Abstract: By applying mathematical knowledge like the queuing theory and the optimization method，this paper makes a thorough analysis of the problem（i.e.determining the optimal number of tollbooths to deploy in a barrier-toll plaza），and construct mathematical models taking y=k（t） （y stands for motorists’ satisfaction） as their objective function.The models are as follows：Firstly，M（p/n/1），here p and n stand for the number of travel lanes and that of passages respectively and each passage has only one tollbooth.Second，M（p/n/2） （means each passage with two tollbooths）.The comparison is made between these two methods by examining the time spent in passing the tollbooths，and get the average delays between M（p/n/1） and M（p/n/2） while different transit capacities are given.Finally detailed information is considered about the general conditions of highways and tollbooths and the possible direction is proposed，in which the model can be further developed，and thus can be employed in much wider fields.

Key words: traffic flow, toll plaza, queuing theory, customer satisfaction, negative index distribution, expected value

摘要： 利用排队论、最优化理论等方法对问题进行了较为全面的分析，在此分析的基础上以司机满意度y＝f（t）为目标函数分别建立了p条车道，n条通道，一条通道上一个收费亭的数学模型M（p，n，1）和一条通道上两个收费亭的数学模型M（p，n，2），通过对建立的模型进行对比给出不同车流量的情况下，一道一亭和一道两亭的平均延误时间。最后综合考虑了高速公路和收费站的基本情况，给出了模型进一步改进的方向，从而进一步扩大了模型的应用范围。

关键词: 交通流, 收费广场, 排队论, 顾客满意度, 负指数函数, 期望值