International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 04, April 2019, pp. 1548–1556, Article ID: IJCIET_10_04_161
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=4
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
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AUTOMATION OF DECISION MAKING
SUPPORT ON THE DISTRIBUTION OF
FINANCIAL RESOURCES ON THE
ELIMINATION OF ACCIDENTS ON RAILWAY
TRANSPORT
Berik Akhmetov
Associate Professor, Yessenov University, Kazakhstan, Aktau
V. Lakhno
Professor, Yessenov University, Kazakhstan, Aktau
V. Malyukov
Professor, Department of Computer systems and networks,
National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine
S. Sarsimbayeva
Associate Professor, K. Zhubanov Aktobe Regional State University, Kazakhstan, Aktobe
T. Kartbayev
Associate Professor, Almaty University of Power Engineering and Telecommunications,
Kazakhstan
A. Doszhanova
Associate Professor, Almaty University of Power Engineering and Telecommunications,
Kazakhstan
A. Abuova
Doctoral Student, Kazakh University Ways of Communications, Almaty, Kazakhstan
ABSTRACT
There was proposed a model for automation of the decision support system (DSS),
which allows to automate the development of recommendations to the heads of the
situational center (SC), which manages all decisions made during the emergency
situation elimination (hereinafter ES). At the same time, we believe that the
management of the SC and emergency responders who work directly at the railway
accident or emergency area can get access to the DSS data. The model is designed to
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Automation of Decision Making Support on the Distribution of Financial Resources on the
Elimination of Accidents on Railway Transport
automate the forecast estimates for various variants of the financial and material
resources distribution, spent on the elimination of an accident or emergency situation
and its consequences.
Key words: decision support system, emergency situation analysis, financial and
material strategy, recommendation generation, mathematical model, game theory.
Cite this Article: Berik Akhmetov, V. Lakhno, V. Malyukov, S. Sarsimbayeva,
T. Kartbayev, A. Doszhanova, A. Abuova, Automation of Decision Making Support
on the Distribution of Financial Resources on the Elimination of Accidents on
Railway Transport, International Journal of Civil Engineering and Technology 10(4),
2019, pp. 1548–1556.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=4
1. INTRODUCTION
The reduction of the scale of the negative effects of technogenic accidents or emergency
situations (ES) on railway transport (RWT) is possible by optimization of decision-making
processes. This applies both in the pre-accident period and directly at the time of the
elimination of the consequences of the accident or emergency. A sufficient condition for
quality decision making, in this situation, in our opinion, can be the use of intellectualized
decision support systems (IDSS) in the tasks of elimination of the consequences of
technogenic accidents or emergencies on RWT. In particular, the development of appropriate
methods and software based on the tasks structuring for such automated DSS remains an
urgent task. And also, models and methods for solving them.
2. LITERATURE REVIEW
Methods for solving the tasks of actions control of rescuers or emergency responders in
conditions of technogenic accidents (TGA) or emergencies on railway transport and the
corresponding mathematical models describing the functioning of the operational units for
their elimination are considered in [2, 3]. Particular attention was paid to the principles of
construction and architecture of automated DSS in extinguishing fires [3-6]. However, these
developments have not given the final software product (SP) in the form of DSS. Decision
support problems for identification and elimination of emergencies based on dynamic expert
systems (ES) [4], intellectualization of the decision support process in emergency situations at
enterprises using information on the state of the environment are described in [5–7].
The reviewed publications [5–11] do not contain descriptive information related to the
prediction of the development of TGA or emergency at RWT with the purpose of
recommendations generation to managers (decision makers or hereafter - DM) in order to
eliminate its consequences [12].
The above mentioned necessitates a reduction in time for the development and adoption of
an reasonable decision by the managers of technogenic ES elimination by the computerization
of identification processes of such situations. It is proposed to solve this relevant problem on
the basis of the application of the game theory.
3. PURPOSE AND OBJECTIVES OF THE STUDY
The purpose of the article is to develop a model for a decision support system for the
distribution of financial and material resources (FMR), aimed at elimination of the
consequences of technogenic accidents and emergency situations on railway transport.
In order to achieve this purpose it is necessary to develop:
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Berik Akhmetov, V. Lakhno, V. Malyukov, S. Sarsimbayeva, T. Kartbayev, A. Doszhanova, A. Abuova
an adaptive model for rational strategy selection for the distribution of financial and
material resources allocated for the elimination of a technogenic accident or an emergency
situation on railway transport; simulation models in the Mathcad environment for solving the
problems and to conduct simulation modeling for various strategies for the distribution of
financial and material resources allocated for the elimination of technogenic accidents or
emergencies on railway transport.
4. METHODS AND MODELS
Let give the formulation of the problem on the situational center financing (hereinafter - SC)
in order to eliminate the consequences of emergency situations on RWT.
We accept that there are two sides involved in the interaction.
The first side - the SC for ES elimination (hereinafter - SCESE), whose head makes the
decision (hereinafter the decision maker - DM).
The second side - directly ES liquidators on RWT in the area of the corresponding works
(hereinafter - LAES).
The condition of each side is characterized by financial and material resources (FMR). It
is assumed that the head of the SCESE will make decisions on the allocation of financial and
material resources, for example, special or construction equipment (except human ones),
which is involved in ES consequences elimination.
In the emergency zone, the decision maker can allocate the FMR, which is spent on
attracting the appropriate specialists for elimination the consequences.
The following assumption has been made: the change rates of the FMR values of the
parties are given: g1  first side (SCESE), g 2  second side (LAES).
Let introduce the following notation:
xt   FMR value at the moment of time
t t  0,1,..., N*  of SCESE;
yt   FMR value at the moment of time t t  0,1,..., N*  , of LAES;
N *  natural number;
r1  the response coefficient of the second side (LAES) on the allocation by the first side
(SCESE) of the FMR for elimination the consequences of an emergency situation (this is due
to the fact that there is a need to work with the FMR that was allocated by SCESE);
r2  the response coefficient of the SCESE on the allocation by the LAES of the FMR on
specialists for elimination the consequences of an emergency situation (this is due to the fact
that the SCESE needs to ensure the specialists working in the emergency area with the FMR).
The interaction of the sides can be written in the following form:
x(t  1)  g1  x  (t )  u (t )  g1  x  (t )  r2  v(t )  g 2  y  (t );
y (t  1)  g 2  y  (t )  v(t )  g 2  y  (t )  r1  u (t )  g1  x  (t );
(1)
here
u(t ), u(t )  [0,1]
and
v (t ), v (t )  [0,1] , implementation of the second-side strategy at the moment of time
- implementation of the first-side strategy at the moment of time
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t,
t;
Automation of Decision Making Support on the Distribution of Financial Resources on the
Elimination of Accidents on Railway Transport
 x, x  0 
x
.
0
,
else


