Purpose. The purpose of this work is to develop a model of a geodetic reference network (in the form of a transition graph), which is located on the territory of mining leases and is prone to disruption as a result of impact of man-made factors to improve the reliability of surveying maintenance of open and underground mining. Methodology. To assess the state of geodetic framework using graph theory and stochastic processes the estimation of its reliability has been done. The analytical model of surveyor-geodetic network as a graph of conversions has been developed. The matrix of conditional distribution functions of duration of stay of the geodetic network in different states and matrix of transition probabilities from the previous state to the next has been complied. The average time of duration of stay of geodetic network in a reliable and unreliable state using semi-Markov process has been estimated. Findings. The choice of mathematical model which describes the state of geodetic network in a particular time to the fullest extent possible has been substantiated. The length of stay of geodetic network in each of its possible fixed states has been determined. Originality. The use of graph theory and stochastic processes to create a mathematical model of transitions of surveyor-geodetic network of a reliable state into an unreliable one as a result of displacement of rocks, the earth's surface and geodetic points located on it has been proposed for the first time. The duration of stay of the geodetic network in each of its possible fixed states has been determined. It allows carrying out a complex of works timely to restore geodetic network to ensure reliable surveying mining and experimental studies. Practical value. The creation of a mathematical model of the geodetic network in the form of the transition graph by applying graph theory and semi-Markov process, allows identifying the time of decrease in reliability of geodetic networks as a result of displacement of rocks under the influence of underground workings and its timely restoration up to reliable condition.

 Наукова періодика України 

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