單服務(wù)排隊(duì)系統(tǒng)MATLAB仿真程序

單服務(wù)臺(tái)系統(tǒng)MATLAB仿真學(xué)號(hào)：1040408115姓名：繆晨引言排隊(duì)是日常生活中經(jīng)常遇到的現(xiàn)象。通常,當(dāng)人、物體或是信息的到達(dá)速率大于完成服務(wù)的速率時(shí),即出現(xiàn)排隊(duì)現(xiàn)象。排隊(duì)越長(zhǎng),意味著浪費(fèi)的時(shí)間越多,系統(tǒng)的效率也越低。在日常生活中,經(jīng)常遇到排隊(duì)現(xiàn)象,如開(kāi)車上班、在超市等待結(jié)賬、工廠中等待加工的工件以及待修的機(jī)器等。總之,排隊(duì)現(xiàn)象是隨處可見(jiàn)的。排隊(duì)理論是運(yùn)作管理中最重要的領(lǐng)域之一,它是計(jì)劃、工作設(shè)計(jì)、存貨控制及其他一些問(wèn)題的基礎(chǔ)。Matlab是MathWorks公司開(kāi)發(fā)的科學(xué)計(jì)算軟件，它以其強(qiáng)大的計(jì)算和繪圖功能、大量穩(wěn)定可靠的算法庫(kù)、簡(jiǎn)潔高效的編程語(yǔ)言以及龐大的用戶群成為數(shù)學(xué)計(jì)算工具方面的標(biāo)準(zhǔn)，幾乎所有的工程計(jì)算領(lǐng)域，Matlab都有相應(yīng)的軟件工具箱。選用Matlab軟件正是基于Matlab的諸多優(yōu)點(diǎn)。排隊(duì)模型服務(wù)臺(tái)服務(wù)臺(tái)三．仿真算法原理（1）顧客信息初始化根據(jù)到達(dá)率人和服務(wù)率從來(lái)確定每個(gè)顧客的到達(dá)時(shí)間間隔和服務(wù)時(shí)間間隔。服務(wù)間隔時(shí)間可以用負(fù)指數(shù)分布函數(shù) 來(lái)生成。由于泊松過(guò)程的時(shí)間間隔也服從負(fù)指數(shù)分布,故亦可由此函數(shù)生成顧客到達(dá)時(shí)間間隔。需要注意的是 的輸入?yún)?shù)不是到達(dá)率人和服務(wù)率從而是平均到達(dá)時(shí)間間隔入和平均服務(wù)時(shí)間/根據(jù)到達(dá)時(shí)間間隔確定每個(gè)顧客的到達(dá)時(shí)刻學(xué)習(xí)過(guò)語(yǔ)言的人習(xí)慣于使用 循環(huán)來(lái)實(shí)現(xiàn)數(shù)值的累加但 循環(huán)會(huì)引起運(yùn)算復(fù)雜度的增加而在仿真環(huán)境中提供了一個(gè)方便的函數(shù) 來(lái)實(shí)現(xiàn)累加功能讀者可以直接引用對(duì)當(dāng)前顧客進(jìn)行初始化。第1個(gè)到達(dá)系統(tǒng)的顧客不需要等待就可以直接接受服務(wù)其離開(kāi)時(shí)刻等于到達(dá)時(shí)刻與服務(wù)時(shí)間之和。（2）進(jìn)隊(duì)出隊(duì)仿真在當(dāng)前顧客到達(dá)時(shí)刻，根據(jù)系統(tǒng)內(nèi)已有的顧客數(shù)來(lái)確定是否接納該顧客。若接納則根據(jù)前一顧客的離開(kāi)時(shí)刻來(lái)確定當(dāng)前顧客的等待時(shí)間、離開(kāi)時(shí)間和標(biāo)志位；若拒絕，則標(biāo)志位置為0.流程圖如下：

