Optimization of the Functioning of a Single-channel Queuing System in Managing the Duration of Service with Restrictions

This work is devoted to research of controlled models of queuing systems which describe functioning of various technical and economic systems. Research of processes taking place in such systems is often connected with the optimization problems solving, for instance, how to maximize income by changing some structural characteristics of the system. The purpose of this study is to construct an optimal strategy for managing the duration of service with restrictions and to calculate the average income per unit of time for the long-term functioning of the system. The paper considers a single-channel queuing system a recurrent incoming flow, managed duration of service and the finite number of places in the queue, in particular, the cases of one and two places in the line were considered. The theorem of searching the extremum of fractional linear functionality under new conditions was formulated and the correctness of its application for the considered model was proved in the course of the work. The practical part of the work includes a numerical example of using the above-mentioned theorem.