(2)
Let describe the procedure.
The first side (for example, the head of the SCESE, or a DM) at the initial moment of time
t  0 increases (or decreases) his financial resources (FMR) from x0 to g1  x(0). Then
he selects a part of the FMR for the acquisition of material resources that are directed to the
emergency situation elimination. The first side chooses the value u0 in order to determine
the size of u(0)  g1  x(0) .
The second side, at the initial moment of time

t  0 increases (or decreases) his FMR
from y 0 to g2  y(0). Then he selects a part of resources to finance emergency situations
elimination specialists. That is, choose a value v0 in order to determine this value of FMR –
v(0)  g2  y(0) .
The selection of the values u(0)  g1  x(0) and v(0)  g2  y(0) by both sides leads to
additional investments for emergency situations elimination on the railway using reaction
coefficients:
r1  u(0)  g1  x(0) ,
r2  v(0)  g 2  y(0) .
The result is an expression for one-step interaction. Similarly, there is described the
interaction for the moments of time t  1 (see expression (1)).
Let define the gain function for two sides of the interaction:
1, x  0, y  0;

K ( x, y )   1, x  0, y  0;
0, else;

(3)
The interaction ends at the moment of time T .
Due to inconsistency, lack of proper awareness, we can admit that each side can assume
that the other side will act towards it in the “worst” way.
We believe that the first side (SCESE) seeks to maximize the gain function K xT , y T  ,
and the second one (LAES) - to minimize the function K xT , yT .
It is easy to see that in the class of pure strategies [13] there are no optimal strategies. But
*
in the class of mixed strategies there is a value of the game v and for any   0 (where the
icon  means dominance) there are   optimal mixed strategies. They are found using the
dominance method developed for endless antagonistic games [14, 15].
These strategies are atomic probabilistic measures concentrated in a finite amount of
points. Depending on how the initial resources of the sides and the parameters defining the
interaction correlate, there may be situations in which both sides suffer losses. These relations
can be determined if, for example, we consider a dynamic game with a non-fixed interaction
time for description of such an interaction.
Let present the formalization of the game with a fixed interaction time T .
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We denote by P0,1 the set of all probability measures defined on the   algebra of
Borel subsets [0,1].
We denote by T the set 0,1,..., N* , where N *  a natural number.
Let denote by K (  , ) the following value:
*
K ( x(T ), y (T ))dd


