Optimal control of queue in the M|G|1|∞ system with possibility of customer admission restriction

Automation and Remote Control. 2015. Vol. 76. No. 3. P. 433–445.

Yu. B. Grishunina

Consideration was given to optimization of the queue control strategy in the MlGl1l queuing system where decision about continuing or stopping admission of customers is made at the service completion instants of each customer in compliance with  the distribution  on the set of decisions depending on the number  of customers remaining in the system. The mean specific income in the stationary mode was used as the efficiency criterion  and the set of permissible strategies coincided with the set of homogeneous randomised Markov strategies. It was proved that if there exists an optimal strategy, then it is degenerate and threshold with one point on control switching, that is, if the number of customers in the system exceeds a certain level, then admission of customers must be stooped or, otherwise, it must be continued.      

Ключевые слова: управляемый полумарковский процесс, система массового обслуживания, оптимальное управление, queuing system, optimal control, controlled semi-Markov process, homogeneous randomized Markov strategy, degenerate threshold strategy, однородная марковская рандомизированная стратегия, вырожденная пороговая стратегия