CN116302507A - Application service dynamic deployment and update method based on vacation queuing - Google Patents

Application service dynamic deployment and update method based on vacation queuing Download PDF

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CN116302507A
CN116302507A CN202310167050.8A CN202310167050A CN116302507A CN 116302507 A CN116302507 A CN 116302507A CN 202310167050 A CN202310167050 A CN 202310167050A CN 116302507 A CN116302507 A CN 116302507A
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edge server
application
task
period
average
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易畅言
尚善飞
吴强
王然
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/50—Allocation of resources, e.g. of the central processing unit [CPU]
    • G06F9/5005—Allocation of resources, e.g. of the central processing unit [CPU] to service a request
    • G06F9/5027—Allocation of resources, e.g. of the central processing unit [CPU] to service a request the resource being a machine, e.g. CPUs, Servers, Terminals
    • G06F9/5055—Allocation of resources, e.g. of the central processing unit [CPU] to service a request the resource being a machine, e.g. CPUs, Servers, Terminals considering software capabilities, i.e. software resources associated or available to the machine
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F8/00—Arrangements for software engineering
    • G06F8/60—Software deployment
    • G06F8/65—Updates
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/44—Arrangements for executing specific programs
    • G06F9/445—Program loading or initiating
    • G06F9/44594—Unloading
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/48—Program initiating; Program switching, e.g. by interrupt
    • G06F9/4806—Task transfer initiation or dispatching
    • G06F9/4843—Task transfer initiation or dispatching by program, e.g. task dispatcher, supervisor, operating system
    • G06F9/4881—Scheduling strategies for dispatcher, e.g. round robin, multi-level priority queues
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F9/00—Arrangements for program control, e.g. control units
    • G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
    • G06F9/46—Multiprogramming arrangements
    • G06F9/50—Allocation of resources, e.g. of the central processing unit [CPU]
    • G06F9/5061—Partitioning or combining of resources
    • G06F9/5072—Grid computing
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D10/00—Energy efficient computing, e.g. low power processors, power management or thermal management

Abstract

The invention discloses a dynamic deployment and update method of application services based on holiday queuing. According to the method, an edge computing system consisting of mobile equipment, an edge server and a cloud server is considered, key performance indexes of the system are analyzed through a queuing theory related model, closed expressions of related indexes including but not limited to average delay of the edge server, probability of application deployment on the edge server, busy period probability and the like are deduced, and an efficient dynamic application deployment and update strategy is provided. The optimization problem is built with the goal of minimizing the average system latency, where storage space and energy consumption are constrained. The method constructs an interior point convex approximate optimization method to determine the user task unloading probability, the application response threshold, the application waiting duration and the edge server computing power resource allocation, so that the average time delay of the whole system is minimum.

Description

Application service dynamic deployment and update method based on vacation queuing
Technical Field
The invention belongs to the field of network resource management, and particularly relates to a dynamic deployment and update method of application services based on vacation queuing.
Background
With the rapid development of smart Mobile Devices (MDs) and sensors, artificial Intelligence (AI) and internet of things (IoT) technologies are widely applied in various scenarios of industrial internet, autopilot, etc. The need for large amounts of storage and computation results in increasingly higher device workloads. MDs have the disadvantages of low energy storage, low computing power, small storage space and the like. Cloud computing has been considered as a solution to overcome the limitations of MDs, and task offloading often introduces significant transmission delays due to the long distance between the cloud server and MDs. Edge computing is proposed as a new paradigm to alleviate the problem of large transmission delays in cloud computing. In an edge computing environment, servers are deployed at the edge of a network, with low latency while retaining the energy efficiency advantages of cloud computing. Application deployment refers to storing an application and its associated library files, data sets, etc. in a server. Based on the method, MDs only need to upload tasks, and the application transmission server is not needed, so that task delay and energy consumption caused by MDs transmission are greatly reduced. Therefore, optimizing the location of an application on an Edge Server (ESs) is critical to maximizing server performance.
It is naturally best if all applications can be deployed on the ES. However, in practice, due to the limited storage space, it is almost impossible to store all applications on one ES at the same time, which has prompted consideration of how to dynamically deploy the applications. The most straightforward Dynamic Application Placement (DAP) is: the ES responds to the task immediately after it arrives. If one ES does not have the required application, it will immediately request the application from the other ES or CS and deploy it. If all the works are processed, the system can clear the corresponding application to make room. However, such policies will lead to frequent placement leading to an increase in energy consumption. Therefore, it is highly desirable to design a more flexible and efficient DAP strategy for the following reasons:
1) For Edge Servers (ESs), optimization is usually aimed at delay and energy consumption, which is contradictory in designing DAP policies. On the one hand, if it is desired to minimize delay, the strategy of responding immediately when a task arrives is typically the first conceivable strategy. However, such a policy may result in frequent updates of the application program, increasing energy consumption. On the other hand, if it is desired to minimize the energy consumption, it is inevitably necessary to consider reducing the frequency of application replacement due to the large amount of energy required to deploy the application. However, everywhere decreasing the frequency of application placement may result in increased latency. Furthermore, without an optimized purge strategy, the application may be requested again just after being purged, which increases not only delay but also energy consumption. Therefore, extensive and thorough consideration is also required when explicitly applying for.
