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

Najiya Fatma, Varun Ramamohan

TL;DR

The paper tackles the problem of steering patient flow in healthcare networks by predicting real-time LOS at potential facilities and using these predictions in a centralized assignment policy (RT-HFA). It introduces two RT-LOS prediction paradigms: an analytical queuing-theoretic (AQT) method and a simulation-driven ML (Sim-ML) method, and demonstrates them via a PHC network in India. Through a detailed PHC case study and comprehensive simulations, the authors show that RT-HFA can markedly reduce LOS at congested facilities and promote equitable resource utilization, with effectiveness strongly dependent on patient compliance. The work provides actionable guidance on deployment trade-offs between predictive accuracy, data requirements, and IT integration, and it discusses scalability and validation considerations for real-world networks. Overall, the dual prediction framework offers a practical path to real-time, network-level optimization of outpatient care delivery.

Abstract

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.

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

TL;DR

The paper tackles the problem of steering patient flow in healthcare networks by predicting real-time LOS at potential facilities and using these predictions in a centralized assignment policy (RT-HFA). It introduces two RT-LOS prediction paradigms: an analytical queuing-theoretic (AQT) method and a simulation-driven ML (Sim-ML) method, and demonstrates them via a PHC network in India. Through a detailed PHC case study and comprehensive simulations, the authors show that RT-HFA can markedly reduce LOS at congested facilities and promote equitable resource utilization, with effectiveness strongly dependent on patient compliance. The work provides actionable guidance on deployment trade-offs between predictive accuracy, data requirements, and IT integration, and it discusses scalability and validation considerations for real-world networks. Overall, the dual prediction framework offers a practical path to real-time, network-level optimization of outpatient care delivery.

Abstract

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.
Paper Structure (18 sections, 2 theorems, 26 equations, 5 figures, 6 tables, 3 algorithms)

This paper contains 18 sections, 2 theorems, 26 equations, 5 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Real-time healthcare facility assignment
  4. Real-time length of stay prediction approaches
  5. Real-time Healthcare Facility Assignment: Algorithm and Case Study Overview
  6. The Algorithm
  7. Case Study Overview: Primary Health Centers
  8. Real-time Length of Stay Prediction
  9. Analytical Queuing-theoretic Approach
  10. General AQT Real-time LOS Prediction Approach for Healthcare Facility Assignment
  11. Real-time LOS prediction at the NCD nurse.
  12. Real-time LOS prediction at the doctor.
  13. Real-time LOS prediction at the laboratory PHC subsystem.
  14. Real-Time LOS prediction at the pharmacy.
  15. Sim-ML Real-time LOS Prediction Approach for HFA
  16. ...and 3 more sections

Key Result

Proposition 4.1

$E[L'] = E[\hat{L}] + (\delta\beta)^T \nabla g(\beta)$. Further, $Var(L') = Var(\hat{L}) + 2Var(\epsilon_r)$.

Figures (5)

  • Figure 1: Patient flow at PHC. OP: Outpatients, IP: Inpatients, CBP: Childbirth patients.
  • Figure 2: Sim-ML real-time length of stay predictor development process.
  • Figure 3: Variation in the number of outpatients and estimation of steady-state effecttive average interarrival time post RT-HFA implementation.
  • Figure 4: $\Delta_{net(\rho-doc)}$ and $\Delta_{net(w)}$ at the doctor's queuing subsystem versus patient compliance with the facility recommendation generated by the RT-HFA algorithm.
  • Figure 5: Variation in LOS estimates at PHC1 and PHC2 with 50% and 25% compliance levels with facility assignments.

Theorems & Definitions (5)

  • Proposition 4.1
  • proof
  • Definition 4.2
  • Proposition 4.3
  • proof