Proof of the conjecture on Markovian queues with Poisson control

초록

This study considers Markovian queues with different service speeds, where the server speed can only be changed at control instants assumed to follow a Poisson process. N & uacute;& ntilde;ez-Queija et al. (Queueing Syst 100:233-235, 2022, Indag Math 34:990-1013, 2023) formulated a conjecture on the asymptotics of the stationary distribution for the scaled process of queue length and server speed as the control rate approaches 0. We completely resolve this conjecture by rigorously analyzing an intuitive explanation of the conjectured result. Furthermore, we extend this result to a renewal control model.

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