2) Many studies consider determining the application location in a static manner. It is not suitable for real-time tasks that arrive at random, such as autopilot and augmented reality. This motivates the design of DAP strategies with long-term performance guarantees.
However, it is very challenging to consider all of the above facts when designing and utilizing a new and efficient edge computing DAP for several reasons:
a. it is a challenge to design a suitable DAP strategy to address the contradiction between delay and energy consumption in edge computation. In particular, such a strategy may require handling random arrivals of computing tasks with heterogeneous demands, and thus require formulating a queuing model for performance evaluation. Furthermore, such DAPs may be required to cope with different demands, such as stringent energy constraints or ultra-low latency.
b. Queue models integrated with advanced DAP policies can be difficult to model and analyze because it is difficult, if not impossible, to obtain their performance in a closed form. For example, the Least Recently Used (LRU) method is simple to apply and is most commonly used for cache updates or application switching domains. Contrary to its popularity, it is challenging to apply the LRU approach to represent delays in a closed form on ESs, let alone other higher-level DAP policies. Furthermore, the performance of such queues is typically non-convex in terms of control strategy. Furthermore, integer constraints in system settings can make corresponding DAP optimizations more challenging.
Disclosure of Invention
The invention aims to: aiming at the singleness of the flow types of the flow scheduling scheme under the existing time-sensitive network, the invention provides a dynamic deployment and update method of application services based on vacation queuing.
The technical scheme is as follows: the method is oriented to multi-user equipment, an edge server and a cloud server, takes user task unloading probability, an application response threshold, application waiting duration and edge server computing power resource allocation as optimization variables, solves a closed expression of a corresponding index based on the vacation queue, and aims at minimizing average task delay of the whole system;
the method comprises the following steps:
(1) Constructing multi-user equipment, an edge server and a cloud server to form an edge computing network, and constructing an edge server task processing delay model according to the edge computing network;
(2) Designing an optimizable dynamic application deployment update strategy, wherein an optimizable variable is an application response threshold value N s Application wait duration omega s The method comprises the steps of carrying out a first treatment on the surface of the At this time, the probability that the task arrives at the waiting duration is:
Figure BDA0004096224340000021
in the method, in the process of the invention,
Figure BDA0004096224340000031
for the rate at which s-type tasks arrive at the edge server, the average duration of the waiting period is:
Figure BDA0004096224340000032
the average duration of the undeployed period is:
Figure BDA0004096224340000033
the average duration of the whole period is calculated as follows:
Figure BDA0004096224340000034
in the method, in the process of the invention,
Figure BDA0004096224340000035
for the average duration of the deployment period +.>
Figure BDA0004096224340000036
For the average duration of the task processing period from the deployment period,/->
Figure BDA0004096224340000037
An average duration of the period increased by the waiting duration;
(3) The complete decision variables of the edge computing system are determined as follows: user task offloading probability beta m,s Applying a response threshold N s Application wait duration omega s Edge server computing power resource allocation f s ；
(4) Calculating the average delay of the whole system, wherein the average delay comprises the calculation time of the task at the mobile device
Figure BDA0004096224340000038
And the calculation time of the task on the edge server +.>
Figure BDA0004096224340000039
The expression of the optimization objective is as follows:
Figure BDA00040962243400000310
in the method, in the process of the invention,
Figure BDA00040962243400000311
average delay, lambda, for processing s-type tasks for mobile device m,s Rate of arrival at mobile device m for s-type task, +.>
Figure BDA00040962243400000312
Time required for requesting application s from cloud server for edge server,/for edge server>
Figure BDA00040962243400000313
The average delay of the s-type task in the edge server is;
(5) Construction optimization problem: based on queuing correlation theory, constructing a system delay minimization function of an edge computing network, and expressing a function of dynamic deployment and update strategy optimization problem of application service based on vacation queuing as follows:
Figure BDA00040962243400000314
the constraint conditions are as follows:
Figure BDA00040962243400000315
Figure BDA00040962243400000316
Figure BDA00040962243400000317
Figure BDA0004096224340000041
Figure BDA0004096224340000042
Figure BDA0004096224340000043
Figure BDA0004096224340000044
Figure BDA0004096224340000045
in the method, in the process of the invention,
Figure BDA0004096224340000046
CPU energy consumption for edge server, w plac The energy expended to deploy an application for an edge server,
