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Analyzing Patient Flow Dynamics: An M/M/1 Queue Model with Vacations in Hospital Outpatient Services. A Case Study of the Regional Hospital, Bamenda

Author

Listed:
  • Leo. Tanyam. Encho

    (Department of Mathematics and Computer Science, The University of Bamenda)

  • Pipima Celestine Mofor

    (Department of Mathematics and Statistics, Alex-Ekweme Federal University Ndufu-Alike)

Abstract

Globally, healthcare systems face the pervasive challenge of optimizing patient flow, minimizing wait times, and enhancing service delivery. In this research work, an M/M/1 queueing system is considered with impatient customers and a variant of multiple vacation policy, where the case that customer impatience is due to the servers’ vacation is examined. Whenever a system becomes empty, the server takes a vacation. However, the server is allowed to take a maximum number of vacations, denoted by K vacations, if the system remains empty after the end of a vacation. We derive the probability generating functions of the steady-state probabilities and obtain the closed-form expressions of the system sizes when the server is in different states. In addition, the closed-form expressions for other important performance measures is obtained. Finally, some numerical results are presented. Our result shows that E(L_K) and the mean system size E(L) all decrease with θ for any finite K whereas P_V and P_b neither increase nor decrease with θ when K = 2 and K = 3.

Suggested Citation

  • Leo. Tanyam. Encho & Pipima Celestine Mofor, 2026. "Analyzing Patient Flow Dynamics: An M/M/1 Queue Model with Vacations in Hospital Outpatient Services. A Case Study of the Regional Hospital, Bamenda," International Journal of Research and Innovation in Applied Science, International Journal of Research and Innovation in Applied Science (IJRIAS), vol. 11(1), pages 558-581, January.
    • Handle: RePEc:bjf:journl:v:11:y:2026:i:1:p:558-581
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