仿典時(shí)間及般看越界？系統(tǒng)是否接納第i個(gè)核客？瑜出轉(zhuǎn)果標(biāo)志佐置仿典時(shí)間及般看越界？系統(tǒng)是否接納第i個(gè)核客？瑜出轉(zhuǎn)果標(biāo)志佐置a\=\+1計(jì)算第i個(gè)佛客的等待時(shí)間.離開(kāi)時(shí)間、標(biāo)志位；1=14-1啞客源加始化計(jì)算第1個(gè)耀客的璃開(kāi)時(shí)剜：i=2四、程序?qū)崿F(xiàn)單服務(wù)臺(tái)服務(wù)，服務(wù)參數(shù)M/M/1,八四.排隊(duì)規(guī)則為 ，以分為單位，仿真時(shí)間24分0鐘。仿真程序代碼如下%總仿真時(shí)間Total_time=240;%到達(dá)率與服務(wù)率lambda=0.1;mu=0.1;%平均到達(dá)時(shí)間與平均服務(wù)時(shí)間arr_mean=1/lambda;ser_mean=1/mu;%可能到達(dá)的最大顧客數(shù)(round：四舍五入求整數(shù))arr_num=round(Total_time*lambda*2);%顧客事件表初始化events=[];%按負(fù)指數(shù)分布產(chǎn)生各顧客達(dá)到時(shí)間間隔events(1,:)=exprnd(arr_mean,1,arr_num);%各顧客的到達(dá)時(shí)刻等于時(shí)間間隔的累積和events(1,:)=cumsum(events(1,:));%按負(fù)指數(shù)分布產(chǎn)生各顧客服務(wù)時(shí)間events(2,:)=exprnd(ser_mean,1,arr_num);%計(jì)算仿真顧客個(gè)數(shù)，即到達(dá)時(shí)刻在仿真時(shí)間內(nèi)的顧客數(shù)len_sim=sum(events(1,:)<=Total_time);%計(jì)算第1個(gè)顧客的信息^y~f%第1個(gè)顧客進(jìn)入系統(tǒng)后直接接受服務(wù)，無(wú)需等待events(3,1)=0;%其離開(kāi)時(shí)刻等于其到達(dá)時(shí)刻與服務(wù)時(shí)間之和events(4,1)=events(1,1)+events(2,1);%其肯定被系統(tǒng)接納，此時(shí)系統(tǒng)內(nèi)共有1個(gè)顧客，故標(biāo)志位%置1events(5,1)=1;%其進(jìn)入系統(tǒng)后，系統(tǒng)內(nèi)已有成員序號(hào)為1member=[1];^y~f%計(jì)算第i個(gè)顧客的信息^y~ffori=2:arr_num%如果第i個(gè)顧客的到達(dá)時(shí)間超過(guò)了仿真時(shí)間，則跳出循環(huán)ifevents(1,i)>Total_timebreak;%如果第i個(gè)顧客的到達(dá)時(shí)間未超過(guò)仿真時(shí)間，則計(jì)算在其%到達(dá)時(shí)刻系統(tǒng)中已有的顧客個(gè)數(shù)elsenumber=sum(events(4,member)>events(1,i));%如果系統(tǒng)已滿，則系統(tǒng)拒絕第i個(gè)顧客，其標(biāo)志位置0ifnumber>=N+1events(5,i)=0;%如果系統(tǒng)為空，則第i個(gè)顧客直接接受服務(wù)elseifnumber==0%其等待時(shí)間為0events(3,i)=0;%其離開(kāi)時(shí)刻等于到達(dá)時(shí)刻與服務(wù)時(shí)間之和events(4,i)=events(1,i)+events(2,i);%其標(biāo)志位置1events(5,i)=1;member=[member,i];%如果系統(tǒng)有顧客正在接受服務(wù)，且系統(tǒng)等待隊(duì)列未滿，則%第i個(gè)顧客進(jìn)入系統(tǒng)elselen_mem=length(member);%其等待時(shí)間等于隊(duì)列中前一個(gè)顧客的離開(kāi)時(shí)刻減去其到%達(dá)時(shí)刻events(3,i)=events(4,member(len_mem))-events(1,i);%其離開(kāi)時(shí)刻等于隊(duì)列中前一個(gè)顧客的離開(kāi)時(shí)刻加上其服%務(wù)時(shí)間events(4,i)=events(4,member(len_mem))+events(2,i);%標(biāo)識(shí)位表示其進(jìn)入系統(tǒng)后，系統(tǒng)內(nèi)共有的顧客數(shù)events(5,i)=number+1;member=[member,i];endendendend五、仿真結(jié)果events=[]number=1number=0events=Columns1through75.641813.205057.515568.388686.578988.8820100.55489.117825.774614.274720.929816.933214.27318.7403000000014.75970000001.0000000000Columns8through14106.9312124.9101129.9854143.3425147.5878151.3098154.211330.02671.02350.56807.11597.148810.85541.05300000000

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