Figure BDA0004096224340000047
for local traffic density, +.>
Figure BDA0004096224340000048
For the traffic density of the edge server s-type queue, μ is the expectation of the spatial distribution occupied by the application on the edge server, σ is the standard deviation of the spatial distribution occupied by the application on the edge server, and ε is the probability that the spatial occupied by all the applications exceeds the storage space of the edge server;
(6) Calculating a closed expression of the inexhaustible index in the steps (2), (4) and (5) according to the holiday queue correlation theory; the average delay of the s-type task in the edge server is as follows:
Figure BDA0004096224340000049
wherein mu is s Rate, η, of processing s-type tasks for edge servers s Requesting time required for an application from a cloud service for an edge server;
the average duration of the task processing period from the deployment period is:
Figure BDA00040962243400000410
the average duration of the period increased by the waiting duration is:
Figure BDA00040962243400000411
average duration of the entire cycle:
Figure BDA00040962243400000412
application A s The probability of occupying the edge server space is:
Figure BDA00040962243400000413
the average duration of busy period is:
Figure BDA00040962243400000414
the average duration of idle period is:
Figure BDA0004096224340000051
the probability of busy period is
Figure BDA0004096224340000052
The probability of idle period is->
Figure BDA0004096224340000053
Substituting all the closed expressions into the (5), wherein the optimization problem related parameters in the (5) have closed expressions;
(7) Obtaining user task unloading probability beta according to an interior convex approximation method m,s Applying a response threshold N s Application waiting holdDuration omega s Edge server computing power resource allocation f s And minimizes the average delay of the system.
Further, in the system model in step (1), M Mobile Devices (MDs), a dedicated Edge Server (ES) deployed at a base station and a Cloud Server (CS) are considered to be composed, and the s-type calculation task takes the average rate as lambda m,s Poisson distribution reaching MD m The calculated amount of the s-shaped task follows the average value of c s Is an exponential distribution of (c). ES's storage space is limited and cloud servers can store applications without limit, and then ES tends to request applications from CS for the following times: η (eta) s ＝D s W, where D s For application A s W is the transmission rate between ES and CS. When the task arrives at the mobile device, at beta m,s And unloading the probability of the task to an edge server for processing, otherwise, the mobile device processes the task by itself. Based on this, the arrival rate of the local processing of the s-type task on the mobile device m can be obtained as follows:
Figure BDA0004096224340000054
the distribution of all the arriving tasks is approximately processed as exponential distribution, and the average calculated amount of the processing tasks of the mobile equipment is obtained as follows:
Figure BDA0004096224340000055
further, according to the classical queuing theory model M/M/1, the average delay of processing tasks on the mobile device is obtained as follows:
Figure BDA0004096224340000056
tasks from MDs are managed in different queues according to task type division, and arriving tasks are also processed in FCFS mode. The task arrival rate of the queue for processing the s-type task on the edge server is as follows:
Figure BDA0004096224340000057
further, when the s-type task is offloaded to the ES, if there is no application A on the ES s The ES will not immediately request application a from the CS s But does not request an application until n s-type tasks are accumulated. Application A is requesting from CS s Previously, ES needed to allocate storage A in advance s Is a space of the above-mentioned device. Due to limited memory space, if allocated to application A s The ES may delete some other applications or files because of insufficient space left. When the s-type task queue Q s When empty, application A s May also be at ω s Is accessed within time, i.e. ES will be at ω s Storing application A s Rather than deleting it. If there is an s-type task at omega s If no task is at ω, then ES will continue to process tasks until the queue becomes empty again s Internally arriving, application A s Will be deleted. For better analysis of the queue model, the overall process is divided into four phases:
a) Deployment period
Figure BDA0004096224340000061
The time period is used to deploy the application;
b) Waiting period
Figure BDA0004096224340000062
When the task queue becomes empty, if at omega, the phase starts s When the task arrives, the stage is immediately finished or omega is completely passed s Time, this phase also ends when the application is deleted;
c) Undeployed period
Figure BDA0004096224340000063
Refers to a period when the application is deleted and the arriving tasks do not accumulate to N;
d) Treatment period
Figure BDA0004096224340000064
I.e. the period of the CPU processing tasks, which can be divided into two categories depending on the latency period and the deployment period entering the period, wherein ∈ ->
Figure BDA0004096224340000065
Representing a processing period entered from a deployment period, +.>
Figure BDA0004096224340000066
Representing a processing period entered from a waiting period.