,
,
i.е.
K * (  , ) 
K ( x(T ), y (T ))dd


,
.
(4)
The value K (  , ) is a gain function in a mixed expansion of the considered game with
a fixed interaction time.
*
As it is known [14, 15], there is a value
strategies, i.e.
v * of such a game in the class of mixed
v*  sup inf K * (  , )  inf sup K * ( , )

and for each

 0

players have


,
(5)
optimal mixed strategies.
These   optimal mixed strategies are probabilistic measures that are concentrated on a
finite amount of points. These points are located using a special procedure.
These results are the tools for solving the problem with a fixed time of interaction between
the sides involved in ES elimination. The solution is to solve consistently some infinite
antagonistic games with discontinuous gain functions on an individual square [20, 21].
Of a particular interest has the case when T = 1, i.e. players take one step. In this case,
during the interaction there are optimal mixed strategies  , , concentrated on a finite
amount of points. Moreover, at these points the values of the probability measure are the
same, i.e. if there are m of such points, then the values of the probability measure are 1 / m
at these points. For our problem formulation (however, for similar problems) there is a
constructive method for finding these points.
*
*
5. EXPERIMENT
The computational experiment is implemented in the Mathcad environment. Let consider a
few specific cases of the process of FMR selection in order to eliminate the consequences of
an accident or emergency situation on railway transport, see fig.1-3.
We also give the results that illustrate the trajectories of players' financial resources in the
case when their initial financial resources make it possible to find optimal pure strategies of
the players.
We should note that for other initial states, the optimal strategies of the players can be
mixed strategies.
The trajectories corresponding to the optimal pure strategies of the players are shown on
Fig. 1–3.
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Automation of Decision Making Support on the Distribution of Financial Resources on the
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As part of the article, we stopped only on these cases, because they illustrate the most
common situations at the interaction of the sides.
Figure 1. The results of the computational experiment №1
Figure 2. The results of the computational experiment № 2
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Berik Akhmetov, V. Lakhno, V. Malyukov, S. Sarsimbayeva, T. Kartbayev, A. Doszhanova, A. Abuova
Figure 3. The results of the computational experiment № 3
The results of test calculations, as well as other calculations carried out within the
framework of the proposed model, showed that their use in real practical problems gives a
great economic effect.
6. DISCUSSION OF THE EXPERIMENT RESULTS
The figure 1 illustrates the situation when the amount of steps in the interaction is more than
one step and the initial financial resources of the players (both SCESE and LAES) enable
them to have optimal pure strategies. In this case, the first player has the opportunity to
achieve his goal, i.e. to keep his resources at an acceptable level.
The figure 2 corresponds to a situation that is symmetrical to the situation shown on
Figure 3.
The figure 3 describes a situation in which both players maintain a balance in the
interaction over the entire time interval, i.e. maintain their financial resources aimed at the ES
elimination on RWT at an acceptable level.
The proposed model is a process of forecasting the results of the FMR distribution
between the sides (SCESE and LAES) involved in the elimination of the consequences of a
technogenic accident or ES on RWT. The disadvantage of the model is the fact that at this
stage there is no full-fledged software implementation. This circumstance still makes it
difficult to obtain a forecast estimate at choosing strategies for FMR distribution, allocated by
the SCESE for emergency situations elimination.
During the computational experiments, it was established that the proposed model makes
it possible adequately to describe dependent movements by the used functions. This provides
an effective toolkit for participants of emergency situations elimination (not only on railway
transport, but also in general cases) in the context of the FMR distribution. In comparison
with existing models, the proposed solution improves the effectiveness and predictability
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indicators for decision makers about the FMR distribution for elimination the consequences of
an accident or an emergency situation on railway transport on an average by 11–16% [4, 6, 8].
The work is a continuation of our researches in the field of game theory application in
order to solve various applied problems [15–20]
7. CONCLUSIONS
The following main results were obtained in the article:
There was substantiated the necessity of using intelligent computer technologies in order
to automate the process of analysis of the selection of a rational strategy for the distribution of
financial and material resources allocated for the elimination of technogenic accidents or an
emergency situation on railway transport; there was described a mathematical model for a
decision support system for recommendations generation to the situational center for
emergency situation elimination and for liquidators working directly at the accident area or in
the emergency situation area. The proposed model allows to automate the forecast estimates
for various variants of the FMR distribution spent on emergency situation elimination and its
consequences. The model is based on solving an endless antagonistic quality game with
discontinuous gain functions. A distinctive feature of our model is that for determining the
optimal mixed strategies there has been proposed a constructive method for finding them.
This made it possible to develop specific recommendations for determination of the FMR
value, which are sufficient to eliminate the consequences of emergency situations and/or
technogenic accidents on railway transport in practice.
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