Two-criteria Optimization of the Quantity of Channels in the Markov Queuing System

In this paper, we study a queuing system of the type M|M|n|N with a common queue. The aim of the work is to find the optimal number of service channels based on two indicators of the system’s performance: the average time to the first long idle and the average revenue to the first long idle (long idle is defined as an idle of a certain duration). The above indicators are calculated using the results of the theory of absorbing Markov chains. In addition, we consider a method for finding the average income before the first long idle using integral equations. To solve assigned task, we use four methods for solving multi-criteria problems: method of the main (leading) criterion, method of consecutive concessions, the ideal point method and the criteria convolution method. A comparative analysis of the results obtained is carried out. All necessary calculations are presented and justified, as well as algorithms for solving this problem are implemented in Python.