Further, the method comprehensively considers the following four policy factors:
a) User task offloading probability beta m,s It should be between 0 and 1, and may take 0 or 1;
b) Applying a response threshold value N s The response threshold should be 1 or more and should be an integer;
c) Application wait duration omega s The application wait duration should be equal to or greater than 0;
d) Edge server computing power resource allocation f s The sum of the computing forces allocated to all queues should be equal to or less than the total computing force of the edge servers.
Further, the average delay of the mobile device processing the s-type task is calculated by the following method:
Figure BDA0004096224340000067
the calculation time of the task on the edge server is calculated by the following method:
Figure BDA0004096224340000068
in the method, in the process of the invention,
Figure BDA0004096224340000069
for the time required for transferring s-type tasks from mobile device m to edge server, it is composed ofThe formula gives: />
Figure BDA00040962243400000610
d s Average size of s-type task, r m For the transmission rate of the mobile device m to the edge server.
Further, the power of the processing task in the step (5) is composed of a busy period and an idle period, wherein the power of the CPU in the idle period is 60% of the busy period. Local traffic density
Figure BDA00040962243400000611
Is calculated by the following method:
Figure BDA0004096224340000071
traffic density for edge server s-queues
Figure BDA0004096224340000072
Is calculated by the following method:
Figure BDA0004096224340000073
the expected μ of the spatial distribution occupied by the application on the edge server is calculated by the following method:
Figure BDA0004096224340000074
the standard deviation sigma of the spatial distribution occupied by the application on the edge server is calculated by the following method:
Figure BDA0004096224340000075
the beneficial effects are that: compared with the prior art, the invention has the following substantial progress and remarkable effects:
1) Considering an edge computing system consisting of MDs, ES and CS, a long term optimization problem is constructed to minimize the average delay of edge computation, with both energy consumption and storage space constrained. In this system, a novel and efficient DAP strategy is employed as proposed by the present invention, with optimizable response thresholds and latencies. Furthermore, the offload probabilities and the computing resource allocations are also considered as optimization variables.
2) The DAP strategy solves the contradiction between delay and energy consumption in edge computation. In particular, the policy may handle random arrival of computing tasks with heterogeneous demands. By means of the relevant theory of holiday queuing, system performance is analyzed and deduced with expressions in closed form, such as average edge server delay, busy period probability, expected length of processing period, etc.
3) To solve the construction problem, the present invention proposes a new approach, called VQODAP, which integrates BB and NOVA to handle integer and non-convex constraints, resulting in an optimal solution for non-convex targets. In the proposed solution we decompose the original problem using BB and apply NOVA to achieve suboptimal.
Drawings
FIG. 1 is a system model diagram of the method of the present invention;
FIG. 2 is a transition diagram of different phases in the present invention;
FIG. 3 is a plot of average system delay lines for different task arrival rates in the example;
FIG. 4 is a plot of average system delay for different energy constraints in the example;
FIG. 5 is a bar graph of average update frequency versus task arrival rate for different available storage spaces in an example.
Detailed Description
For a detailed description of the disclosed embodiments of the present invention, the present invention is further described below with reference to the accompanying drawings and detailed description.
Firstly, in an edge computing system, a dynamic application deployment update strategy capable of optimizing an application response threshold and application waiting duration is provided, and the user task unloading probability is added, so that the optimization of computing power resource allocation of an edge server is realized, and the average system delay is minimized.
The main idea of the invention is to design an optimizable dynamic application deployment updating strategy, and to assist with other optimization variables to minimize the system delay. The key is to dynamically apply the deployment update strategy for the design: when a task is offloaded to an edge server, if there is no application on the edge server, it will not immediately request an application from the cloud server, but will not request an application until n tasks are accumulated. The application may also be accessed for a period of time when the task queue is empty, i.e., the edge server will store the application during that time, rather than delete it. If there is a task arriving within that time, the edge server will continue to process tasks until the queue becomes empty again, and if no task arrives within that time, the application will be deleted.
