單服務(wù)排隊(duì)系統(tǒng)MATLAB仿真程序

1、單服務(wù)臺(tái)系統(tǒng)MATLAB仿真學(xué)號(hào)：15 姓名：繆晨一、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?？傊抨?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

2、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)模型三. 仿真算法原理(1)顧客信息初始化根據(jù)到達(dá)率入 和服務(wù)率來(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) exprnd()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 exprnd() 的輸入?yún)?shù)不是到達(dá)率 入和服務(wù)率口而是平均到達(dá)時(shí)間間隔1/入和平均服務(wù)時(shí)間1/卩。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) C 語(yǔ)言 的人習(xí)慣于使用FOR循環(huán)來(lái)實(shí)現(xiàn)數(shù)值的累加，

3、但FOR循環(huán)會(huì)引起運(yùn) 算復(fù)雜度的增加 而在MATLAB仿真環(huán)境中，提供了一個(gè)方便的函數(shù) cumsum() 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：訃牛K容的離開(kāi)時(shí)i=2N箍工樸按渝、第i牛嗾窖？ ”/林*kfifKmAi+I1*1 MSfii節(jié)操客的VWHM.育開(kāi)時(shí)訶、標(biāo)志位；四

4、、程序?qū)崿F(xiàn)單服務(wù)臺(tái)服務(wù)，服務(wù)參數(shù) M/M/1,入二卩二，排隊(duì)規(guī)則為FIFO，以 分為單位，仿真時(shí)間240分鐘。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 =;mu =;%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_n

5、um);%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_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)else number = 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 0

6、 if number = 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) else if number = 0%其等待時(shí)間為 0 events(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)else len_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even

7、ts(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 =Columns1 through 7000000 0000 000000 0000000000000015 throu

8、gh 21000000000000Columns8 through1400 000 000 0Columns00 000 000 0Columns22 through 280 0 00 0 000 000 000 00 0 00 0 00 0 000 000 000 0Columns 29 through 35Columns 36 through 420 0 00 00 0000Columns 43 through 48000000000000000000events =Columns1 through 70000000000 0000000000000015 through 21000000

9、000000Columns8 through1400 000 000 0Columns00 000 000 0Columns22 through 280 0 00 0 000 000 000 00 0 00 0 00 0 0Columns 36 through 4200 000 000 0Columns 29 through 3500000 000000 0Columns 43 through48000000 0 00 0 00 0 0number =1 number =events =Columns 1 through 70 00000 00 0 0 000 0 0 00Columns 8

10、through 1400000000000000000000 0Columns 15 through 210 0 00 0 000 000 000 00 0 00 0 00 0 0Columns 29 through 350 0 000 000 000 0Columns 22 through 280 0 00 0Columns 36 through 4200 000 000 00 0 00 0 00 0 0Columns 43 through 480000 0 00 0 00events =Columns 1 through 7000000 00 00 00 00 0Columns 8 thr

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13、 through 140 0 00 0 0 000 0 0 0Columns 15 through 210 00 00 00 00 00 00 0 00 0 00 0 0Columns 22 through 280 0 00 0 000 000 000 0Columns 29 through 3500 000 000 00 0 00 0 00 0 0Columns 36 through 4200000 000000 0Columns 43 through480 000 000 00 0 00 0 00 0 0number =1 number =number = events =Columns1

14、 through7000000 0000 0000 0Columns8 through14000000000000000000Columns15through2100 000 000 0Columns00 000 000 0Columns00000000000022 through 2800000000000029 through 350 0 00 0 000 000 000 0Columns 36 through 4200 000 000 00 0 00 0 00 0 0Columns 43 through 480 0 000 00000events =Columns 1 through 7

15、000000 00 00 00 00 0Columns 8 through1400 00000000 0 0000 0 0Columns 15 through 210 0 00 0 000 000 000 00 0 00 0 00 0 000 000 000 0Columns 22 through 28Columns 29 through 3500 000 000 00 0 00 0 00 0 00 0000000 0000000 0Columns 36 through42Columns 43 through 480 0 00number =1number =0events =Columns

16、1 through 70 0 00 00 0 0 00 0 0 0Columns 8 through 14000 00 0000 00 0Columns 15 through21000 0 000000000000 00 0 00 0 0Columns 22 through 280 0 0 0 0 00 0 0 0 0 00 0 0 0Columns 29 through 3500 000 000 00 0 00 0 00 0 0Columns 36 through 420 00 00 00 00 00 0Columns 43 through 480 0 00 0 00 0 000000000

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