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arXiv · 2509.24541

Markov Decision Processing Networks

Sanidhay Bhambay·Thirupathaiah Vasantam·Neil Walton
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Abstract

We introduce Markov Decision Processing Networks (MDPNs) as a multiclass queueing network model where service is a controlled, finite-state Markov process. The model exhibits a decision-dependent service process where actions taken influence future service availability. Viewed as a two-sided queueing model, this captures settings such as assemble-to-order systems, ride-hailing platforms, cross-skilled call centers, and quantum switches. We first characterize the capacity region of MDPNs. Unlike classical switched networks, the MDPN capacity region depends on the long-run mix of service states induced by the control of the underlying service process. We show, via a counterexample, that MaxWeight is not throughput-optimal in this class, demonstrating the distinction between MDPNs and classical queueing models. To bridge this gap, we design a weighted average reward policy, a multiobjective MDP that leverages a two-timescale separation at the fluid scale. We prove throughput-optimality of the resulting policy. The techniques yield a clear capacity region description and apply to a broad family of two-sided matching systems.

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Sanidhay Bhambay, Thirupathaiah Vasantam, Neil Walton. 2025-09-29. Markov Decision Processing Networks. https://arxiv.org/abs/2509.24541

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