2013 HiMCM B题特等奖学生论文下载3956

2013 HiMCM B题特等奖学生论文下载3956

 

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论文摘要如下：

Summary

 

Queueing system is a common model in our life. This time, our goal is to build a mathematical model of a 150-people queueing system which meets the manager’s requirement of an average queue length less than 2 people and an average waiting time less than 2 minutes to improve customer satisfactory.

 

To analyze this queueing system, we put forward two models which can verify each other, they are: the mathematical model and the simulation model. In the mathematical model we use the knowledge of probability theory, hoping to figure out a recursion formula about the probability of the state of queue at a certain time. In order to reach this goal, we perfectly described the state of queue at a certain time by defining several variables. Using this model, we can figure out the two important parameters, which are the average length of queue and the average waiting time.

 

Then we put forward a simulation model. In the given situation, we put forward an algorithm which can simulate and measure the whole process of how the 150 customers come and leave. Using Monte Carlo method, we simulated the process for many times and then got the average length of queue as well as the average waiting time.

 

After comparison, the average queue length and waiting time got from the two models coincided with each other perfectly, the average waiting time is about 4.9 minutes while the average queue length is about 2.4 people. Since the simulation model calculated faster, we decided to take it as the only used analyzing model in the following discussions.

 

Results above showed that the current situation couldn’t meet the manager’s requirement, so we put forward several solutions from different perspectives to meet the manager’s requirement and improve customers’ satisfaction, such as improving the service efficiency through training to change the probability distribution of service time; establishing online bank to lower the everyday customer flow to increase time between arrivals; we can also establish a new service window. For each solution, we discussed the minimal change to meet our goal.

 

At last, we gathered all our model results, and take several reasonable ones of them as the suggestion to the manager, in which way he can choose one according to the actual condition of his bank.

 

2013 HiMCM特等奖论文完整版 下载链接