Mathematical Model for Assessing the Performance Characteristics of Medical Information and Measuring Systems

The work is devoted to the development of a mathematical model for the evaluation of non-stationary performance characteristics of medical information-measuring systems used in medicine to assess the condition of patients in critical health and life situations. The model is a unilinear mass service system with a finite queue, Poisson input flow and impatient requests, adequately describing the functioning of real-time medical systems including under conditions of equipment malfunctions and failures. The paper presents a system of Kolmogorov differential equations describing the mass service system under study, as well as its solution based on the method of probability transformation matrix. Expressions for finding the probabilities of the system states at an arbitrary moment of time are obtained, as well as non-stationary characteristics of the system performance, such as loss probability, throughput, and transient time. The results of numerical calculations are presented for a system with a buffer size equal to two packets at different ratios of the intensity of leaving impatient requests from the queue and service intensity.