Optimal patient routing policies at diagnosis-stage in Outpatient Department non-preemptive queues

The diagnosis-stage is always the bottleneck stage for the normal arriving patient flow and the referral patient flow influx in Outpatient Department (OD) in Chinese hospital. And the referral patient has high-priority than the normal arriving patient in general. How to minimize the referral patients mean waiting time and meanwhile keeping the normal patients queue stable? Around the goal a general two types of patient flow with non-preemptive and homogeneous server queueing model is established. An optimal patients routing policies named admissible policy is proposed and the main result formulas are developed. Some analysis around the result is made to verify the validity of the admissible policy. Based on result analysis a new question about server fairness workload is discovered in future research.