Queuing Theory And Its Application

There are many people in our country. The problem of the difficulty of seeing a doctor often appears.When we go to the hospital,We often encounter the problem that we need to take a long time to wait in line.To some extent, it delays the patient’s condition.It also brings a serious impact on the hospi-tal. So no matter for people or for the hospital,solving the problem of queuing, improving the operational efficiency of the medical and health field is of great practical significance.There was a paper that pointed out that we should set up the number of the doctors according to different time periods in a day.But in real life,the doctors of the hospital can not frequently replaced.The possibility of the im-plementation of the plan is little. So in this paper, We strive to close to the reality, and determine the optimal number of doctors in case the number of doctors are fixed.A hospital pediatric outpatient data as the research object in this pa-per.We separate the data of the morning and the afternoon,because the hospi-tal have a lunch break at noon and doctors don’t work in the lunch break.Based on the queuing theory, We determine the optimal number of pediatric doctor to achieve the maximum objective function values,under the condition of consid-ering the degree of patient waiting and the doctor’s working intensity.Among them, the objective function is the hospital’s net income.We use the total wait-ing time of all patients in a day,to describe the degree of patient waiting.We adopt the number of patients that an average of a doctor accepts in one day to depict the doctor’s working intensity.We through the use of Matlab software and SPSS software,we have ob- tained some results.We know that the patient’s arrival distribution is the beta distribution.The doctor’s service distribution is the lognormal distribution.And the distribution of the total number of patients is also the lognormal distri-bution.The parameters of the above distribution in the morning and in the afternoon is not the same.Because of the queuing system is more complicat-ed,so we adopt stochastic simulation method.We use the ideas of monte carlo simulation,with the help of Matlab software,and use the distributed parameter that have been obtained,to simulate according to the established model.Then we get some results,including the average intensity of the doctor’s work and the degree of patient waiting and net income of the hospital in one day,in the case of different number of doctors.Finally the results are compared and analyzed.We can determine the optimal number of doctors.The next step,We change the parameters of the patient’s arrival distribu-tion to observe the influence of the characteristics of the patient’s arrival on the queuing system.In the end,We get the value in the critical parameters of the congestion phenomenon.The hospital can use this parameter as a reference.If it is higher than this value,so the hospital don’t have to worry about conges-tion;on the contrary,the hospital needs to take measures,on the one hand,the hospital use the guide for peak and tell people to avoid concentration.On the other hand,the hospital need to arrange more doctors in the first accepts the time period to ease the congestion phenomenon.