Modeling the communication network to control the action fire units to extinguish fires of various complexity

Introduction. The organization of radio communication at the fire, as an important part of the fire units operating management, should be given a considerable attention. The effectiveness of fire units operating management depends largely on thesteady of the radio network operation, in which, depending on the complexity of the situation, can work different officials who control the process of extinguishing the fire.

Methods. Modelling of radio network operation is based on Queuing theory methods. A list of n States in which the communication network and the corresponding transition graph can is compiled. Taking into account the generally accepted assumptions on the basis of the transition graph, a system of n differential equations connecting the probabilities of States and the intensity of the transition to these States is compiled. The stationary case is considered. Based upon the obtained solutions the efficiency of the radio network is estimated.

Results. The article presents three variants for which the possible States are described, graphs are constructed and systems of equations are composed. In the first variant, three officials interact inside the radio network, in the second, four officials interact. In the third variant the option of interaction between four fire units operating management with other hierarchy of management is considered. In the first two cases, analytical solutions for the States probabilities are obtained, for the third case, a solution using numerical methods is proposed. For each case, the critical States affecting the control stability are determined. The obtained solutions are followed by examples.

Conclusion. The possibility of modeling the radio communication network at the fire, as an important element of controlling of fire departments operating is demonstrated. Three variants of interaction between officials with use of a radio communication network are given. The mathematical models developed for the under consideration cases allow to estimate the probably characteristics of the radio network functioning. It allows us to assess the possibility of the probably of critical modes appearance that affect the effectiveness of the fire units operating management and the success his implementation.

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