The method of evaluating the operation of service programs at nodes of the distribution system is proposed, which consists in the use of a predictive control model, is proposed. A general analysis was carried out between the use of one of the existing and reviewed methods of determining the evaluations of nodes in distributed systems based on models with consideration and prognostic control, where their main characteristics are considered. Features are presented of using PID regulators based on models of dynamic systems are analyzed. The experimental results of the proposed method of determining performance evaluations of applied applications in distributed structures based on the predictive control model are described.
Currently, the use of applications in distributed
structures rather than monolithic ones is gaining
more and more popularity. The need to use
distributed applications based on modern software
and technical complexes is caused not only by the
spread of large data centers of cloud providers, but
also by the increasingly frequent emergence of
corporate networks in commercial and budget
organizations. In this connection, there are
problems related to the assessment of efficiency
of the use of applications and security in the work
of computing and network resources of the
corporate network [
In the sphere of security of systems, there is a problem of identifying unauthorized actions by intruders. Such actions lead to a change in the evaluations of the efficiency and productivity of the nodes in relation to the reference (previously measured) values.
Using model-based assessments in existing industrial or IT infrastructures to configure autoscaling of corporate network nodes also results in significant cost savings.
The purpose of the paper is to study the functioning of service applications on the nodes of a distributed structure using dynamic systems and the Model of Predictive Control (MPC). The study includes obtaining estimates of service application performance in a distributed system based on load effects by means of a series of requests to the object of study, which are formed using reference trajectories.
on Nodes in Parallel and
Method of solving the problems of determining the estimates of the use of this function on nodes in parallel and distributed structures
In order to solve the problems of determining
the estimates of node performance, models of
parallel and
distributed
structures
based
on
reference algorithms for problem solving are
proposed [
ℎ ( ): + → {0,1}.
At the same time, hi(t) = 1 if the application located on the node at time t is available to solve task A. Otherwise, if hi(t) = 0, then the application on the node at time t is unavailable.
Performance estimates for applications located
on a distributed structure take other ratios. Thus,
for a model with a schedule of a distributed
structure, the efficiency assessment takes the form
[
Acceleration S shows how many times the
application's problem solving time can be reduced
by using a parallel structure [
The next assessment of the performance of
applications on nodes in parallel structures is
efficiency, which is defined [
=
.
The described model of using this function on a parallel structure is simple to calculate estimates. However, in this model, the value of their estimates is determined only after the completion of the task, when the total time Т is known. In addition, the model requires knowledge of the time of solving the problem by the best from a set of sequential algorithms Т0 on one of the nodes on the parallel structure.
Another approach to using similar models for job evaluations employs distributed structures in connection with two aspects. Firstly, nodes in distributed structures due to their heterogeneity (3) (4) (5) (6) = ( ) ( ) where T(A) is the reference time for solving the task А by the application.
The reference time ( ) is the time of solving task А by the ith application on the node using the fastest sequential algorithm, where ( ) > 0.
Also, for applications located on a distributed
structure, such additional estimates as [
and the complexity of the task. The
calculation of the reference performance of the
system
π(A,t)
πi(A,t) is called [
( , ) . distributed structure with a schedule (8), the resources
Therefore, it is incorrect to enter the concept of acceleration to the applications in the distributed structure, since it is not clear about which node is to calculate the acceleration parameter itself. On this basis, a more general concept of relative acceleration is introduced, which is determined as follows: ( 1, 2) = 1 2
The ratio (10) shows the evaluation of the acceleration S for the model with the schedule R1 relative to the other system R2 as the ratio of their time of solving the problem A on the applications in the distributed structure. Also, for a schedule model, it is customary to perform the acceleration evaluation S for each node of the distributed structure as follows: = ( , ) = ∑ ( )ℎ ( ) = (⃗ ( ), ℎ⃗( )), (7) fulfilled. the set: where with full availability of applications on nodes hi(t) ≡ 1 in the process of solving the problem and with the same performance of the distributed structure will coincide with the reference performance of the parallel structure as the condition ∙ 0 will be
At the same time, the model with the schedule ℜ for solving problems from the set Λ is called = < ⃗ ( ), ℎ⃗( ) >. (8) (9) (10) (11) as the ratio of the reference time of solving problem А to the time of solving this problem in a distributed structure based on a schedule model. 4.
The proposed method of solving the problem of determining the performance of applications in distributed structures is based on the following aspects. Firstly, such a model of research as a
Therefore, evaluations of the study of an object (service applications) and the regulator of load effects in distributed structures (Fig. 1) can be obtained in this way:
To determine the main characteristics of the object of study (k, θ, τ) it is necessary to perform its identification according to the models (13–17).
To determine the main characteristics of the regulator, the calculations according to the model (18) are performed. estimate of the object of research and regulator of load effects in distributed structures
Although this method has become widely used since the early 80’s of the 20th century, it has today been
improved management with and practiced in
classical negative feedback.
This method is based on predicting the behavior of the used to adjust inaccuracies related to external obstacles and inaccuracy of the mathematical model in relation to the control object. To do this, a regulator is created that uses the empirical model of the control object to predict its further behavior. proposed method of determining the evaluations of applications at nodes in a distributed structure Characteristics The nature of the submission of a distributed structures is carried out, which is reduced to the maximization or minimization in time of the selected criterion.
