j * Server processed time delay
Step 53, calculating the time delay T of the task left in the local processing i (t) time delay to offload to MEC processingAnd (T) i (t) + δ) where δ is the delay tolerance, ifThe task is at MEC j * And processing, otherwise, locally processing, and updating the task allocation strategy S (t).
The specific steps of the step 6 are as follows:
and 61, obtaining the optimal channel resource allocation under the fixed task unloading allocation according to the step 4.
And step 62, obtaining the optimal task unloading distribution strategy under the fixed channel according to the step 5.
And step 63, repeating the steps 61 and 62 until the optimal channel allocation and task scheduling strategy is obtained.
Has the beneficial effects that: the invention aims to comprehensively consider the task amount of a user, the computing capacity of an MEC server, the computing capacity of a mobile terminal and the occupation condition of channel resources, aim at maximizing task completion benefits, distribute computing resources and channel resources, establish a multi-user multi-MEC computing unloading frame, ensure the stability of an MEC server task extrusion queue and solve under KKT conditions by utilizing the Lyapunov theory, and realize the optimal multi-user multi-MEC task unloading resource scheduling. The invention fully considers the service diversity, carries out priority division on the tasks, improves the user side income to the maximum extent and realizes the multi-user multi-MEC task unloading resource scheduling.
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FIG. 1 is a diagram of multi-user multi-MEC task offload resource scheduling based on edge-end coordination;
fig. 2 is a schematic diagram of a multi-user multi-MEC computing offloading scenario based on edge-end collaboration.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention comprehensively considers the task amount of the user, the computing capacity of the MEC server, the computing capacity of the mobile terminal and the channel resource occupation condition, aims at maximizing task completion benefits, distributes computing resources and channel resources, establishes a multi-user multi-MEC computing unloading frame, ensures the stability of the MEC server task extrusion queue and the KKT condition by utilizing the Lyapunov theory to solve, and realizes the optimal multi-user multi-MEC task unloading resource scheduling.
The invention discloses a multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation, which comprises the following steps:
step 11, as shown in fig. 2, it is considered that, at time t, all users have I tasks that need to be executed locally or unloaded to the MEC for processing at time K, where a set J of the MEC is {1, 2, 3Denotes the ith task, I ═ 1, 2, 3, …, I; describing task m by using task model i Size: d i (t) (bit), i.e. task m i The packet size of (d); task m i The workload to be processed is D i (t)X i (CPU cycles) wherein X i Represents the CPU cycle required for processing 1bit data volume; setting the spectrum bandwidth possessed by MEC j to be B j (t) has N j (t) subcarriers, each subcarrier having a bandwidth ofAccording to the Shannon formula, the task m on the subcarrier n i Has a data transmission rate of
Task m i Total data transmission rate of
Wherein N is j (t) represents the number of subcarriers,. pi i,n (t) is a channel allocation indicator when pi i,n When (t) is 1, it means that subcarrier n is allocated to task m i Unloading is carried out; when pi i,n When (t) is 0, it indicates that subcarrier n is not allocated to task m i Unloading is carried out; p is a radical of i Representing a task m i The transmitting power of the terminal; h is n,j Denotes the channel gain of the user subcarrier n, sets the mobility of the user not high during the task unloading, so h n,j =127+logd i,j ,d i,j Representing a task m i The distance between the user terminal and MEC j; sigma 2 Is the channel noise power; task m i The transfer delay offloaded to MEC j is
Step 12, when the user leaves the task in the local processing, the time delay only comprises the task processing time; consider a mobile user terminal u i Has a CPU processing capacity ofThe local execution latency is
Step 13, the time delay for unloading the task to the MEC server is composed of the following three parts: a. b, when a large number of tasks need to be unloaded to the edge cloud for processing, the loads of the MEC servers are exceeded, and the tasks may need to be queued in each MEC server, namely queuing waiting time, c, and task processing time;
