=Paper=
{{Paper
|id=Vol-2740/20200380
|storemode=property
|title=Ergonomics of Cyberspace. Mathematical Modeling to Create Groups
of Operators for Error-Free and Timely Implementation of Functions in a Distributed Control System
|pdfUrl=https://ceur-ws.org/Vol-2740/20200380.pdf
|volume=Vol-2740
|authors=Evgeniy Lavrov,Nadiia Pasko,Olga Siryk,Oleksandr Burov,Viacheslav Osadchyi
|dblpUrl=https://dblp.org/rec/conf/icteri/LavrovPSBO20
}}
==Ergonomics of Cyberspace. Mathematical Modeling to Create Groups
of Operators for Error-Free and Timely Implementation of Functions in a Distributed Control System==
https://ceur-ws.org/Vol-2740/20200380.pdf
Ergonomics of Cyberspace. Mathematical Modeling to
Create Groups of Operators for Error-Free and Timely
Implementation of Functions in a Distributed Control
System
Evgeniy Lavrov1’[0000-0001-9117-5727]’,Nadiia Pasko2’[0000-0002-9943-3775]’,Olga Siryk3’[0000-0001-
9360-4388]’
,Oleksandr Burov4’[0000-0003-0733-1120]’,,Viacheslav Osadchyi 5’[0000-0001-5659-4774]
1
Sumy State University, Sumy, Ukraine
2
Sumy National Agrarian University, Sumy, Ukraine
3
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
4
Institute of Information Technologies and Learning Tools, Kyiv, Ukraine
5
Bogdan Khmelnitsky Melitopol State Pedagogical University, Melitopol, Ukraine
prof_lavrov@hotmail.com
Abstract. The problem of designing group activities of operators in distributed
information environments is considered. An optimization model is proposed for
choosing the option of assigning functions to a group of operators for the basic
model of the algorithm for executing an application in the form of an event
graph. The model can be used in decision support systems by the operator-
manager of critical control systems.
Keywords: Ergonomics, Cyberspace, Human-Operator, Human-Machine, Reli-
ability, Modeling, Cybersecurity, Control System, Critical System.
1 Introduction
Fundamental changes in computer control tools and methods [1] for complex distrib-
uted objects, such as energy systems, oil and gas transportation systems, transport and
research systems [2-5], training systems [6-9] have fundamentally changed the work
of people in distributed information environments. The technology of interaction be-
tween operators and control objects through complex information models has changed
and become more complicated [1, 10]. The share of group activities has increased
when operators jointly implement the specified control technologies, despite the fact
that they may be located at a great distance from each other [1, 10]. With the increase
in the technical and organizational complexity of such ergatic control systems, the
cost of operator’s errors, failures and malfunctions of information technology equip-
ment also increases [1, 2, 10, 11]. With the introduction of computer-aided decision
support methods and artificial intelligence, the role of a person does not decrease, but
also increases significantly [1, 3, 10], especially in the context of combating cyber-
criminals and various cyber-attacks on information systems [12].
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
2 Problem Statement
The main goal of the ergonomic support of complex control systems is to minimize
the risks caused by the erroneous actions of people-operators [3, 10, 13-16], by taking
into account engineering-psychological and ergonomic restrictions, the individual
characteristics of operators and by “adapting” technology to a person [16-18].
In recent years, emphasis from studying and solving problems of the so-called
“physical” ergonomics (anthropometric, physiological, etc. problems) shifted to solv-
ing problems of providing cognitive comfort for operators and tasks of “organization-
al” ergonomics [2, 3, 11, 16-18]. This implies the taskі of determining the number of
personnel, the qualifications of people, the distribution of functions between operators
and the design of methods for interaction between operators. This task of the prompt
organization of operator interaction is especially acute in cases related to non-standard
or emergency situations, as well as in the tasks of managing security incidents. The
operator-manager, who takes over the organization of the elimination of the problem
situation, must quickly distribute the functions between individual operators. In this
case, the requirements [18-20] should be taken into account:
Maximizing the probability of error-free execution of the application (elimination
of the problem situation);
Restrictions on the timing of activities;
Opportunities for organizing joint activities (forming a team or group of operators
compatible with each other): technologically (means of labor, communication
channels, information models, etc.) [18-20]; psychologically [25-27]; other.
