Abstract
Queuing theory is used to develop recommendations for constructing queuing systems efficiently, organizing the associated operations and functionalities, and regulating request flows for optimal performance. This paper presents a study of the income functional for two specific cases of controlled queuing systems: the M/G*/1/N* system for a controlled service duration and number of waiting spaces, and the G*/M/n/m queuing system with a controlled arrival flow. The construction of a controlled semi-Markov process and the construction of an income functional on its trajectories were used as the basis for this study. The task is to find the optimal control strategy in the given queuing systems. An algorithm for finding optimal strategies applicable to similar queuing systems to increase their functioning efficiency when controlling the system’s main characteristics was developed for both systems.
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