wherein the unloading transmission time isA queue waiting time ofSetting the CPU processing capability of MEC j toTask m i Is treated for a time ofThus, task m i The total latency to offload to the execution at MEC server j is
Step 14, for any MEC server, the task arrival process is modeled as a Bernoulli process, and the task arrival rate of the MEC server j is set to be lambda j (ii) a The number of tasks waiting in the queue is assumed to be the queue state: q j (t) {0, 1, 2, 3. }, queue Q of MEC j j (t) the update formula is
Q j (t+1)=Q j (t)-V j (t)+A j (t)
Wherein, V j (t) represents the processing speed of the task at MEC j, i.e. at time tThe process in a time of length 1 completes V j (t) tasks; a. the j (t) indicates whether the task arrives at time t, A j (t) is an element of {0, 1 }; thus, there is Pr { A j (t)=1}=λ j And Pr { A j (t)=0}=1-λ j (ii) a Based on the litter's law, considering that the execution delay including the queuing delay and the processing delay is proportional to the average queue length of the task buffer in K time points, the average queue length is expressed as follows:
step 15, set u i Representing a task m i At the expected profit, L (T), formulated according to its priority i ) Representing a task m i At time T i Internally completing the paid delay loss;
wherein, C is a proportionality coefficient, which is determined according to the sensitivity of the system to time delay, the larger C is, the larger the time delay loss caused by time delay is, and C is 1 in the invention; rho i In order to lose the tolerance of time delay, when the time delay is less than the tolerance, the time delay does not influence the satisfaction of a user, namely the income of the user is not lost, and when the time delay is more than rho i The delay affects the user satisfaction and correspondingly causes delay loss.
step 21, task m i The yield of the offloading to MEC processing is Wherein u is i Representing a task m i At the expected profit, L (T), formulated according to its priority i,j (t)) is task m i Latency penalty incurred by offloading to MEC processing;
Step 23, the symbols pi are distributed by joint optimization of the subcarriers i,n (t) task assigner s i,j (t) obtaining an optimization problem with the goal of maximizing the total profit for the user-side task completion over a period of time:
wherein C1 ensures that a task can only be selected to be processed locally or offloaded to a MEC server for execution; c2 ensuring s i,j (t) is a binary variable; c3 ensuring pi i,n (t) is a binary variable; c4 ensures that one subcarrier can be allocated to only one user at most; c5 ensuring that the base station allocates transmission power to users not exceeding the maximum transmission power, p, of the base station max Is the maximum transmit power of the base station; c6 ensuring that unload transfer energy does not exceed task m i Residual energy of the mobile terminal equipmentC7 ensuring that task execution latency satisfies maximum latency requirementExpected benefit u per task in the objective function due to optimization problem P1 i Is fixed and does not vary with time t, the delay loss function L (-) is a linear function, thus resulting in a simplified optimization problem P2:
step 3, ensuring a steady state: the stability of the task backlog queues of each MEC server is guaranteed, and the problem is simplified into the optimal task unloading resource scheduling strategy under the steady-state condition based on the Lyapunov theory; the method comprises the following specific steps:
step 31, setting the task arrival state of each queue as a bernoulli process, and making Θ (t) ═ Q 1 (t),Q 2 (t),...,Q j (t),...,Q J (t)) represents the queue state, Θ (t) being based on the task arrival rate λ j Evolving at a time slot t e {0, 1, 2. }; defining a quadratic lyapunov function:
ω j representing a weight set, wherein different weights can cause different queues to have different positions in a task scheduling strategy, and setting all omega j Are both 1; obviously, the Lyapunov function is non-negative if and only if all Θ's are j (t) is 0, L (Θ (t)) equals 0;
step 32, defining the mean of the differences of the quadratic lyapunov functions at a time as the lyapunov drift function Δ (Θ (t)) in order to predict the changes of the respective queue states:
Wherein, the first and the second end of the pipe are connected with each other,represents the mean of the differences of the quadratic lyapunov functions;
this drift is the expected change in the lyapunov function over a time instant;
step 33, at each time t, observing the current Θ (t) value and taking control action, according to the consistent Θ (t), greedy minimizing drift plus penalty function expectation:
step 34, determining a time delay sensitive parameter v 0 V is provided 0 1, the optimization problem P2 is reduced to:
step 4, channel allocation: under the condition that a task unloading distribution strategy is given, converting an optimization problem P3 into a channel resource distribution problem, and solving optimal channel distribution by utilizing a KKT condition; the method comprises the following specific steps:
step 41, setting given task unloading distribution strategy S' i,j (t), the optimization problem P3 is a question of R i,j (t) convex problem, assuming there are l tasks to offload to MEC processing, i.e. S i,j The number of (t) ═ 1 is l, and the optimization objective function is converted into the following formula:
f(R ij (t),S′ ij (t)) is with respect to R ij (t);
step 42, since f (R) i,j (t),S′ i,j (t)) is a convex function and all constraints are linear functions, so the optimization problem is a convex optimization problem, from the KKT condition, one can obtain information about R i,j (t) optimal solution
Step 43, construct the lagrangian function of the optimization problem as follows:
Wherein, mu i,j Is the undetermined coefficient of each constraint condition;
if R is i,j (t) and μ i,j The KKT condition is satisfied at any point, yielding:
by solving the above equation, the optimal R is obtained i,j (t):
From this, a fixed task offload distribution policy S 'can be derived' i,j (t) optimal solution:
step 5, task scheduling: given a channel resource allocation strategy, the optimization problem P3 can be converted into a 0-1 integer programming problem; the method comprises the following specific steps:
step 51, setting a given channel resource allocation strategy, and converting the optimization problem P3 into a 0-1 integer programming problem as follows:
step 52, at each time t, the task allocation strategy S (t) is solved by taking the total time delay of all task processing as a target, namely, the optimal MEC server corresponding to each task is solved, and each task is unloaded to the optimal MEC j * Server processed time delay
Step 53, calculating the time delay T of the task left in the local processing i (t) time delay to offload to MEC processingAnd (T) i (t) + δ) where δ is the delay tolerance, ifTaskThen at MEC j * And processing, otherwise, locally processing, and updating the task allocation strategy S (t).
Step 6, joint optimization: alternately iterating step 4 and step 5 until the user benefit in a period of time is maximized, specifically comprising the following steps:
step 61, obtaining the optimal channel resource allocation under the fixed task unloading allocation according to step 4;
Step 62, obtaining an optimal task unloading allocation strategy under the fixed channel according to the step 5;
and step 63, repeating the steps 61 and 62 until the optimal channel allocation and task scheduling strategy is obtained.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (2)
1. A multi-user multi-MEC task unloading resource scheduling method based on edge-end cooperation is characterized in that: the method comprises the following steps:
step 1, task analysis: analyzing the task completion time delay and determining the task completion benefit;
in the step 1, the benefit is determined by two factors: expected profit values generated by the attributes of the tasks and time delay loss generated in the task processing process; the specific steps of the step 1 are as follows:
step 11, considering that all users have I tasks to be executed locally or unloaded to the MEC for processing at time t within K times, where a set J of the MEC is {1,2,3, …, J …, J }, and a set of the tasks isDenotes the ith task, I ═ 1,2,3, …, I; describing task m by using task model i Size: d i (t), i.e. task m i The packet size of (d); task m i The workload to be processed is D i (t)X i Wherein X is i To representCPU cycle required for processing 1bit data volume; setting the spectrum bandwidth possessed by MEC j to be B j (t) has N j (t) subcarriers, each subcarrier having a bandwidth ofAccording to the Shannon formula, the task m on the subcarrier n i Has a data transmission rate of
Task m i Total data transmission rate of
Wherein N is j (t) represents the number of subcarriers,. pi i,n (t) is a channel allocation indicator when pi i,n When (t) is 1, it means that subcarrier n is allocated to task m i Unloading is carried out; when pi i,n When (t) is 0, it indicates that subcarrier n is not allocated to task m i Unloading is carried out; p is a radical of i Representing a task m i The transmitting power of the terminal; h is n,j Denotes the channel gain of the user subcarrier n, sets the mobility of the user not high during the task unloading, so h n,j =127+logd i,j ,d i,j Representing a task m i The distance between the user terminal and MEC j; sigma 2 Is the channel noise power; task m i The transfer delay offloaded to MEC j is
