Determination of probabilities of involvement of operational and rescue departments to elimination of emergency events

Размещено на http://www.allbest.ru/

Occupational and Life Safety Department

O.M. Beketov National University of Urban Economy in Kharkiv

Determination of probabilities of involvement of operational and rescue departments to elimination of emergency events

Anatoliy Rogozin cand. tech. sciences, Associate Professor,

Mykhailo Vorozhbiian doctor of tech. sciences, Professor, Occupational and Life Safety Department

Maryna Ivashchenko cand. tech. sciences, Associate Professor, Occupational and Life Safety Department

Summary

The article presents the development of an approach to assessing the probabilities of operational activities of civil defense units. Existing approaches to modeling operational activities do not fully meet the requirements for the accuracy of estimating the parameters of activities at low intensity of emergencies. This fact is explained by the limited data available for analysis. The article considers the case when up to three emergencies can occur with the involvement of three units. 3s a result of the study, the calculated equations were obtained, which allow to estimate the probabilities of finding civil defense units in the process of liquidation of emergencies.

Keywords: probability estimation, response, rescue unit, random process, queuing theory.

Ensuring the security of the population and territories from the implementation of threats of various kinds is one of the main functions of the state. A necessary condition for ensuring the effectiveness of the civil protection function is the adequacy of measures and the number of forces to existing threats on the territory.

The problem of scientific reasoning of the optimal composition of civil defense forces on the territory is complex and requires special research related to the assessment of the territory, their mathematical description, mathematical modeling and mathematical and statistical analysis of aspects of response to destructive events in the territory.

The successful solution of this problem is directly related to the reliability and solidity of information support. From the study of patterns that are objectively inherent in the process of responding to emergencies, and it is necessary to begin to address issues of determining the optimal quantitative indicators of the rapid reaction force. operational civil defense liquidation

For effective organization of civil defense on the territory, it is necessary to properly justify the parameters of civil defense forces on the territory, and for this it is necessary to have a mechanism for assessing the total workload of civil defense forces, their functioning, most of which is random and well described by various probabilistic models [1-6].

With the help of these models it is possible to estimate the probabilities of different parameters of the process of functioning of civil defense forces in the territory, ignore it's unlikely conditions (that very rare events) and justify, thus, quantitative parameters of civil defense forces of a particular territory, characterize the process of occurrence and elimination of emergencies. Thus, from a methodological point of view, the most adequate to the nature and nature of the research problem are methods of systems analysis, mathematical statistics, probability theory and random processes on the basis of which you can find important patterns of emergency response [7-8]. The basic principle of the organization of civil defense forces is as follows [9]: they must be organized in such a way that at any time to any emergency occurred in the territory immediately respond with a set of forces and means adequate to the nature and scale of the event. In the conditions of constant dynamic processes taking place on the territory of administrative formations, it is not possible to find the "absolute optimum" in solving such tasks, but given the appropriate limitations and simplifications of the emergency response process it is possible to approach.

To address the issues of determining the quantitative indicators of civil defense forces at the present stage, we can distinguish two main approaches: regulatory and calculation.

For all the positive aspects of the normative approach to determining the quantitative parameters of operational forces, it does not fully take into account the specifics of the territory in relation to the level of existing hazards and the intensity of their implementation. The calculated approach for individual sections of the territory allows taking into account with a sufficient level of adequacy certain local features of the area in terms of manifestations of threats of different nature, certain indicators of force response to emergencies.

Therefore, the issue of determining ways to determine the probabilistic characteristics of the involvement of rescue units is relevant and timely.

The essence and advantages of the method of mathematical modeling in relation to the tasks of the organization of rapid response forces are discussed in detail in [10, 11]. The works provide an overview of different types of mathematical models for research and organization of rapid response to emergencies in urban areas. The functioning of the civil defense forces is associated with the manifestation of a number of characteristic features:

- the probabilistic nature of the distribution of the need to act as intended on the time axis;

the probabilistic nature of the distribution of the need to act on purpose in space (territory);

the probabilistic nature of the distribution of the need to act on the value with the involvement of different amounts of forces and means.

According to the first of these features, modeling activities are carried out using the theory of queuing.

A detailed review of mathematical models based on the methods of queuing theory is contained in [11 -12]. All models are based on the assumption that call flows are stationary Poisson and the time of employment is described by the indicative distribution law. The experience of using such models in [13-14] confirms the adequacy of their application and the reliability of the results. The disadvantages of using models based on the theory of queuing can be identified as follows:

the possibility of deviation of the real distribution of the flow of calls from stationarity;

deviation of the real distribution of time of involvement of elements of system from the indicative law;

the inability to establish the parameters of the distribution law with sufficient accuracy in the case of low intensity of emergencies.

In [14] a descriptive model of the process of functioning of system elements is presented. The model allows you to calculate the probability and average length of time the system is in any state of event service, as well as the frequency of transition of the system to these states. Also a review of similar developments is given in [15].

The approach of modeling the activities of operational units is based on the theory of queuing has significant limitations due to insurmountable difficulties in assessing the parameters of activities with relatively low intensity of threats of various kinds in the area, namely the inability to accurately assess the flow of emergencies.

The purpose of the article is to obtain the calculation equations for estimating the probabilities of involvement of rescue units in the elimination of emergencies.