Specifically, the application service dynamic deployment and update method based on holiday queuing comprises the following steps:
step 1, establishing a system model
In the system model, M Mobile Devices (MDs), a special Edge Server (ES) and a Cloud Server (CS) which are deployed at a base station are considered to form, and the s-type calculation task has average speed of lambda m,s Poisson distribution reaching MD m The calculated amount of the s-shaped task follows the average value of c s Is an exponential distribution of (c). ES's storage space is limited and cloud servers can store applications without limit, and then ES tends to request applications from CS for the following times: η (eta) s ＝D s W, where D s For application A s W is the transmission rate between ES and CS. When the task arrives at the mobile device, at beta m,s And unloading the probability of the task to an edge server for processing, otherwise, the mobile device processes the task by itself. Based on this, the arrival rate of the local processing of the s-type task on the mobile device m can be obtained as follows:
Figure BDA0004096224340000081
the distribution of all the arriving tasks is approximately processed as exponential distribution, and the average calculated amount of the processing tasks of the mobile equipment is obtained as follows:
Figure BDA0004096224340000082
further according to the classical queuing theory model M/M/1, the average delay of processing tasks on the mobile device is obtained as follows:
Figure BDA0004096224340000083
tasks from MDs are managed in different queues according to task type division, and arriving tasks are also processed in FCFS mode. The task arrival rate of the queue for processing the s-type task on the edge server is as follows:
Figure BDA0004096224340000091
step 2, designing dynamic application deployment update strategy
When the s-type task is offloaded to the ES, if there is no application A on the ES s The ES will not immediately request application a from the CS s But does not request an application until n s-type tasks are accumulated. Application A is requesting from CS s Previously, ES needed to allocate storage A in advance s Is a space of the above-mentioned device. Due to limited memory space, if allocated to application A s The ES may delete some other applications or files because of insufficient space left. When the s-type task queue Q s When empty, application A s May also be at ω s Is accessed within time, i.e. ES will be at ω s Storing application A s Rather than deleting it. If there is an s-type task at omega s If no task is at ω, then ES will continue to process tasks until the queue becomes empty again s Internally arriving, application A s Will be deleted. For better analysis of the queue model, the overall process is divided into four phases:
a) Deployment period
Figure BDA0004096224340000092
The time period is used to deploy the application;
b) Waiting period
Figure BDA0004096224340000093
When the task queue becomes empty, if at omega, the phase starts s When the task arrives, the stage is immediately finished or omega is completely passed s Time, this phase also ends when the application is deleted;
c) Undeployed period
Figure BDA0004096224340000094
Refers to a period when the application is deleted and the arriving tasks do not accumulate to N;
d) Treatment period
Figure BDA0004096224340000095
I.e. the period of the CPU processing tasks, which can be divided into two categories depending on the latency period and the deployment period entering the period, wherein ∈ ->
Figure BDA0004096224340000096
Representing a processing period entered from a deployment period, +.>
Figure BDA0004096224340000097
Representing a processing period entered from a waiting period.
At this time, the probability that the task arrives at the waiting duration is:
Figure BDA0004096224340000098
in the method, in the process of the invention,
Figure BDA0004096224340000099
the rate at which the s-type task reaches the edge server. The average duration of the waiting period is:
Figure BDA00040962243400000910
the average duration of the undeployed period is:
Figure BDA00040962243400000911
the average duration of the whole period is calculated as follows:
Figure BDA00040962243400000912
in the method, in the process of the invention,
Figure BDA00040962243400000913
for the average duration of the deployment period +.>
Figure BDA00040962243400000914
For the average duration of the task processing period from the deployment period,/->
Figure BDA0004096224340000101
Is the average length of the period increased by the waiting duration.
Step 3, constructing optimization problem
The method comprehensively considers the following four policy factors:
a) User task offloading probability beta m,s It should be between 0 and 1, and may take 0 or 1;
b) Applying a response threshold value N s The response threshold should be 1 or more and should be an integer;
c) Application wait duration omega s The application wait duration should be equal to or greater than 0;
d) Edge server computing power resource allocation f s The sum of the computing forces allocated to all queues should be equal to or less than the total computing force of the edge servers.
Calculating the average delay of the whole system, wherein the average delay comprises the calculation time of the task at the mobile device
Figure BDA0004096224340000102
And the calculation time of the task on the edge server +.>
Figure BDA0004096224340000103
The optimization objectives are:
Figure BDA0004096224340000104
in the method, in the process of the invention,
Figure BDA0004096224340000105
average delay, lambda, for processing s-type tasks for mobile device m,s Rate of arrival at mobile device m for s-type task, +.>
Figure BDA0004096224340000106
Time required for requesting application s from cloud server for edge server,/for edge server>
Figure BDA0004096224340000107
Is the average delay of s-type tasks in the edge server. The optimization problem is as follows:
Figure BDA0004096224340000108
the constraint conditions are as follows:
Figure BDA0004096224340000109
Figure BDA00040962243400001010
Figure BDA00040962243400001011
Figure BDA00040962243400001012
Figure BDA00040962243400001013
Figure BDA00040962243400001014
Figure BDA00040962243400001015
Figure BDA00040962243400001016
in the method, in the process of the invention,
Figure BDA00040962243400001017
CPU energy consumption for edge server, w plac The energy expended to deploy an application for an edge server,
Figure BDA00040962243400001018
for local traffic density, +.>
Figure BDA00040962243400001019
For the traffic density of the edge server s-type queue, μ is the expected spatial distribution of applications on the edge server, σ is the standard deviation of the spatial distribution of applications on the edge server, and ε is the probability that the spatial distribution of all applications exceeds the edge server storage space.
