Minimal cost service rate in priority queuing models for emergency cases in hospitals

Performance measures and waiting time cost for higher priority patients with severe cases over lower priority patients with stable cases using preemptive priority queuing model were obtained. Also, a total expected waiting time cost per unit time for service and the expected service cost per unit time for priority queuing models: M/M/2: ∞/NPP and M/M/2: ∞/PP were respectively formulated and optimized to obtain optimum cost service rate that minimizes the total cost. The results were applied to obtain optimum service rate that minimizes the total cost of providing and waiting for service at the emergency consulting unit of hospital.