MATHEMATICAL APPARATUS FOR OPTIMIZING THE FUNCTIONING OF THE CENTERS FOR VERIFICATION OF MEASURING INSTRUMENTS OF EMERCOM OF RUSSIA IN CASE OF NON-STATIONARY FLOWS OF APPLICATIONS

The paper presents a mathematical apparatus for optimizing the functioning of the Federal State Institution «Center for Material, Technical and Metrological Support of the Ministry of EMERCOM of Russia» for verifying radiation measuring instruments and nuclear constants EMERCOM of Russia in conditions of pronounced instability of the input streams of applications. It is shown that seasonal fluctuations in the intensity of instrument intake lead to a sharp increase in waiting time in the queue and a significant increase in the period of absence of measuring instruments in operation, which negatively affects both the efficiency of emergency rescue operations and the continuity of radiation monitoring. To formalize the functioning of the verification centers, a multi-channel queuing model of the G/G/C type is used, which makes it possible to quantify the impact of the load factor on queue dynamics. The model takes into account the structure of the input stream, differences in the types of devices in terms of the complexity of verification, transport delays and the limited capacity of the verification facilities. The damage caused by the lack of instruments is represented by two independent components: exponential, which characterizes an increase in risk during delays in emergency rescue operations, and linear, reflecting a decrease in the effectiveness of radiation monitoring. Based on the obtained dependencies, the task of minimizing cumulative losses is formulated, including damage from the lack of measuring instruments and the cost of transferring some of the instruments to external commercial organizations. The optimal value of the share of the redistribution of applications has been determined, ensuring the minimization of total losses, while ensuring the sustainability of the work of the Federal State Institution «Center for Logistics and Metrological Support of EMERCOM of Russia». The proposed mathematical apparatus can be used to plan verification work, calculate the need for commercial services, assess the risks of reducing metrological readiness and increasing the stability of the radiation safety system of EMERCOM of Russia.