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

Physics-Informed Multi-Agent Coordination is a framework that embeds Baskett-Chandy-Muntz-Palacios (BCMP) queueing networks as structural physical priors within a decentralized multi-agent reinforcement learning (MARL) architecture to optimize hospital patient flow. This method addresses the degradation of classical stationary BCMP models, which fail under real-world state-dependent dynamics where finite departmental capacities cause blocking and non-linear congestion cascades.

The framework formulates hospital resource management as a Decentralized Partially Observable Markov Decision Process (Dec-POMDP), allowing autonomous departmental agents to cooperatively negotiate patient routing and dynamic service scaling. Agents exchange localized action fingerprints to mitigate environmental non-stationarity without excessive communication overhead, optimizing a spatially decomposed reward structure.

Empirical evaluations using MIMIC-IV data demonstrate that this cooperative approach substantially reduces cumulative system delay compared to static Markovian approximations, heuristic dispatchers, and independent multi-agent baselines. Specifically, the cooperative MARL policy achieved an approximate 56-fold reduction in cumulative patient delay (2081.2 hours) compared to static baselines (117,478.1 hours), while effectively eliminating queue accumulation in General Medicine and minimizing bottlenecks in Emergency and Med/Surg units.

The material examines hospital patient flow through the lens of stochastic network modeling and argues that classical queueing-network abstractions, especially stationary BCMP networks, become unreliable once patient dynamics are state-dependent. In standard BCMP models, arrival rates, service times, and routing probabilities are typically assumed to be stationary and independent of the system state, yielding tractable product-form solutions. The paper’s central insight is that this convenience comes at a cost: real hospital flows often depend on patient acuity, bed occupancy, staffing availability, escalation risk, and cross-departmental contention, so a model that treats these effects as fixed parameters can misrepresent congestion, delays, and throughput.

Its key contribution is to propose an alternative coordination framework based on physics-informed multi-agent methods. Rather than relying on a single globally stationary queueing model, the approach distributes coordination across agents representing departments, beds, teams, or patient classes, with decisions guided by flow-conservation principles and state-dependent dynamics. The “physics-informed” element suggests that the coordination mechanism is constrained by structural invariants of the patient flow system—such as work-in-progress balance, capacity limits, and routing continuity—so that local agent behavior remains coherent with the global dynamics of the hospital. In effect, the paper positions multi-agent coordination as a way to recover robustness and realism where stationary queueing theory degrades.

This matters because hospital patient flow is a high-stakes, high-uncertainty operational problem where poor models can lead to inefficient bed use, delayed care, and unstable throughput. By moving beyond stationary BCMP assumptions, the work bridges operations research, stochastic control, and multi-agent systems, offering a more scalable and adaptable foundation for dynamic resource coordination in healthcare. For a technically literate audience, the value lies less in a single algorithmic novelty than in the broader argument: that realistic hospital optimization requires models that explicitly account for state-dependent dynamics, and that multi-agent coordination can be a principled way to do so.