Step 4, deducing a closed expression by means of a holiday queue
And calculating a closed expression of the index according to the holiday queue correlation theory.
The average delay of the s-type task in the edge server is as follows:
Figure BDA0004096224340000111
wherein mu is s Rate, η, of processing s-type tasks for edge servers s The time required for the edge server to request an application from the cloud service. The average duration of the task processing period from the deployment period is:
Figure BDA0004096224340000112
the average duration of the period increased by the waiting duration is:
Figure BDA0004096224340000113
average duration of the entire cycle:
Figure BDA0004096224340000114
application A s The probability of occupying the edge server space is:
Figure BDA0004096224340000115
the average duration of busy period is:
Figure BDA0004096224340000116
the average duration of idle period is:
Figure BDA0004096224340000117
the probability of busy period is
Figure BDA0004096224340000118
The probability of idle period is->
Figure BDA0004096224340000119
Step 5, interior convex optimization algorithm
Aiming at the difficulty of integer constraint, a branch-and-bound algorithm is adopted, and the whole problem is divided into system enumeration of candidate sub-problems through state space searching. The optimization problem is still a non-convex problem by relaxing the integer constraint by the BB. The NOVA is used in solving the sub-problem, the key idea being to replace the non-convex objects and constraints with the appropriate convex functions to converge on a smooth solution. Instead of a non-convex target, the following formula is used:
Figure BDA00040962243400001110
in the formula, κ is a regular parameter. Instead of the non-convex constraint, the following formula is used:
Figure BDA0004096224340000121
wherein L is h Is Lipschitz constant.
In order to fully explain the dynamic application deployment update strategy proposed by the present invention, the performance is evaluated by the following three indexes:
(1) Averaging system delay;
(2) Average update frequency-task arrival rate ratio.
In this embodiment, all Matlab-written algorithms and simulation experiments were completed on 2.9ghz zcpu and 16G memory PC. Assuming that there are 20 mobile devices, 20 applications, the task arrival is random. The dynamic application update strategy proposed by the invention is called VQODAP, and other comparison methods are as follows:
a) FRA: once the task arrives, the ES will immediately request the relevant application from the CS, and after all relevant tasks are processed, the ES will immediately delete the relevant application to free up memory for undeployed applications.
b) NRSA: if a task arrives, but no corresponding application is found, the application is not requested immediately, but is requested again after the same type of task has accumulated to n.
c) AKMA: after all tasks are processed, the system begins to wait for a fixed period of time. If a task arrives within the waiting time, the system immediately starts servicing until the system becomes empty again. The response strategy is the same as FRA.
Fig. 3 shows the average system delay at different average arrival rates. At low loads, AKMA reduces the frequency of application deployment by optimizing latency, thereby reducing average system latency. At high loads, the NRSA helps the MDs to offload more tasks to the ES by controlling the response threshold. The advantages of AKMA and NRSA are combined, and VQODAP performs best regardless of load. Fig. 4 illustrates the average system delay under different energy constraints, it being observed that the average delay decreases with relaxation of the energy constraints. As can be seen from the figure, the VQODAP average system delay is the shortest under all energy constraints E. Fig. 5 shows the ratio of application update frequency to task arrival rate at different storage spaces, which value for the VQODAP method decreases with increasing available storage space, being the lowest value in all cases, indicating that the update frequency of VQODAP is the lowest, thus indicating that its energy consumption for application update is the least.

