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

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.