Step 12, when the user leaves the task in the local processing, the time delay only comprises the task processing time; consider a mobile user terminal u i Has a CPU processing capacity of f i l Then the local execution delay is
Step 13, the time delay for unloading the task to the MEC server is composed of the following three parts: a. b, when a large number of tasks need to be unloaded to the edge cloud for processing, the loads of the MEC servers are exceeded, and the tasks may need to be queued at each MEC server, namely queuing waiting time, c, task processing time;
Wherein the unloading transfer time isThe queue waiting time isSetting the CPU processing capability of MEC j toTask m i Is treated for a time ofThus, task m i The total latency to offload to the execution at MEC server j is
Step 14, for any MEC server, the task arrival process is modeled as a Bernoulli process, and the task arrival rate of the MEC server j is set to be lambda j (ii) a The number of tasks waiting in the queue is assumed to be the queue state: q j (t) {0,1,2,3, … }, queue Q of MEC j j (t) the update formula is
Q j (t+1)=Q j (t)-V j (t)+A j (t)
Wherein, V j (t) represents the processing speed of the task at MEC j, i.e. V is processed and completed within a time of length 1 at time t j (t)A task; a. the j (t) indicates whether the task arrives at time t, A j (t) is an element of {0,1 }; thus, there is Pr { A j (t)=1}=λ j And Pr { A j (t)=0}=1-λ j (ii) a Based on the litter's law, considering that the execution delay including the queuing delay and the processing delay is proportional to the average queue length of the task buffer in K time points, the average queue length is expressed as follows:
step 15, set u i Representing a task m i At the expected profit, L (T), formulated according to its priority i ) Representing a task m i At time T i Internally completing the paid delay loss;
c is a proportionality coefficient and is determined according to the sensitivity of a system to time delay, and the larger C is, the larger the time delay loss caused by the time delay is; rho i In order to lose the tolerance of time delay, when the time delay is less than the tolerance, the time delay does not influence the satisfaction of a user, namely the income of the user is not lost, and when the time delay is more than rho i The time delay affects the satisfaction degree of the user, and correspondingly time delay loss is generated;
step 2, problem formation: forming an optimization problem by taking the overall efficiency of the maximized task completion as a target;
in the step 2, a user benefit value is introduced as an index for measuring the system performance, and an optimization problem is established with the aim of maximizing the user-side task completion total benefit within a period of time; the method comprises the following specific steps:
step 21, task m i The yield of the offloading to MEC processing is Wherein u is i Representing a task m i At the expected profit, L (T), formulated according to its priority i,j (t)) is task m i Latency penalty incurred by offloading to MEC processing;
Step 23, the symbols pi are distributed by joint optimization of the subcarriers i,n (t) task assigner s i,j (t) obtaining an optimization problem with the goal of maximizing the total profit for the user-side task completion over a period of time:
wherein C1 ensures that a task can only be selected to be processed locally or offloaded to a MEC server for execution; c2 ensuring s i,j (t) is a binary variable; c3 ensures pi i,n (t) is a binary variable; c4 ensures that one subcarrier can be allocated to only one user at most; c5 ensuring that the base station allocates transmission power to users not exceeding the maximum transmission power, p, of the base station max Is the maximum transmit power of the base station; c6 ensuring that unload transfer energy does not exceed task m i Residual energy of the mobile terminal equipmentC7 ensuring that task execution latency satisfies maximum latency requirementExpected benefit u per task in the objective function due to optimization problem P1 i Is fixed and does not vary with time t, the delay loss function L (-) is a linear function, thus resulting in a simplified optimization problem P2:
step 3, ensuring a steady state: the stability of the task backlog queue is ensured to simplify the problem;
