=Paper= {{Paper |id=Vol-3288/short11 |storemode=property |title=Models and Methods for Determining Application Performance Estimates in Distributed Structures (short paper) |pdfUrl=https://ceur-ws.org/Vol-3288/short11.pdf |volume=Vol-3288 |authors=Viktor Grechaninov,Oleksandr Khoshaba,Hennadii Hulak,Yuliia Zhdanova,Iryna Melnyk |dblpUrl=https://dblp.org/rec/conf/cpits/GrechaninovKHZM22 }} ==Models and Methods for Determining Application Performance Estimates in Distributed Structures (short paper)== https://ceur-ws.org/Vol-3288/short11.pdf

Models and Methods for Determining Application Performance
Estimates in Distributed Structures
Viktor Grechaninov1, Oleksandr Khoshaba1, Hennadii Hulak2, Yuliia Zhdanova2,
and Iryna Melnyk2
1
Institute of Mathematical Machines and Systems, 42 Glushkova ave., Kyiv, 03187, Ukraine
2
Borys Grinchenko Kyiv University, 18/2 Bulvarno-Kudriavska str., Kyiv, 04053, Ukraine

Abstract
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.

Keywords 1
Predictive control model, distributed systems, proportional-integral-differential, PID,
regulator, automated control system.

1. Introduction information structures, putting additional nodes
into operation, etc. [2, 3].
In the sphere of security of systems, there is a
Currently, the use of applications in distributed
problem of identifying unauthorized actions by
structures rather than monolithic ones is gaining
intruders. Such actions lead to a change in the
more and more popularity. The need to use
evaluations of the efficiency and productivity of
distributed applications based on modern software
the nodes in relation to the reference (previously
and technical complexes is caused not only by the
measured) values.
spread of large data centers of cloud providers, but
Using model-based assessments in existing
also by the increasingly frequent emergence of
industrial or IT infrastructures to configure auto-
corporate networks in commercial and budget
scaling of corporate network nodes also results in
organizations. In this connection, there are
significant cost savings.
problems related to the assessment of efficiency
of the use of applications and security in the work
of computing and network resources of the 2. Research Purpose
corporate network [1]. The most common
problems include changing the estomates of the The purpose of the paper is to study the
efficiency and productivity of nodes of a functioning of service applications on the nodes
distributed system as a result of its modernization of a distributed structure using dynamic systems
with software and technical means, installing and the Model of Predictive Control (MPC). The
patches on the operating systems of nodes, adding study includes obtaining estimates of service
new ones, as well as studying the software code of application performance in a distributed system
existing service applications, implementing based on load effects by means of a series of
scripts for performing work on deploying requests to the object of study, which are formed
using reference trajectories.

CPITS-2022: Cybersecurity Providing in Information and Telecommunication Systems, October 13, 2022, Kyiv, Ukraine
EMAIL: grechaninov@nas.gov.ua (V. Grechaninov); oleksandr.khoshaba@gmail.com (O. Khoshaba); h.hulak@kubg.edu.ua (H. Hulak);
y.zhdanova@kubg.edu.ua (Y. Zhdanova); iy.melnyk@kubg.edu.ua (I. Melnyk)
ORCID: 0000-0001-6268-3204 (V. Grechaninov); 0000-0001-5375-6280 (O. Khoshaba); 0000-0001-9131-9233 (H. Hulak); 0000-0002-
9277-4972 (Y. Zhdanova); 0000-0001-6041-6145 (I. Melnyk)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)

