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高速公路收費口的優(yōu)化設置
摘 要
如今，隨著(zhù)人們的生活節奏逐漸加快，高速公路上車(chē)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(shí)間、減輕交通擁塞狀況以及贏(yíng)得司機滿(mǎn)意度等方面起著(zhù)舉足輕重的作用。本文主要針對這1實(shí)際情況建立數學(xué)模型，來(lái)解決相關(guān)的問(wèn)題。
根據實(shí)際情況，本文給出了1個(gè)合理且可行的隨機模型。在模型中，本文首先根據收集的數據計算出其收費口在單位時(shí)間里到達的車(chē)輛數和每1輛車(chē)的服務(wù)時(shí)間所服從的分布，然后把整個(gè)處理過(guò)程劃分成4個(gè)主要部分：輸入過(guò)程，排隊規則，服務(wù)方式，輸出過(guò)程。既然到達車(chē)輛的數量服從泊松分布，服務(wù)時(shí)間服從負指數分布，在等待服務(wù)的車(chē)輛遵循先來(lái)先服務(wù)的規則下，那么，本文通過(guò)M/M/K ,M/M/1及相關(guān)其他方法計算出車(chē)輛在收費站等待的概率以及包括等待時(shí)間和服務(wù)時(shí)間的總時(shí)間期望值，在保證最短等待時(shí)間的條件下得到高速公路收費亭數量和服務(wù)人員的服務(wù)速率的最佳設計方案。
最后，本文提出了1些設置高速公路收費口的收費亭數量和提高服務(wù)人員服務(wù)速率的建議，比如采用更先進(jìn)的服務(wù)設備來(lái)縮短服務(wù)時(shí)間等。
關(guān)鍵詞： 擬合檢驗法；負指數分布；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
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