Application Research Of Queuing Theory Model In Medical Service System

Objectives: To study the application scope and condition of theoretical knowledge and models of queuing theory in medical service system, seeking for convenient and practical parameter estimation software, through the analysis of queuing system model application example in hospital, deeply research queuing theory model application in medical service system.Methods: The theoretical knowledge of queuing theory used in medical service system was deeply researched. The convenient and practical parameter estimation software was collected. Through survey of outpatient departments and check departments of three A hospital in Wuhan, four models were selected, including M/M/c model applied in hospital emergency room queuing system, M/D/c model applied in the dynamic ECG examination queuing system in a hospital, G/M/c model applied in a dental's center in a hospital, and G/Ek/c model applied in a eye specialist out-patient department. This paper studied application of the four models, through data collection, model fitting, application software for parameter estimation, got commonly used fit index of queuing theory for the evaluation of the current queue status and projections for the hospital management, and provide some scientific suggestion for improving medical service efficiency and optimizing medical resource.Results: (1) In M/M/c model application, according to the emergency medicine department reached the current average rate of 9(patients / hour) of the case, when there are 4 doctors, the hospital emergency medical system utilization is 93.75%, the queue average of 16.73 people per hour, people line up the number of 12.98 per hour, the average waiting time for patients was 1.44 hours. It showed that the congestion was serious. Assumed to increase one doctor, system utilization was 75.00%, 5.14 persons per hour in the queue, the queue number of 139 persons per hour, the average waiting time for patients was 0.15 hours, congestion has been greatly improved. So we proposed the hospital increase one doctors in emergency medicine department.(2)In M/D/c model application, according to the hospital dynamic ECG examination room reached the current average rate of 12.6 (patients / day) of the case, and the hospital had 15 dynamic ECG equipments, the system was busy 94.5% of the time, the probability of new patients waiting was average of 0.74, and an average of 6.7 patients per day were waiting in the system, the average waiting time was 3.8 hours. Forecast to 18 units, the probability of patients waiting was only 0.21, just 0.5 people on average captain, waiting time is less than half an hour, basically solved the case of queue congestion. So we proposed the hospital on the basis of 15 equipments increase 3 units.(3)In G/M/c model application, in view of currently available 10 oral doctors, the system service utilization was 0.96, new patient waiting the average probability was 0.85, and an average of 19.5 patients per hour in the system waiting in the queue, the average waiting time was 2.04 hours. Assuming add two doctors, the system busy probability was 80%, the average waiting time was 0.19 hours, new patient average waiting probability was 0.35, average queue length is 3.4 patients, 6.5 patients were in busy time. It was able to solve the congestion of queuing situation. So we proposed the hospital increase two dentists.(4)In G/Ek/c model application, the average arrival rate of patients was 4.88 (patients / hour), when there are three experts, the out-patient eye specialist department appeared to be quite busy, the system utilization rate was 98.84%, 19.96 people per hour in the queue, the number of people queuing was16.99 per hour, the average waiting time for patients was 3.54 hours, and more than 10 people in the queue with probability of 0.6868. Assumed to increase one expert, the system utilization rate was 82.50%, 4.14 persons per hour in the queue, the average waiting time for patients was 0.17 hours, and 10 people in the queue reduced the probability of 0.03. The effect of increasing an expert is obvious and congestion has been greatly improved. So we proposed the hospital increase one expert in out-patient eye specialist department. The four queuing theory model fitted well calculated to make assessment and prediction, draw a scientific reference, to provide data for decision support.Conclusion: In medical service system, using methods and models of queuing theory, combined with hospital data, through the model fitting, the proper appropriate queuing model are able to be established. Using the facilitated queuing theory software, according to the results of parameter estimation, and through the evaluation and forecast on the configuration of personnel or equipments, under certain circumstances, it can help hospitals optimize the allocation of resources, improve service efficiency and provide scientific suggestion for the realization of the full use of the limited resources. Because of the difficulty of model fitting, there are still some limitations for application.