Dynamic optimization, which is used in the method of solving the problem differential algebraic equations (DEA) to perform numerical solutions. One of the most popular control (MPC) method (Fig. 2). The main purpose of using
MPC is to
minimize the difference between the given value of the controlled variable and the predictions of the model. optimization of the research object (service applications in a cluster structure)
The model of the control object is usually chosen to be linear, but in this paper we will show the operation of control with predictive models on a non-linear model (Fig. 5). In the case of determining the estimates of applications in distributed systems, a given non-linear model of the control object (service applications) is set as the trajectory of the reference effect of the load (u). As a result of this formalization of the subject area, we will get the following model of predictive control in the form of the variable y (Fig. 2): ( )
2 + 2 ( ) ( (− ) + 1) parameters as transmission coefficient (k), delay time (θ), and time constant (τ) are most often determined. Fig. 1
with the calculated parameters of the regulator (18, Fig. 3) and the research object (13, Fig. 1) is denoted as y.
Models of dynamic systems often have a delay link in their structure, the cause of which is the peculiarities of technological processes. Also, in dynamic systems, the impact on the research object and the reaction of the research object is a function of time (12). Therefore, the reaction to the impact of the research object can be determined both by the current and previous values of the impact on it. As a result, the dynamic system has inertia.
At the same time, during the development of
such systems with a delay, rather efficient PIDs
and some other regulators with a special structure
are mostly used. Also the advantage in use is
given to the PID family of regulators due to their
simplicity, efficiency and prevalence. It is known
[
During work with PID regulators, more than a
hundred options for determining their settings
were created [
In the classical theory of automatic control, the regulator structure is selected from the control object model, for example (13)–(17). At the same time, difficult control objects require the use of complex regulators. However, in practice, in the vast majority of cases, regulation is reduced to the use of PID regulators according to the model: 1 = (1 + + ).
(18)
PID controllers do not always provide the required quality of regulation, but due to the simplicity of their structure and a large number of theoretical and practical methods of their adjustment, PID controllers are the main ones in practical application.
Several types of criteria are used to assess the
quality of transient processes: direct, integral and
frequency. The most important direct indicators
are the maximum deviation module |ymax| and
adjustment time Tp. Among others, integral and
frequency indicators are most often used. For
example, among frequency indicators of quality
(MS), the sensitivity function [
1 ( ∙ ) ∙ ( ∙ ) + 1 | (19) where P(s) and C(s) are transmission functions of the control object and regulator; ω is circular frequency; j is an imaginary unit.
Experimental studies of the models and the for conducting experimental research and data collection, which consists of the following main components: a benchmark, a load balancer and nodes of a distributed (cluster) structure.
Let’s consider the main tasks performed by each of the main components. The benchmark, according to the reference trajectory of the load impact u (Fig. 2), ensured the generation of a series of requests during certain time intervals for the load balancer. The load balancer, in turn, performed traffic redirection (a series of requests) according to the algorithm of uniform distribution to the nodes of the cluster structure. After that, the benchmark received a series of requests from the load balancer and recorded the response time (RT). As a result, an assessment of the load effects (LE) on the service programs of nodes of the cluster structure was used, which was performed as follows: = ⋅ (20) where RTi is time of processing and transportation of a series of requests to the research object; PTi is the period between the generation of successive series of requests for the research object; k is a correction factor equal to 10.
Assessment of load effects (LE) corresponds to the notation y, which is shown in Fig. 2.
The experimental data obtained in this way were analyzed. The results of the analysis of the use of the predictive control model are shown in Fig. 5. following task was set: based on the given values of the reference effects (u), to obtain the values of the estimates of the load effects. Next, it was necessary to build and optimize the model based on the transmission function (13) and the PID regulator.
The assessment of load effects (20) is shown in the graph of Fig. 5 and corresponds to the inscription
Process
Data. In the course experimental studies, the estimate (20)
of was obtained as a reaction of the system (Fig. 2) to the load effects u (the lower part of the graph in Fig. 5). The values obtained as a result of optimization are shown in Fig. 5 and labeled as Optimized FOPDT (upper part of the graph).
According to the analysis shown in Fig. 5 for the research object (service applications) the transfer function was determined according to (13) with the parameters shown in Table 2. The root mean square error based on the found parameters (Table 2) was 7589.8. = ⋅ 100 % .
Values of the parameters (initial values) where R0 is the estimate of the root mean square error obtained as a result of optimization of the parameters of the transition function of the research object and the PID of the regulator; R is initially obtained estimate of the root mean square error as a result of determining the parameters of the transition function of the research object and the PID regulator.
In this work, the use of the method of control management (MPC, Fig. 2) made it possible to increase the accuracy of the predictive model by 70.22%.
The following software was used during the experimental research: the Ubuntu version 21.04 operating system, a cluster structure based on MicroK8s and Docker containers.
So the presentation of distributed structures as dynamic systems allows: To receive information about existing changes (for improvement or deterioration) of qualitative and quantitative assessments of the main characteristics of applications on nodes contained in distributed (cluster) structures in connection with their purposeful (sanctioned) changes in the software code or changes in the software settings environment (operating systems, system utilities). Create an automatic control system that works in real time by determining the optimal characteristics of the transfer function of the model of the research object and the PID regulator. On the basis of the obtained automatic control system, determine the margin of safety of the distributed (cluster) structure due to the appearance of unaccounted for external or internal excitations (noises) on the research objects or the software environment.