Abstract:
This study presents a mathematical model capable of evaluating non-stationary operating modes of medical information-measurement systems in order to improve their efficiency. Such systems play a critical role in medicine and are used for forecasting and assessing patient conditions in life-threatening situations. The mathematical model introduced in this work is a multichannel queuing system with impatient requests in a transient regime, along with its performance characteristics. This type of model appropriately describes real-time medical information systems not only during normal operation but also under conditions of reboot, failure, or equipment malfunction. To analyze the transient regime of the multichannel queuing system with impatient requests, a system of Kolmogorov differential equations is used, along with a solution based on the probability transition matrix method. The study derives expressions for determining the average number of requests in the buffer, the probability of request servicing, the absolute and relative throughput of the system, and the transient time. The paper presents the results of a transient regime analysis for an M/M/2/4 system with impatient requests, including numerical calculations for various service rates and abandonment rates of impatient requests from the queue.
Keywords:queuing systems, transient behavior, service probability, probability transformation matrix, throughput, non-stationary states.