134
3. Method of Determining Estimates characterized by the presence of a schedule and is
defined as:
on Nodes in Parallel and
ℎ𝑖 (𝑡): 𝑅 + → {0,1}. (3)
Distributed Structures
At the same time, hi(t) = 1 if the application
Method of solving the problems of located on the node at time t is available to solve
determining the estimates of the use of this task A. Otherwise, if hi(t) = 0, then the application
function on nodes in parallel and distributed on the node at time t is unavailable.
structures Performance estimates for applications located
In order to solve the problems of determining on a distributed structure take other ratios. Thus,
the estimates of node performance, models of for a model with a schedule of a distributed
parallel and distributed structures based on structure, the efficiency assessment takes the form
reference algorithms for problem solving are [5]:
proposed [1–4]. In this regard, the determination 𝑇(𝐴)
of node performance estimates, which is based on 𝐸𝑡 = . (4)
𝑇(𝐴)
the model of a parallel system, uses a reference
sequential algorithm for solving some problem A where T(A) is the reference time for solving the
by an application in time T [2, 4]. In this case, the task А by the application.
acceleration estimate is used, which is defined as: The reference time 𝑇(𝐴) is the time of solving
𝑇0 task А by the ith application on the node using the
𝑆= . (1) fastest sequential algorithm, where 𝑇(𝐴) > 0.
𝑇
Also, for applications located on a distributed
where T0 is solution time of reference problem А structure, such additional estimates as [5, 6] are
by the application on one device (node) using the introduced: the performance of the reference
fastest sequential algorithm. system and the complexity of the task. The
Acceleration S shows how many times the calculation of the reference performance of the
application's problem solving time can be reduced system π(A,t) [5–7] is necessary for the
by using a parallel structure [3]. calculation of T(A).
The next assessment of the performance of The reference performance of the structure
applications on nodes in parallel structures is πi(A,t) is called [7] the performance of the ith node
efficiency, which is defined [1, 3] as: of the distributed system when solving the
𝑆 𝑇0 problem A:
𝐸= = . (2)
𝑛 𝑛𝑇 𝐿(𝐴)
𝜋𝑖 (𝐴) = . (5)
The described model of using this function on 𝑇𝑖 (𝐴)
a parallel structure is simple to calculate
where L(A) is a function of the complexity of the
estimates. However, in this model, the value of
task execution by the application on the
their estimates is determined only after the
distributed structure.
completion of the task, when the total time Т is
The task complexity function L(A) is defined
known. In addition, the model requires knowledge
on some set of tasks Λ and expresses a priori
of the time of solving the problem by the best from
knowledge of its complexities:
a set of sequential algorithms Т0 on one of the
nodes on the parallel structure. 𝐿(𝐴): 𝛬 → 𝑅 + . (6)
Another approach to using similar models for
For example, the complexity function of the
job evaluations employs distributed structures in
performance of the task L(A) by an application on
connection with two aspects. Firstly, nodes in
a distributed structure can include an estimate of
distributed structures due to their heterogeneity
the number of elementary operations, which are
may have different values of application
calculated using the complexity theory [8–10] . To
performance estimates as these nodes have
solve the problems of determining the evaluations
different computing resources. Secondly, nodes in
of node performance in parallel and distributed
distributed structures may be unavailable at
structures, a model with a schedule is introduced,
certain time intervals during the solution of the
which describes the concept of the reference
entire problem.
performance of the structure as the sum of the
Let us consider one of the models for
reference performances of the nodes [7]:
applications to distributed structures,which is