Markov random processes are divided into discrete continuous and continuous-discrete random variables. We will consider the random process of occurrence and elimination of emergencies, provided the intensity of the transition to different states, ie the process will be described by differential equations whose coefficients do not depend on time and accordingly in this case we will consider a homogeneous Markov process. Consider the case where up to three emergencies involving up to three units are possible. The graph of states for this case is presented in (Fig. 1).

Given the intensity of the transition from the previous state to the next state with the involvement of n units will be equal to Л-кп, where кп, is the probability of involving n units to eliminate the emergency and the intensity of the transition to the previous state is equal to p. We compose the differential equations of the process of transition from state to state, in the left part of each of the equations we write the derivative of the probability of the i-th state p(t). In the right part - the sum of the products of the probabilities of all states on the intensity of the corresponding flows

Fig. 1. Count the states of occurrence of up to three emergencies with involvement up to three units for their elimination

of events minus the total intensity of all flows that derive the system from this /-th state, multiplied by the probability of this state. Let us supplement the equations thus constructed with the normative condition. Kolmogorov's equations for this case are as follows:

Since the number of possible states was limited when considering the process, the probabilities calculated by equations (2) will differ from the actual values. The adequacy of the obtained ratios was determined on the basis of the estimation of the relative error of the probability p0 relative to the probability of the state when no extraordinary event calculated according to the queuing approach will be eliminated. Figure 2 shows the dependence of the relative error on the change of the parameters of the random process land p.

Fig.2. Dependence of the relative error of the probability of a state when the consequences of any emergency situation are not eliminated on the change of process parameters X and ц.

The relative error in the low intensity range of emergencies does not exceed 2%, so the calculated ratios agree well with the probabilities calculated by the call service approach as a queuing system, which gives grounds to use them to determine the number of units in low risk areas.

Studies of the Markov process, which corresponds to a situation where the occurrence of up to three emergencies involving three units simultaneously, revealed that the calculated ratios of the probability of the system in different states of emergency response adequately describe the operational process, the relative error does not exceed 2 %.

As follows, the proposed approach allows to model the operational activities of civil defense units with a high level of adequacy in conditions of low intensity of calls to units.

References

1. Guo, Q., Shi, K., Jia, Z., Jeffers, Z. (2013). Probabilistic Evaluation of Structural Fire Resistance. Fire Technology. SFPE, 49(3), 793-811.

2. Walker, W. E. (1975). Applying systems analysis to the fire service. Fire Engineering,

3. Rennemo, S. J. (2014). A three-stage stochastic facility routing model for disaster response planning.Journal Transportation Research. Part E, (62), 11 6-135.

4. Gutjahr, W. J. Nolz, P. C. (2015). Multicriteria optimization in humanitarian aid. European Journal of Operational Research. 252(2), 351-366.

5. Coskun, N. Erol, R. (2010). An Optimization Model for Locating and Sizing Emergency Medical Service Stations. Journal of Medical Systems. (34), 43-49.

6. Beraldi, P. A., Bruni, M. E. (2009). Probabilistic model applied to emergency service vehicle location. European journal of Operational Research. 196(1), 323-331.

7. Walker, W. E. (1975). An Analysis of the Deployment of Fire-Fighting Resources in Denver, Colorado. Rand Corporation,

8. Rohozin, A. S. (2014). Analiz likvidatsii nadzvychainykh sytuatsii pryrodnoho ta tekhnohennoho kharakteru na terytorii Kyivskoi, Kharkivskoi, Luhanskoi, Odeskoi oblastei. Proceedings Scientific publication of Kharkiv National University of the Air Force, 3(40), 190-192.

9. Brushlinskogo, N. N. (red.) (1988). Sistemnyj analiz i problemy pozharnoj bezopasnosti narodnogo hozjajstva. Moscow: Stroyizdat.

10. Alehin, E. M. (1997) Metodologicheskie, teoreticheskie i prikladnye aspekty problem proektirovanija protivopozharnyh sluzhb v gorodah. Sat. Proceedings of VNIIPO Ministry of Internal Affairs of the Russian Federation, 29-41.

11. Belov, V. A. (2010) Proektirovanie garnizonov pozharnoj ohrany na osnove tehnologij imitacionnogo modelirovanija (Dysertatsiia kandydata tekhnichnykh nauk). Academy of the State Fire Service EMERCOM of Russia. Moscow, Russia.

12. Grishin, A. F. (1988) Razrabotka rekomendacij po sovershenstvovaniju operativnoj dejatel'nosti pozharnoj ohrany gorodov i naselennyh punktov na osnove primenenija metodov imitacionnogo modelirovanija (Dysertatsiia kandydata tekhnichnykh nauk).

13. Higher School of the Ministry of Internal Affairs of the USSR, Moscow.

14. Chaiken, J. M. (1978) Transfer of emergency service deployment models to operating agences. Institute for Operations Research and the Management Sciences, (7), 719-731.

15. Krasavin, A. V. (2010) Normirovanie resursovpozharnoj ohrany. Moscow: Jeko-Press.

16. Krasavin, A. V. (2005) Normirovanie osnovnyh resursov podrazdelenij municipal'noj pozharno-spasatel'noj sluzhby (Dysertatsiia kandydata tekhnichnykh nauk). Academy of the State Fire Service EMERCOM of Russia, Moscow.

Размещено на Allbest.ru