Physics-Informed Multi-Agent Coordination for Hospital Patient Flow Optimization

Guoqing Zhang, Rafik Hadfi, Takayuki Ito

Efficient patient flow coordination across autonomous hospital departments is critical for mitigating overcrowding and balancing resource utilization. While classical queueing theory, specifically open Baskett--Chandy--Muntz--Palacios (BCMP) networks, provides an interpretable mathematical topology for healthcare operations, analytical models rely on stationary assumptions and fixed routing matrices that degrade under state-dependent real-world dynamics. Conversely, centralized reinforcement learning approaches struggle to accommodate the decentralized structure of hospital governance, where individual clinical departments function with localized observations, heterogeneous resources, and divergent operational objectives. In this paper, we present a Multi-Agent Systems (MAS) framework titled \emph{Physics-Informed Multi-Agent Coordination}, which embeds empirically calibrated BCMP queueing topologies as physical priors within a decentralized multi-agent reinforcement learning architecture. Formulated as a Decentralized Partially Observable Markov Decision Process (Dec-POMDP) under coupled resource constraints, our method enables autonomous departmental agents to cooperatively…