135
𝑛 as the ratio of the reference time of solving
𝜋(𝐴, 𝑡) = ∑ 𝜋𝑖 (𝐴)ℎ𝑖 (𝑡) = (𝜋 ⃗ (𝑡)), (7)
⃗ (𝐴), ℎ problem А to the time of solving this problem in a
distributed structure based on a schedule model.
𝑖=0
where with full availability of applications on
nodes hi(t) ≡ 1 in the process of solving the 4. Method of Solving the Problem
problem and with the same reference Determining the Performance
performance, where πi(A) = π0, the reference
performance of the distributed structure will The proposed method of solving the problem
coincide with the reference performance of the of determining the performance of applications in
parallel structure as the condition 𝑛 ∙ 𝜋0 will be distributed structures is based on the following
fulfilled. aspects. Firstly, such a model of research as a
At the same time, the model with the schedule distributed structure is a dynamic system.
ℜ for solving problems from the set Λ is called Therefore, evaluations of the study of an object
the set: (service applications) and the regulator of load
⃗ (𝑡) >. effects in distributed structures (Fig. 1) can be
⃗ (𝐴), ℎ
𝑅 =<𝜋 (8)
obtained in this way:
For a model with the schedule ℜ, the reference  To determine the main characteristics of the
time for solving problem A is called the value T(A) object of study (k, θ, τ) it is necessary to
[5–7], which is determined by the following perform its identification according to the
relation: models (13–17).
𝑡  To determine the main characteristics of the
𝑇(𝐴) = 𝑡: ∫ 𝜋(𝐴, 𝜏)𝑑𝜏. (9) regulator, the calculations according to the
𝑡=0
model (18) are performed.
In the general case, the acceleration indicators
for the parallel structure are defined as the ratio of
the time of solving the problem by the application
at one node to the time of solving the problem on
the whole system based on the ratio (1). In a
distributed structure with a schedule (8), the
resources of the nodes may be different. Figure 1: General scheme for determining the
Therefore, it is incorrect to enter the concept of estimate of the object of research and regulator
acceleration to the applications in the distributed of load effects in distributed structures
structure, since it is not clear about which node is
to calculate the acceleration parameter itself. On Secondly, the proposed method uses the
this basis, a more general concept of relative reference function of the load effect on the object
acceleration is introduced, which is determined as of research, which can be represented by both
follows: linear and non-linear model.
The comparative characteristics of the existing
𝑇1
𝑆(𝑅1 , 𝑅2 ) = . (10) and proposed methods of determining the
𝑇2 evaluations of application functions at the nodes
The ratio (10) shows the evaluation of the in the distributed structure are presented in
acceleration S for the model with the schedule R1 Table 1, which shows the main distinctive
relative to the other system R2 as the ratio of their features.
time of solving the problem A on the applications The method of control with predicting models
in the distributed structure. Also, for a schedule is one of the modern methods of management
model, it is customary to perform the acceleration theory, which is most effectively used in
evaluation S for each node of the distributed management of technological processes.
structure as follows: Although this method has become widely used
since the early 80’s of the 20th century, it has today
𝑇𝑖 been improved and practiced in classical
𝑆𝑖 = . (11)
𝑇 management with negative feedback. This
The ratio (11) shows the estimate of method is based on predicting the behavior of the
acceleration Si for the ith application on the node control object on different types of input
influences. Feedback in such control systems is

136
used to adjust inaccuracies related to external distributed structures is carried out, which is
obstacles and inaccuracy of the mathematical reduced to the maximization or minimization in
model in relation to the control object. To do this, time of the selected criterion.
a regulator is created that uses the empirical model Dynamic optimization, which is used in the
of the control object to predict its further behavior. proposed method of solving the problem of
determining application performance estimates in
Table 1 distributed structures, effectively uses systems of
Comparative characteristics of the existing and differential algebraic equations (DEA) to perform
proposed method of determining the evaluations numerical solutions. One of the most popular
of applications at nodes in a distributed structure practical implementations of dynamic
optimization includes the model predictive
Existing Proposed
Characteristics control (MPC) method (Fig. 2). The main purpose
method method
of using MPC is to minimize the difference
The nature of the In the form of a In the form of a
submission of a static system dynamic system
between the given value of the controlled variable
distributed and the predictions of the model.
system
Models of Schedule model Model of
research prognostic
control
Input parameters Time to solve a Time to process
of a model problem on a the request to
desktop the service
application program
Object of Desktop Service
research programs are programs are
located at the located at the
Figure 2: Practical implementation of dynamic
distributed distributed optimization of the research object (service
system nodes system nodes applications in a cluster structure)
Output Efficiency, Parameters of
parameters of a acceleration, the model of The model of the control object is usually
model productivity, the object of
chosen to be linear, but in this paper we will show
complexity study,
parameters of the operation of control with predictive models on
control a non-linear model (Fig. 5). In the case of
regulator determining the estimates of applications in
Load effect tools A set of A set of distributed systems, a given non-linear model of
consecutive consecutive and the control object (service applications) is set as
algorithms parallel series of the trajectory of the reference effect of the load
based on requests based
reference on the
(u). As a result of this formalization of the subject
algorithm reference area, we will get the following model of predictive
trajectory control in the form of the variable y (Fig. 2):
𝑑𝑦
In many cases, the problems listed above and 𝜏 = −𝑦 + 𝑘𝑢, 0 ≤ 𝑢 ≤ 500. (12)
𝑑𝑡
related to the evaluation of the performance of
applications on nodes in distributed structures, Management models with the following
can be effectively solved with the help of some set transferable functions are defined for the research
of dynamic optimization algorithms [11]. In the object (service applications in distributed
field of management of service applications on structures):
nodes of distributed structures, using dynamic 𝑦(𝑠) 𝑘 𝑒𝑥𝑝(−𝜃𝑠)
optimization methods it is possible to maintain a = . (13)
𝑢(𝑠) 𝜏𝑠 + 1
given level according to the reference trajectory
of load effects. Such a level may have a non-linear 𝑦(𝑠) 𝑘 𝜔2 𝑒𝑥𝑝(−𝜃𝑠)
function of the trajectory according to which load = 2 . (14)
𝑢(𝑠) 𝑠 + 2𝜉𝜔𝑠 + 𝜔 2
effects on the research object are performed. For
this purpose, with the help of the optimality 𝑦(𝑠) 𝑘 𝑒𝑥𝑝(−𝜃𝑠)
function used, the best management of the process = . (15)
of load effect on service applications of 𝑢(𝑠) 𝑠