Various network methods can be used to simulate the activities of operators,
e.g.[13, 21]; but the most convenient tool is a functional network (FN) [18-20], which
allows not only description of the activity but also evaluation of its reliability charac-
teristics. To assess the reliability of the activity, mathematical models and a software-
modeling complex were developed [22-24], and a number of optimization tasks were
solved, including distribution of functions between operators .However, the issues of
organizing group activities are not fully resolved in the ergonomics of automated
control systems [24-27]. In this regard, the objective of this work is to determine the
problem of forming a group of compatible operators working in a single information
space, who are assigned to perform discrete algorithmic activities to execute applica-
tions arriving at random times (with the distribution of individual operations between
specific operators) in order to maximize the probability of error-free execution under
constraint on mathematical expectation of runtime.
3 Results
3.1 The principle of formalizing the problem situation of group activity
optimization
The principle of formalizing the problem situation of group activity optimization:
Describe in natural language the sequence of work to complete the application.
Following the identified logic, develop a FN model that describes the activities for
the implementation of the application (work schedule).
Make the transition from the work graph to the event graph (as events we use
events consisting in the fact that some operation was performed correctly or per-
formed with some violation (Fig. 1demonstrates an example of the transition from
the work graph to the event graph).
Considering the possibility of alternative assignments of operators to separate op-
erations (with different probabilities of transition from state to state and different
runtime characteristics), build on the basis of an event graph a model of semi-
Markov decision-making process (SMDMP) for assigning operators to perform in-
dividual operations (taking into account their compatibility in a group).
Formalize the optimization problem for SMDMP.
Fig.1. An example of the process model for implementing the simplest application: a - work
graph; P - work operation; K - operation control; b – graph of events [18,25].
3.2 Model for designing group activities
Let us select the absorbing vertices among the SMDMP vertices. Let the vertices
1,2,...,rl are the vertices with acceptable outcomes. For non-absorbing vertices, we
define the probabilities of finding the process in these initial states:
a=(ar+1,ar+2,…,an), so that
N
a 1,
i r 1
i
(1)
where N is the number of states, r is the number of absorbing states.
We assume that K is the set of all operators. K0 is the cardinality of K. At each ver-
tex i there can be Ki of alternative assignments. Each variant is associated with a set of
transitions from vertex i to vertex j when choosing the k-th solution, kϵKi, with corre-
sponding probabilities and transition times.Thus, the k-th solution corresponds to the
assignment of the operator kϵKiϵK to the stage of the technological process, which
corresponds to state i of the SMDMP. Pij(k) is the probability of the transition of the
process from state i to state j when choosing the k-th alternative. Where in:
p
j
(k )
ij 1 at all i and all k Ki (2)
Tij(k) is the average time of transition from state i to state j when choosing the k-th
alternative. Then the average time of the i-th work with the k-th solution, Ti(k), is de-
fined as:
Ti ( k ) Pij( k ) * Tij( k ) (3)
j
It is necessary to maximize Pr- the probability of absorption in the r-state (or in
states of the r-type):
N
Pr Pi (rlk ) * xi( k ) (4)
l i r 1 kK i
Here x(k)i defines a solution: x(k)i>0 if the k-th alternative is selected at the i-th vertex,
and x(k)i=0, if another solution is chosen. It is also necessary: introduce Boolean varia-
bles δ(k)i (to ensure the uniqueness of solutions and the formation of conditions for the
dependence of the vertices: here k is the operator, i is vertex of the SMDMP).
Let's make the matrix [Qmj] consisting of zeros and ones and each row of which
determines one of the possible groups ("teams") of operators for joint work in the
information space. The number of matrix rows is the number of possible groups, the
number of matrix columns is K0. We can formalize our task as follows:
N
Prm Pir(ik ) xi( k ) max (5)
l i r 1 kK i
N
x
kK
(k )
j Pij( k ) xi( k ) a j , j r 1, r 2,..., N
i r 1 kK
(6)
N
P T
i r 1 j k K i
(k ) (k ) (k )
ij ij ix T0 (7)
kK i
i
(k )
qmk 1, at all i (8)
l( k ) v( k ) ... n( k ) , at all k K (9)
xi( k ) M i( k ) 0, at all i and all k K i (10)
xi( k ) w i( k ) 0, at all i and all k K i (11)
r N
P
j 1 i r 1 kK i
(k )
ij xi( k ) 1 (12)
xi( k ) 0, at all i and all k K i . (13)
Here M and w are a very large and very small numbers.
This task can be easy solved in the environment of any decision support system.
4 Conclusion
The share of group operator activity is growing sharply in modern management sys-
tems. The reliability of control processes substantially depends on the optimality of
the distribution of functions between individual operators. The proposed model of
organizing group activities takes into account the reliability and time characteristics of
the operators, their compatibility with each other and maximizes the probability of
error-free execution of tasks, entering the system. The development was tested during
the practical design and operation of control systems for various purposes and can be
recommended for building decision support systems for operators of control systems.
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