Queuing System Modeling Based On Change Point Estimation

The phenomenon of patient congestion in hospitals in my country is becoming more and more serious.Outpatient departments are often overcrowded and medical staff are overwhelmed.This phenomenon has severely affected the quality of medical services and the satisfaction of patients with medical services.There are many reasons for congestion in hospitals.For example,it is common that one person goes to see a doctor,while some friends(or relatives)accompany with it.At the same time,the arrival rate of patients has changed significantly with time.The demand also fluctuates accordingly.There usually has been huge fluctuations in the arrival of patients over time.During peak hours,the needs of patients may exceed the service capabilities of medical staff,resulting in insufficient number of doctors and excessive waiting time for patients.During the period when the patient arrival rate is low,the utilization rate of medical staff may be too low,resulting in a waste of medical resources.For patients,delaying too long in the queue may affect the condition of the disease,Therefore,it is necessary to discover changes in the patient’s arrival law in time.The modeling of the queuing system based on change point estimation in this paper mainly includes the following three aspects: 1.Introduce the method of change point estimation.2.Introduce the relationship between the change point estimation method and the queuing system,that is,apply the change point estimation method to the arrival process of the queuing system.3.Introduce how to get the relevant index values of the queuing system.4.Apply the method of change point estimation to specific medical queuing scenarios.In the literature,a common practice for this time-varying queuing system is to divide a day into n time periods of the same length for theoretical research.The idea of this article is to consider whether there is a change point,before this point the data obeys one distribution,after this point the data obeys another distribution,that is,consider applying the method of change point estimation to the arrival process of the queuing system.This goal can be achieved with the help of the method based on the change point model control chart in the field of quality control.The control chart method based on the change-point model can realize online change-point monitoring and obtain the estimated value of the change-point,and can be extended to the situation of multiple change-points.The problem solved by the classic queuing model is a mathematical model under steady-state conditions.When the arrival rate of patients changes,this makes the system non-existent or there is no steady-state for a long period of time.At this time,the classic queuing theory,the model cannot be directly applied to the evaluation of the queuing system,so this paper uses numerical simulation to obtain the waiting time and queue length.Taking the data of the arrival time of patients in a week in a community hospital as an example,we found the changes in the distribution of patient arrivals.After obtaining the result of the change point estimation,if there is a change point,indicators such as the waiting time of the patient are obtained based on the queuing model,so as to accurately describe the arrival process of the patient in a day.