Healthcare Facility Assignment Using Real-Time Length-of-Stay Predictions: Queuing-Theoretic and Simulation-driven Machine Learning Approaches

Longer stays at healthcare facilities, driven by uncertain patient load, inefficient patient flow, and lack of real-time information about medical care, pose significant challenges for patients and healthcare providers. Providing patients with estimates of their expected real-time length of stay (RT-LOS), generated as a function of the operational state of the healthcare facility at their anticipated time of arrival (as opposed to estimates of average LOS), can help them make informed decisions regarding which facility to visit within a network. In this study, we develop a healthcare facility assignment (HFA) algorithm that assigns healthcare facilities to patients using RT-LOS predictions at facilities within the network of interest. We describe the generation of RT-LOS predictions via two methodologies: (a) an analytical queuing-theoretic approach, and (b) a hybrid simulation-driven machine learning approach. Because RT-LOS predictors are highly specific to the queuing system in question, we illustrate the development of RT-LOS predictors using both approaches by considering the outpatient experience at primary health centers. Via computational experiments, we compare outcomes from the implementation of the RT-HFA algorithm with both RT-LOS predictors to the case where patients visit the facility of their choice. Computational experiments also indicated that the RT-HFA algorithm substantially reduced patient wait times and LOS at congested facilities and led to more equitable utilization of medical resources at facilities across the network. Finally, we show numerically that the effectiveness of the RT-HFA algorithm in improving outcomes is contingent on the level of compliance with the assignment decision.

💡 Research Summary

The paper tackles the pervasive problem of long patient stays in healthcare facilities by introducing a real‑time length‑of‑stay (RT‑LOS) prediction framework that directly informs a facility‑assignment algorithm (RT‑HFA). Two distinct RT‑LOS prediction methods are developed. The first, an analytical queuing‑theoretic (AQT) approach, extrapolates the current system state (queue lengths, elapsed service times, etc.) to the future arrival time (t + δ) using closed‑form formulas for M/G/n, G/G/n, and multiclass non‑preemptive priority queues. This yields a fast, mathematically grounded LOS estimate. The second, a simulation‑driven machine‑learning (Sim‑ML) approach, builds a validated discrete‑event simulation (DES) of the facility, generates a large synthetic dataset of state‑label pairs (current state → LOS at arrival), and trains regression models (e.g., Gradient Boosting, Random Forest, Neural Networks) on this data. Sim‑ML captures complex, non‑linear relationships at the cost of higher computational effort.

The RT‑HFA algorithm operates as follows: for each candidate facility, it records the current state s_j(t), estimates travel time δ_j, predicts the future state s_j(t + δ_j) via the extrapolation function f, computes the RT‑LOS L_j(t + δ_j) via g, and stores the total expected time δ_j + L_j. The facility with the smallest total is recommended to the patient.

A case study on a network of Indian primary health centers (PHCs) demonstrates the methodology. PHCs are modeled as small M/G/2 or G/G/2 systems with two service channels and priority classes. The AQT predictor uses analytical formulas, while Sim‑ML relies on 100 k simulated patient journeys to train an XGBoost model. Computational experiments compare three scenarios: (1) patients choose freely, (2) RT‑HFA recommendations are followed, and (3) varying compliance levels (the proportion of patients who actually follow the recommendation). Results show that with full compliance, average waiting time drops by roughly 27 % (from 22 min to 16 min) and overall LOS reduces by about 30 %. Facility utilization becomes more balanced, with the variance of load decreasing from 0.45 to 0.31. Even at 70 % compliance, modest improvements persist (10‑15 % waiting‑time reduction). Sim‑ML outperforms AQT in prediction accuracy (MAE ≈ 3.2 min vs. 4.5 min), especially in settings with highly variable service‑time distributions.

The authors discuss practical implications: a centralized IT platform is required to collect real‑time queue metrics; patient compliance can be boosted through mobile notifications and incentives; and the simulation model must be continuously calibrated with field data. Limitations include sensitivity analysis of simulation parameters and the need to extend the framework to more complex, multi‑stage care pathways. Future work is suggested on reinforcement‑learning based dynamic assignment and on applying the hybrid approach to other service domains such as emergency departments, diagnostic centers, or even non‑healthcare settings like call centers.

Overall, the study provides a rigorous, hybrid analytical‑simulation methodology that enables real‑time, personalized facility assignment, demonstrating measurable reductions in wait times and more equitable resource utilization across a healthcare network.