Claims (7)

1. A dynamic deployment and update method of application service based on vacation queuing is characterized in that: the method is based on vacation queuing, is oriented to multi-user equipment, an edge server and a cloud server, takes user task unloading probability, an application response threshold value, application waiting duration time and edge server computing power resource allocation as optimization variables, solves a closed expression of a corresponding index based on the vacation queuing, and aims at minimizing average task delay of the whole system;
the method comprises the following steps:
(1) Constructing multi-user equipment, an edge server and a cloud server to form an edge computing network, and constructing an edge server task processing delay model according to the edge computing network;
(2) Designing an optimizable dynamic application deployment update strategy, wherein an optimizable variable is an application response threshold value N s Application wait duration omega s At this time, the probability that the task arrives at the waiting duration is calculated as:
Figure FDA0004096224330000011
in the method, in the process of the invention,
Figure FDA0004096224330000012
the rate at which an s-type task reaches an edge server;
the average duration of the waiting period is:
Figure FDA0004096224330000013
the average duration of the undeployed period is:
Figure FDA0004096224330000014
the average duration of the whole period is calculated as follows:
Figure FDA0004096224330000015
in the method, in the process of the invention,
Figure FDA0004096224330000016
for the average duration of the deployment period +.>
Figure FDA0004096224330000017
For the average duration of the task processing period from the deployment period,/->
Figure FDA0004096224330000018
An average duration of the period increased by the waiting duration;
(3) The complete decision variables of the edge computing system are determined as follows: user task offloading probability beta m,s Applying a response threshold N s Application wait duration omega s Edge server computing power resource allocation f s ；
(4) Calculating the average delay of the whole system, wherein the average delay comprises the calculation time of the task at the mobile device
Figure FDA0004096224330000019
And the calculation time of the task on the edge server +.>
Figure FDA00040962243300000110
The optimization objectives are:
Figure FDA00040962243300000111
in the method, in the process of the invention,
Figure FDA00040962243300000112
average delay, lambda, for processing s-type tasks for mobile device m,s Rate of arrival at mobile device m for s-type task, +.>
Figure FDA0004096224330000021
Time required for requesting application s from cloud server for edge server,/for edge server>
Figure FDA0004096224330000022
The average delay of the s-type task in the edge server is;
(5) Construction optimization problem: based on queuing correlation theory, constructing a system delay minimization function of an edge computing network, and expressing a function of dynamic deployment and update strategy optimization problem of application service based on vacation queuing as follows:
Figure FDA0004096224330000023
the constraint conditions are as follows:
Figure FDA0004096224330000024
Figure FDA0004096224330000025
Figure FDA0004096224330000026
Figure FDA0004096224330000027
Figure FDA0004096224330000028
Figure FDA0004096224330000029
Figure FDA00040962243300000210
Figure FDA00040962243300000211
in the method, in the process of the invention,
Figure FDA00040962243300000212
CPU energy consumption for edge server, w plac Energy consumed for deploying an application for an edge server,/->
Figure FDA00040962243300000213
For local traffic density, +.>
Figure FDA00040962243300000214
For the traffic density of the s-shaped queue of the edge server, mu is the expected space distribution occupied by the application on the edge server, sigma is the standard deviation of the space distribution occupied by the application on the edge server, and mu is the probability that the space occupied by all the applications exceeds the storage space of the edge server;
(6) Calculating closed expressions of the inexhaustible indexes in the steps (2), (4) and (5) according to the holiday queue correlation theory;
the average delay of the s-type task in the edge server is as follows:
Figure FDA00040962243300000215
wherein mu is s Rate, η, of processing s-type tasks for edge servers s Requesting time required for an application from a cloud service for an edge server;
the average duration of the task processing period from the deployment period is:
Figure FDA00040962243300000216
the average duration of the period increased by the waiting duration is:
Figure FDA0004096224330000031
average duration of the entire cycle:
Figure FDA0004096224330000032
application A s The probability of occupying the edge server space is:
Figure FDA0004096224330000033
the average duration of busy period is:
Figure FDA0004096224330000034
the average duration of idle period is:
Figure FDA0004096224330000035
the probability of busy period is
Figure FDA0004096224330000036
The probability of idle period is->
Figure FDA0004096224330000037
Substituting all the closed expressions into the step (5), wherein the optimization problem related parameters in the step (5) have closed expressions;
(7) Obtaining user task unloading probability beta according to an interior convex approximation method m,s Applying a response threshold N s Application wait duration omega s Edge server computing power resource allocation f s And minimizes the average delay of the system.
2. The holiday queuing-based application service dynamic deployment and update method of claim 1, wherein: in the step (1), M mobile devices are considered in a system model, a special edge server and a cloud server which are deployed at a base station form the system model, and an s-type calculation task takes the average speed as lambda m,s Poisson distribution reaching MD m The calculated amount of the s-shaped task follows the average value of c s An exponential distribution of (2);
the edge server has limited storage space and the cloud server can store applications without limit, and then the edge server tends to request the applications from the cloud server in the following time: η (eta) s ＝D s W, where D s For application A s W is the transmission rate between the edge server and the cloud server;
when the task arrives at the mobile device, at beta m,s And unloading the probability of the task to an edge server for processing, otherwise, the mobile device processes the task by itself.