in the step 3, the stability of the task backlog queues of each MEC server is ensured, the problem is simplified to solve the optimal task unloading resource scheduling strategy under the steady-state condition based on the lyapunov theory, and the specific steps are as follows:
step 31, setting the task arrival state of each queue as a bernoulli process, and making Θ (t) ═ Q 1 (t),Q 2 (t),…,Q j (t),…,Q J (t)) represents the queue state, Θ (t) being based on the task arrival rate λ j Evolving at a time slot t e {0,1, 2. }; defining a quadratic lyapunov function:
ω j Representing a weight set, wherein different weights can cause different queues to have different positions in a task scheduling strategy, and setting all omega j Are both 1; obviously, the Lyapunov function is non-negative if and only if all Θ's are j (t) is 0, L (Θ (t)) equals 0;
step 32, defining the mean of the differences of the quadratic lyapunov functions at a time as the lyapunov drift function Δ (Θ (t)) in order to predict the changes of the respective queue states:
wherein, the first and the second end of the pipe are connected with each other,represents the mean of the differences of the quadratic lyapunov functions;
this drift is the expected change in the lyapunov function over a time instant;
step 33, at each time t, observing the current Θ (t) value and taking control action, according to the consistent Θ (t), greedy minimizing drift plus penalty function expectation:
step 34, determining a time delay sensitive parameter v 0 V is provided 0 1, the optimization problem P2 is reduced to:
step 4, channel allocation: determining optimal channel allocation by a given task unloading allocation strategy;
in the step 4, under the condition that a task unloading allocation strategy is given, converting the optimization problem P3 into a channel resource allocation problem, and solving optimal channel allocation by using a KKT condition; the method comprises the following specific steps:
Step 41, setting given task unloading distribution strategy S' i,j (t), the optimization problem P3 is a question of R i,j (t) convex problem, assuming there are l tasks to offload to MEC processing, i.e. S i,j The number of (t) ═ 1 is l, and the optimization objective function is converted into the following formula:
f(R ij (t),S′ ij (t)) is with respect to R ij (t);
step 42, since f (R) i,j (t),S′ i,j (t)) is a convex function and all constraints are linear functions, so the optimization problem is a convex optimization problem, from the KKT condition, one can obtain information about R i,j (t) optimal solution
Step 43, construct the lagrangian function of the optimization problem as follows:
wherein, mu i,j Is the undetermined coefficient of each constraint condition;
if R is i,j (t) and μ i,j The KKT condition is satisfied at any point, yielding:
by solving the above equation, the optimal R is obtained i,j (t):
From this, a fixed task offload distribution policy S 'can be derived' i , j (t) optimal solution:
step 5, task scheduling: determining optimal task scheduling by a given channel resource allocation strategy;
in the step 5, a given channel resource allocation strategy is set, and the optimization problem P3 is converted into a 0-1 integer programming problem; the method comprises the following specific steps:
step 51, setting a given channel resource allocation strategy, and converting the optimization problem P3 into a 0-1 integer programming problem as follows:
step 52, at each time t, the task allocation strategy S (t) is solved by taking the total time delay of all task processing as a target, namely, the optimal MEC server corresponding to each task is solved, and each task is unloaded to the optimal MEC j * Server processed time delay
Step 53, calculating the time delay T of the task left in the local processing i (t) time delay to offload to MEC processingAnd (T) i (t) + δ) where δ is the delay tolerance, ifThe task is at MEC j * Processing, otherwise, processing locally, and updating a task allocation strategy S (t);
step 6, joint optimization: and combining the steps 4 and 5 to obtain optimal channel allocation and task scheduling.
2. The multi-user multi-MEC task offload resource scheduling method based on edge-to-end coordination according to claim 1, characterized in that: the specific steps of the step 6 are as follows:
step 61, obtaining the optimal channel resource allocation under the fixed task unloading allocation according to step 4;
step 62, obtaining an optimal task unloading distribution strategy under the fixed channel according to step 5;
and step 63, repeating the steps 61 and 62 until the optimal channel allocation and task scheduling strategy is obtained.
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