# Discrete Markov model of information and communication processes for crowd formation

## Authors

• Valentyn Petryk Institute of special communications and information protection of National technical university of Ukraine ”Igor Sikorsky Kyiv polytechnic institute”, Kyiv,
• Yevhen Horondei Institute of special communications and information protection of National technical university of Ukraine ”Igor Sikorsky Kyiv polytechnic institute”, Kyiv,

## Keywords:

crowd, modeling, software, information and communication processes, information and psychological influence, random variable, characteristics of the random variable, mathematical model

## Abstract

The discrete Markov model of information and communication processes that take place in the crowd during its formation is considered. The context of the model description is based on the use of probabilistic characteristics and Markov chains. The use of Markov chains in the context of the study of crowd formation is due to the need to determine the possibility of the crowd functioning in a given state, including the possibility of the process of mutual agreement of probabilistic random variables. Thus, the purpose of this model is to analyze the information and communication processes in the formation of the crowd, because the course of processes into the crowd directly depends on the state in which the crowd is represented and the values of random variables. This allows you to identify and predict the possible course of events in the crowd during its formation. In this case, the whole process of crowd formation can be divided into a certain set of states in which the crowd passes under the influence of external factors. Using the formed states, random sizes of the process of formation of the crowd are defined. This makes it possible to construct a random variable distribution function based on the laws of probability theory, which makes it possible to determine with a given accuracy what is the probability of realization of a certain random variation of the studied transient process. To determine the possibility of functioning of the transient process, the average value of a random variable that realizes the mathematical expectation is calculated. To determine the scattering index of the value of the mathematical expectation, the value of the variance is calculated. Since the process in the course of its implementation can be performed partially, fully, or not performed at all, the standard deviation is calculated, which shows how much on average the specific values of the random variable deviate from their mean value. Thus, the discrete Markov model of information and communication processes for crowd formation allows developing an algorithm that can determine the type of crowd, the possibility of a certain transition process, and the representation of crowd objects in space in the form of clusters. The peculiarity of this model is that the results of the obtained values are processed with a given accuracy.

## Author Biographies

### Valentyn Petryk, Institute of special communications and information protection of National technical university of Ukraine ”Igor Sikorsky Kyiv polytechnic institute”, Kyiv,

candidate of state-owned management,
associate professor, associate professor
at the management and tactical and

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2020-07-09

## How to Cite

Petryk, V., & Horondei, Y. (2020). Discrete Markov model of information and communication processes for crowd formation. Information Technology and Security, 8(1), 81–91. https://doi.org/10.20535/2411-1031.2020.8.1.218008

## Section

MATHEMATICAL AND COMPUTER MODELING