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

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.