Arrival Control in Quasi-Reversible Queueing Systems: Optimization and Reinforcement Learning
This work addresses queueing system optimization for network management, but it appears incremental as it generalizes existing concepts like balanced arrival rates to a broader class.
The paper tackles optimizing arrival rates in quasi-reversible queueing systems by introducing balanced arrival control policies that preserve quasi-reversibility, and applies these to admission control using optimization and reinforcement learning frameworks.
In this paper, we introduce a versatile scheme for optimizing the arrival rates of quasi-reversible queueing systems. We first propose an alternative definition of quasi-reversibility that encompasses reversibility and highlights the importance of the definition of customer classes. In a second time, we introduce balanced arrival control policies, which generalize the notion of balanced arrival rates introduced in the context of Whittle networks, to the much broader class of quasi-reversible queueing systems. We prove that supplementing a quasi-reversible queueing system with a balanced arrival-control policy preserves the quasi-reversibility, and we specify the form of the stationary measures. We revisit two canonical examples of quasi-reversible queueing systems, Whittle networks and order-independent queues. Lastly, we focus on the problem of admission control and leverage our results in the frameworks of optimization and reinforcement learning.