137
𝑦(𝑠) 𝑘 𝑒𝑥𝑝(−𝜃𝑠) During work with PID regulators, more than a
= . (16) hundred options for determining their settings
𝑢(𝑠) 𝑠2 were created [13–16]. This number is determined
by the difference in the reference models of the
𝑦(𝑠) 𝑘 𝑒𝑥𝑝(−𝜃𝑠)
= . (17) dynamics of technological processes, the quality
𝑢(𝑠) 𝑠(𝜏𝑠 + 1) criteria of transient processes, the conditions of
Based on the models described above, such their application, the accuracy and reliability of
parameters as transmission coefficient (k), delay the algorithms for calculating and optimizing their
time (θ), and time constant (τ) are most often parameters. The basis of the use of regulators in
determined. dynamic structures is the study of object control
Thus, as a result of the load effects on the systems, in which the delay time for a change in
research object, the reaction of the system the controlling effect takes most of the time for the
(distributed structure) in the form of reaction of the object of study.
measurements (request processing) is marked (yt). In the classical theory of automatic control, the
The model built on the basis of the scheme of regulator structure is selected from the control
Fig. 1 with the calculated parameters of the object model, for example (13)–(17). At the same
regulator (18, Fig. 3) and the research object (13, time, difficult control objects require the use of
Fig. 1) is denoted as y. complex regulators. However, in practice, in the
vast majority of cases, regulation is reduced to the
use of PID regulators according to the model:
5. Peculiarities of using PID
1
Regulators based on Models 𝑢 = 𝐾𝑝 (1 + + 𝑇𝑑 𝑠). (18)
𝑇𝑖 𝑠
of Dynamic Systems
PID controllers do not always provide the
required quality of regulation, but due to the
Models of dynamic systems often have a delay
simplicity of their structure and a large number of
link in their structure, the cause of which is the
theoretical and practical methods of their
peculiarities of technological processes. Also, in
adjustment, PID controllers are the main ones in
dynamic systems, the impact on the research
practical application.
object and the reaction of the research object is a
Several types of criteria are used to assess the
function of time (12). Therefore, the reaction to
quality of transient processes: direct, integral and
the impact of the research object can be
frequency. The most important direct indicators
determined both by the current and previous
are the maximum deviation module |ymax| and
values of the impact on it. As a result, the dynamic
adjustment time Tp. Among others, integral and
system has inertia.
frequency indicators are most often used. For
At the same time, during the development of
example, among frequency indicators of quality
such systems with a delay, rather efficient PIDs
(MS), the sensitivity function [12] is very often
and some other regulators with a special structure
used, which is defined as follows:
are mostly used. Also the advantage in use is
given to the PID family of regulators due to their 1
𝑀𝑆 = 𝑚𝑎𝑥 | | (19)
simplicity, efficiency and prevalence. It is known 𝜔 𝑃(𝑗 ∙ 𝜔) ∙ 𝐶(𝑗 ∙ 𝜔) + 1
[12] that earlier in more than 90% of cases when
using technological process control systems in where P(s) and C(s) are transmission functions of
dynamic systems, PID regulators were used the control object and regulator; ω is circular
(Fig. 3). frequency; j is an imaginary unit.

