\section{Related Works} \label{related}
The papers \cite{alex, narahari-fair, wangbandit} considered the fair allocation problem in bandits in the stochastic setting. The paper \cite{huang2023queue} considered the scheduling problem in the adversarial setting for stabilizing queues. However, they do not consider the reward maximization problem under the queue stability constraints, which can be trivially solved in our setting by a randomized policy. 