MODELING AND ANALYSIS OF OUTPATIENT FLOW DYNAMICS: A QUEUEING THEORY AND MACHINE LEARNING APPROACH IN A NIGERIAN HOSPITAL
DOI:
https://doi.org/10.60787/jnamp.vol72no.663Keywords:
Healthcare operations, Queueing theory, Machine Learning, predictive modeling, Outpatient flow, Resource optimization, Hybrid analyticsAbstract
Prolonged waiting times in hospital outpatient departments (OPDs) significantly impede healthcare delivery in resource-constrained settings. This study critically evaluates the applicability of the M/M/S queueing model to a Nigerian hospital OPD, and demonstrates the necessity of a hybrid framework integrating queueing theory with machine learning (ML) for accurate analysis and forecasting. Primary data on patient arrivals and service times were collected over a two-week period during peak hours (9:00 a.m.–2:00 p.m.). The system was modeled as an M/M/S queue, revealing critical overload (ρ = 1.16). Kolmogorov–Smirnov tests rejected the exponential distribution assumptions for inter-arrival and service times, invalidating the M/M/S model for precise prediction. Subsequently, a Random Forest regressor (R² = 0.89) and Support Vector Machine classifier (accuracy = 86%) were developed to model complex arrival patterns and demand levels. We propose a hybrid framework that uses queueing theory for systemic diagnosis and ML for predictive modeling. This approach provides a robust, generalizable methodology for dynamic staffing and resource optimization in realistic healthcare environments.
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References
Hall, R. W. (1999). The challenge of designing and managing patient-centered care. Journal
of Healthcare Management, 44(1), 45–58.
Nsude, F. I., Elem, U. O., & Bassey, U. (2017). Analysis of multiple queue server system. International Journal of Scientific & Engineering Research, 8(1), 1700–1709.
Taha, H. A. (2007). Operations research: An introduction (8th ed.). Prentice Hall.
Vanberkel, P. T., Boucherie, R. J., Hans, E. W., Hurink, J. L., & Litvak, N. (2009). Efficiency evaluation for pooling resources in health care. 1-17. Paper presented at 15th Anniversary Annual CTIT Symposium 2009, Enschede, Netherlands.3. https://doi.org/10.1016/j.orhc.2020.100273
Green, L. V., Soares, J., Giglio, J. F., & Green, R. A. (2006). Using queueing theory to increase the effectiveness of emergency department provider staffing. Academic Emergency Medicine,
(1), 61–68.
Fomundam, S., & Herrmann, J. W. (2007). A survey of queuing theory applications in healthcare (ISR Technical Report 2007-24).
University of Maryland. Okereke, C. N., Eze, J. C., & Nwachukwu, U. L. (2022). Challenges of applying quantitative models in Nigerian health sector planning. African Journal of Operational Research, 3(1),
–59.
Hassan, A., Mensah, J., & Adeyemi, O. (2023). Integrating machine learning with queueing theory for hospital service optimization. BMC Health Services Research, 23(1), 1124.
Jared, R., Zhen, Z., Jingshan, L., & Shu-yin, Y. (2009). Design and analysis of a healthcare clinic for homeless people using simulations. International Journal of Health Care Quality Assurance, 23(6), 607–620.
Hall, R. W., Belson, D., Murali, P., & Dessouky, M. (2006). Modeling patient flows through the healthcare system. In R. W. Hall (Ed.), Patient flow: Reducing delay in healthcare delivery (pp. 1–42). Springer.
Mmahi, E. C. (2025). Optimization of multiphase queuing models for antenatal care units in Nigerian public hospitals. EKETE International Journal of Advanced Research, 3(3), 1–15.
Siddharthan, K., Jones, W. J., & Johnson, J. A. (1996). A priority queuing model to reduce waiting times in emergency care. International Journal of Health Care Quality Assurance, 9(5), 10–16.
Obamiro, J. K. (2010). Queuing theory and patient satisfaction: An overview of terminology and application in ante-natal care unit. Bulletin of Petroleum Gas University of Ploiesti, 62(1),1–10.
Gross, D., Shortle, J. F., Thompson, J. M., & Harris, C. M. (2008). Fundamentals of queueing theory (4th ed.). Wiley. Green, L. V. (2019). Queueing analysis in healthcare. In R. Hall (Ed.), Handbook of healthcare system scheduling (pp. 23–45). Springer.
Zhang, F., Chen, H., & Li, Y. (2020). Modeling patient flow and service efficiency using stochastic and hybrid methods. Operations Research for Health Care, 27(1), 100275.
Akçalı, E., & Green, L. V. (2021). Queueing models in healthcare systems. European Journal of Operational Research, 289(2), 479–493.
Efrosinin, D., Vishnevsky, V., Stepnova, N., & Sztrik, J. (2025). Use cases of Machine Learning in Queuing Theory Based on GI/G/K System. Mathematics, 13(5), 776.
Hassan, A., Mensah, J., & Adeyemi, O. (2023). Integrating machine learning with queueing theory for hospital service optimization. BMC Health Services Research, 23(1), 1124.
Asiedu, E., Osei, P., & Ameyaw, S. (2020). Application of queueing theory to outpatient service delivery: Evidence from a developing country. Operations Research in Health Care, 26, 100265.
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