6. Experimental Research
Experimental studies of the models and the
proposed method of determining application
performance estimates in distributed structures
were conducted on the basis of the system shown
in Fig. 4.

Figure 3: Scheme of PID regulator

138
Figure 4: The system of conducting experimental Figure 5: Results of the analysis of the use of the
research predictive control model

Fig. 4 presents a general scheme of the system When performing experimental studies, the
for conducting experimental research and data following task was set: based on the given values
collection, which consists of the following main of the reference effects (u), to obtain the values of
components: a benchmark, a load balancer and the estimates of the load effects. Next, it was
nodes of a distributed (cluster) structure. necessary to build and optimize the model based
Let’s consider the main tasks performed by on the transmission function (13) and the PID
each of the main components. The benchmark, regulator.
according to the reference trajectory of the load The assessment of load effects (20) is shown
impact u (Fig. 2), ensured the generation of a in the graph of Fig. 5 and corresponds to the
series of requests during certain time intervals for inscription Process Data. In the course of
the load balancer. The load balancer, in turn, experimental studies, the estimate (20) was
performed traffic redirection (a series of requests) obtained as a reaction of the system (Fig. 2) to the
according to the algorithm of uniform distribution load effects u (the lower part of the graph in
to the nodes of the cluster structure. After that, the Fig. 5). The values obtained as a result of
benchmark received a series of requests from the optimization are shown in Fig. 5 and labeled as
load balancer and recorded the response time Optimized FOPDT (upper part of the graph).
(RT). As a result, an assessment of the load effects According to the analysis shown in Fig. 5 for
(LE) on the service programs of nodes of the the research object (service applications) the
cluster structure was used, which was performed transfer function was determined according to
as follows: (13) with the parameters shown in Table 2. The
root mean square error based on the found
𝑅𝑇𝑖 parameters (Table 2) was 7589.8.
𝐿𝐸 = 𝑘 ⋅𝑙𝑛 𝑙𝑛 (20)
𝑃𝑇𝑖
where RTi is time of processing and transportation Table 2
of a series of requests to the research object; PTi Parameters of the research object mode
is the period between the generation of successive Values of the
series of requests for the research object; k is a Parameters of the model parameters
correction factor equal to 10. (initial values)
Assessment of load effects (LE) corresponds Transmission coefficient (k) 0.06
to the notation y, which is shown in Fig. 2. Delay time (θ) 2.32
The experimental data obtained in this way Time constant (τ) 0
were analyzed. The results of the analysis of the
use of the predictive control model are shown in
Fig. 5. The parameters of the control regulator were
also determined (Table 3) using the efficiency
indicator of the optimization process:
𝑅0
𝐸= ⋅ 100 % . (21)
𝑅

