Optimization of the Queuing System Structure in order to Increase the Average Time until the Leaving of the First Impatient Customer at Minimal Cost

This study investigates the Markov queuing system M | M | n | ∞ with impatient customers, where the average time until the leaving of the first impatient customer is distributed exponentially with the specified parameter. The goal of the study is to investigate the described queuing system and solve the problem of two-criteria optimization. During the study of the system functioning, the average time until the first impatient client leaves the queue and the income received during this time will be calculated for a different numbers of channels via simulation model. The correctness of the obtained values will be checked using analytical solution methods. Based on the obtained values of criteria, the problem of two-criteria optimization will be solved in several ways using a program written in Python. The results obtained in this paper can be used for analysis of the effectiveness and optimization of emergency services and other systems with the same key criteria.