摘 要
如今，随着人们的生活节奏逐渐加快，高速公路上车辆的不断增多，高速公路收费亭数量的最佳设计方案在缩短司机的等待时间、减轻交通拥塞状况以及赢得司机满意度等方面起着举足轻重的作用。本文主要针对这1实际情况建立数学模型，来解决相关的问题。
根据实际情况，本文给出了1个合理且可行的随机模型。在模型中，本文首先根据收集的数据计算出其收费口在单位时间里到达的车辆数和每1辆车的服务时间所服从的分布，然后把整个处理过程划分成4个主要部分：输入过程，排队规则，服务方式，输出过程。既然到达车辆的数量服从泊松分布，服务时间服从负指数分布，在等待服务的车辆遵循先来先服务的规则下，那么，本文通过M/M/K ,M/M/1及相关其他方法计算出车辆在收费站等待的概率以及包括等待时间和服务时间的总时间期望值，在保证最短等待时间的条件下得到高速公路收费亭数量和服务人员的服务速率的最佳设计方案。
最后，本文提出了1些设置高速公路收费口的收费亭数量和提高服务人员服务速率的建议，比如采用更先进的服务设备来缩短服务时间等。
关键词： 拟合检验法；负指数分布；泊松分布；[M/M/1]：[ /FCFS]模型；[M/M/4]：[ /FCFS]模型
Abstract
Nowadays , along with the accelerating of the people’s life rhythm as well as the increasing of vehicle on the highway , the best design program of the number of the highway fare charging reception plays an important part in shorting drivers’ waiting time , lighting traffic crowed and wining the drivers’ satisfaction . This essay majoring aimed at the practical circumstances of establishing mathematics model to solve the related problems .
According to the actual situation , this essay have produced a reasonable and feasible probabilistic random model . As for the model , First , according to the collecting data , this essay calculate the distribution of the quantity of vehicles arriving in the unite time and the time of each vehicle’s service time , Then recognize the whole disposing process as four major parts : the import course ,lining up rules , the service way , the export course . since the number of the arrived automatics should comply with the Poisson’s distribution and the service time with Negative exponent , and with the obedience of the waiting-for-service automatics to the rule of first come first serviced . in that case , due to M/M/K , M/M/1 model as well as another methods . this essay can infer the rate of vehicle for waiting , the total expecting time of waiting time and service time . Ensuring the shortest time for waiting , we need to mare the best design program for the number of highway fare charging reception and service ration of workman .
At last , this essay offer some suggestion on improving the service ration of workman . such as , adopting more outstanding service equipment to shorten the time for service .
Keywords: Fitting inspection method ; negative exponent distribution ; Poissons distribution ; [ M/M/1 ]: [/FCFS ] model ; [ M/M/4 ]: [/FCFS ] mode