3. The holiday queuing-based application service dynamic deployment and update method of claim 2, wherein: the arrival rate for local processing of s-type tasks on mobile device m is:
Figure FDA0004096224330000041
the distribution of all the arriving tasks is approximately processed as exponential distribution, and the average calculated amount of the processing tasks of the mobile equipment is obtained as follows:
Figure FDA0004096224330000042
further according to the classical queuing theory model M/M/1, the average delay of processing tasks on the mobile device is obtained as follows:
Figure FDA0004096224330000043
tasks from the mobile device are managed in different queues according to the task type division, and the arrived tasks are processed in an FCFS mode;
the task arrival rate of the queue on the edge server for processing the s-type task is:
Figure FDA0004096224330000044
4. the holiday queuing-based application service dynamic deployment and update method of claim 1, wherein: when the s-type task is offloaded to the edge server, if there is no application A on the edge server s The edge server will not immediately request application a from the cloud server s Rather, the application is not requested until n s-type tasks are accumulated;
requesting application A from cloud server s Previously, the edge server needs to allocate storage a in advance s Because of the limited memory space, if allocated to application A s The edge server has the possibility of deleting part of other application programs or files due to insufficient remaining space;
when the s-type task queue Q s When empty, application A s May also be at ω s Is accessed within a time period, i.e. the edge server will be at ω s Storing application A s Rather than deleting it; if there is an s-type task at omega s If no task is at ω, the edge server will continue to process tasks until the queue becomes empty again s Internally arriving, application A s Will be deleted;
for better analysis of the queue model, the overall process is divided into four phases:
a) Deployment period
Figure FDA0004096224330000045
The time period is used to deploy the application;
b) Waiting period
Figure FDA0004096224330000046
When the task queue becomes empty, if at omega, the phase starts s When the task arrives, the stage is immediately finished or omega is completely passed s Time, this phase also ends when the application is deleted;
c) Undeployed period
Figure FDA0004096224330000047
Refers to a period when the application is deleted and the arriving tasks do not accumulate to N;
d) Treatment period
Figure FDA0004096224330000051
I.e. the period of the CPU processing tasks, which can be divided into two categories depending on the latency period and the deployment period entering the period, wherein ∈ ->
Figure FDA0004096224330000052
Representing a processing period entered from a deployment period, +.>
Figure FDA0004096224330000053
Representing a processing period entered from a waiting period.
5. The holiday queuing-based application service dynamic deployment and update method of claim 1, wherein: the method comprehensively considers the following four policy factors:
a) User task offloading probability beta m,s It should be between 0 and 1, and may take 0 or 1;
b) Applying a response threshold value N s The response threshold should be 1 or more and should be an integer;
c) Application wait duration omega s The application wait duration should be equal to or greater than 0;
d) Edge server computing power resource allocationf s The sum of the computing forces allocated to all the queues is less than or equal to the total computing force of the edge server.
6. The holiday queuing-based application service dynamic deployment and update method of claim 1, wherein: the average delay of the mobile device for processing the s-type task is obtained by the following calculation formula:
Figure FDA0004096224330000054
the calculation of the calculation time of the task on the edge server is as follows:
Figure FDA0004096224330000055
in the method, in the process of the invention,
Figure FDA0004096224330000056
the time required to transfer an s-type task from mobile device m to the edge server is derived from the equation:
Figure FDA0004096224330000057
d s average size of s-type task, r m For the transmission rate of the mobile device m to the edge server.
7. The holiday queuing-based application service dynamic deployment and update method of claim 1, wherein: the power of the processing task in the step (5) consists of a busy period and an idle period, wherein the power of a CPU in the idle period is 60% of the power in the busy period;
local traffic density
Figure FDA0004096224330000058
Is calculated as follows:
Figure FDA0004096224330000059
traffic density for edge server s-queues
Figure FDA00040962243300000510
The calculation formula of (2) is as follows:
Figure FDA00040962243300000511
the calculation formula of the expected μ of the spatial distribution occupied by the application on the edge server is as follows:
Figure FDA00040962243300000512
the calculation formula of the standard deviation sigma of the space distribution occupied by the edge server is as follows:
Figure FDA0004096224330000061
CN202310167050.8A 2023-02-27 2023-02-27 Application service dynamic deployment and update method based on vacation queuing Pending CN116302507A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116680062A (en) * 2023-08-03 2023-09-01 湖南博信创远信息科技有限公司 Application scheduling deployment method based on big data cluster and storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116680062A (en) * 2023-08-03 2023-09-01 湖南博信创远信息科技有限公司 Application scheduling deployment method based on big data cluster and storage medium
CN116680062B (en) * 2023-08-03 2023-12-01 湖南博创高新实业有限公司 Application scheduling deployment method based on big data cluster and storage medium

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