摘 要
如今，隨著人們的生活節奏逐漸加快，高速公路上車輛的不斷增多，高速公路收費亭數量的最佳設計方案在縮短司機的等待時間、減輕交通擁塞狀況以及贏得司機滿意度等方面起著舉足輕重的作用。本文主要針對這1實際情況建立數學模型，來解決相關的問題。
根據實際情況，本文給出了1個合理且可行的隨機模型。在模型中，本文首先根據收集的資料計算出其收費口在單位時間裡到達的車輛數和每1輛車的服務時間所服從的分佈，然後把整個處理過程劃分成4個主要部分：輸入過程，排隊規則，服務方式，輸出過程。既然到達車輛的數量服從泊松分佈，服務時間服從負指數分佈，在等待服務的.車輛遵循先來先服務的規則下，那麼，本文通過M/M/K ,M/M/1及相關其他方法計算出車輛在收費站等待的概率以及包括等待時間和服務時間的總時間期望值，在保證最短等待時間的條件下得到高速公路收費亭數量和服務人員的服務速率的最佳設計方案。
最後，本文提出了1些設定高速公路收費口的收費亭數量和提高服務人員服務速率的建議，比如採用更先進的服務裝置來縮短服務時間等。
關鍵詞： 擬合檢驗法；負指數分佈；泊松分佈；[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