139
where R0 is the estimate of the root mean square internal excitations (noises) on the research
error obtained as a result of optimization of the objects or the software environment.
parameters of the transition function of the
research object and the PID of the regulator; R is 8. References
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 [1] M. Vladymyrenko, et al., Analysis of
the PID regulator. Implementation Results of the Distributed
In this work, the use of the method of control Access Control System, in VI International
management (MPC, Fig. 2) made it possible to Scientific and Practical Conference
increase the accuracy of the predictive model by Problems of Infocommunications. Science
70.22%. and Technology, 2019, pp. 39–44. doi:
10.1109/PICST47496.2019.9061376.
[2] V. Buriachok, V. Sokolov, P. Skladannyi,
Table 3
Security Rating Metrics for Distributed
Parameters of the control regulator
Wireless Systems, in 8th International
Values Conference on “Mathematics. Information
Parameters
of parameters Technologies. Education,” vol. 2386, 2019,
of the regulator
of the regulator pp. 222–233.
Proportional gain 18.3 [3] V. Astapenya, et al., Analysis of Ways and
Integral gain 2.3 Methods of Increasing the Availability of
Derivative gain 0 Information in Distributed Information
Initial root mean square Systems, in 8th International Conference on
7589.8 Problems of Infocommunications, Science
error
The final root mean and Technology, 2021, pp. 174–178. doi:
2259.9 10.1109/PICST54195.2021.9772161.
square error
[4] A. Afanasiev, M. Posypkin, A. Khritankov,
Analytical Model for Evaluating the
The following software was used during the Performance of Distributed Systems,
experimental research: the Ubuntu version 21.04 Software Products and Systems, vol. 4, 2009,
operating system, a cluster structure based on pp. 60–64.
MicroK8s and Docker containers. [5] A. Khritankov, Mathematical Model of
Performance Characteristics of Distributed
7. Conclusions Computing Systems, in 50th scientific
conference of MIPT, 2007, pp. 86–88.
So the presentation of distributed structures as [6] A. Khritankov, On Performance
dynamic systems allows: Characteristics of Distributed Systems, in
 To receive information about existing changes 51st scientific conference of MIPT, 2008.
(for improvement or deterioration) of [7] A. Khritankov, Models and algorithms for
qualitative and quantitative assessments of the load distribution. Algorithms based on QS
main characteristics of applications on nodes networks, Information technologies and
contained in distributed (cluster) structures in computing systems, vol. 3, 2009, pp. 33–48.
connection with their purposeful (sanctioned) [8] M. Posypkin, A. Khritankov, On the Concept
changes in the software code or changes in the of Acceleration and Efficiency in Distributed
software settings environment (operating Systems, in All-Russian Scientific
systems, system utilities). Conference “Scientific Service on the
 Create an automatic control system that works Internet: Solving Big Problems,” 2008, pp.
in real time by determining the optimal 149–155.
characteristics of the transfer function of the [9] A. Khritankov, Evaluation of the Efficiency
model of the research object and the PID of Distributed Systems in Solving Problems
regulator. of Variable Size, Scientific and technical
bulletin of St. Petersburg State University
 On the basis of the obtained automatic control
ITMO, vol. 2, 2010, pp. 66–71.
system, determine the margin of safety of the
[10] M. Posypkin, A. Khritankov, On the Concept
distributed (cluster) structure due to the
of Performance in Distributed Computing
appearance of unaccounted for external or

140
Systems, in ISA RAS, vol. 32, 2008, pp. 26–
32.
[11] V. Grechaninov, et al., Decentralized Access
Demarcation System Construction in
Situational Center Network, in Workshop on
Cybersecurity Providing in Information and
Telecommunication Systems II, vol. 3188,
no. 2, 2022, pp. 197–206.
[12] J. L. Balcazar, J. Dıaz, J. Gabarro, Structural
Complexity II, vol. 22. EATCS Monographs
on Theoretical Computer Science, 1990. doi:
10.1007/978-3-642-75357-2.
[13] J. L. Balcazar, J. Dıaz, J. Gabarro, Structural
Complexity I, 2nd Ed. Theoretical Computer
Science, An EATCS Series, 1995. doi:
10.1007/978-3-642-79235-9.
[14] O. Goldreich. P, NP, and NP-Completeness:
The Basics of Complexity Theory.
Cambridge University Press, 2010.
[15] K. J. Åström, T. Hägglund, Advanced PID
control, USA, Instrumentation, Systems, and
Automation Society, 2006.
[16] A. O’Dwyer, Handbook of PI and PID
Controller Tuning Rules, London, Imperial
Colledge Press, 2006.

141