單服務(wù)排隊系統(tǒng)MATLAB仿真程序

1、單服務(wù)臺系統(tǒng)MATLAB真一、引言排隊是日常生活中經(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，即出現(xiàn)排隊現(xiàn)象。排隊越長,意味著浪費的時間越多，系統(tǒng)的效率也越低。在日常生活中，經(jīng)常遇到排隊現(xiàn)象，如開車上班、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?，排隊現(xiàn)象是隨處可見的。排隊理論是運作管理中最重要的領(lǐng)域之一，它是計劃、工作設(shè)計、存貨控制及其他一些問題的基礎(chǔ)。Matlab是MathWorks公司開發(fā)的科學(xué)計算軟件，它以其強(qiáng)大的計算和繪圖功能、大量穩(wěn)定可靠的算法庫、簡潔高效的編程語言以及龐大的用戶群成為數(shù)學(xué)計算工具方面的標(biāo)準(zhǔn)，幾乎所有的工程計算領(lǐng)域，Mat

2、lab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。二、排隊模型三、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)率來確定每個顧客的到達(dá)時間間隔和服務(wù)時間問隔。服務(wù)間隔時間可以用負(fù)指數(shù)分布函數(shù)exprnd()來生成。由于泊松過程的時間間隔也服從負(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)率而是平均到達(dá)時間間隔1/入和平均服務(wù)時間1/。根據(jù)到達(dá)時間問隔，確定每個顧客的到達(dá)時刻.學(xué)習(xí)過C語言的人習(xí)慣于使用FOR循環(huán)來實現(xiàn)數(shù)值的累加，但FOR循環(huán)會引起運算復(fù)雜度的增加而在MATLABggt環(huán)境中，提供了一個

3、方便的函數(shù)cumsum()來實現(xiàn)累加功能讀者可以直接引用對當(dāng)前顧客進(jìn)行初始化。第1個到達(dá)系統(tǒng)的顧客不需要等待就可以直接接受服務(wù)其離開時刻等于到達(dá)時刻與服務(wù)時間之和。(2) 進(jìn)隊出隊仿真在當(dāng)前顧客到達(dá)時刻，根據(jù)系統(tǒng)內(nèi)已有的顧客數(shù)來確定是否接納該顧客。若接納則根據(jù)前一顧客的離開時刻來確定當(dāng)前顧客的等待時間、離開時間和標(biāo)志位；若拒絕，則標(biāo)志位置為0.流程圖如下：四、程序?qū)崿F(xiàn)單服務(wù)臺服務(wù)，服務(wù)參數(shù)M/M/1,入=，排隊規(guī)則為FIFO,以分為單位，仿真時間240分鐘。仿真程序代碼如下咨、仿真時間Total_time=240;雍U達(dá)率與服務(wù)率lambda=;mu=;%乎均到達(dá)時間與平均服務(wù)時間arr_me

4、an=1/lambda;ser_mean=1/mu;初能到達(dá)的最大顧客數(shù)(round:四舍五入求整數(shù))arr_num=round(Total_time*lambda*2);9傾客事件表初始化events=;%$負(fù)指數(shù)分布產(chǎn)生各顧客達(dá)到時間間隔events(1,:)=exprnd(arr_mean,1,arr_num);%各顧客的到達(dá)時刻等于而問間隔的象積和events(1,:)=cumsum(events(1,:);9敞負(fù)指數(shù)分布產(chǎn)生各顧客服務(wù)時間events(2,:)=exprnd(ser_mean,1,arr_num);%計算仿真顧客個數(shù)，即到達(dá)時刻在仿真時間內(nèi)的顧客數(shù)len_sim=su

5、m(events(1,:)<=Total_time);%*%計算第1個顧客的信息%*9第1個顧客進(jìn)入系統(tǒng)后直接接受服務(wù)，無需等待events(3,1)=0;沖離開時刻等于其到達(dá)時刻與服務(wù)時間之和events(4,1)=events(1,1)+events(2,1);%其肯定被系統(tǒng)接納，此時系統(tǒng)內(nèi)共有1個顧客，故標(biāo)志位唯1events(5,1)=1;沮進(jìn)入系統(tǒng)后，系統(tǒng)內(nèi)已有成員序號為1member=1;%*%計算第i個顧客的信息%*fori=2:arr_num淤口果第i個顧客的到達(dá)時間超過了仿真時間，則跳出循環(huán)ifevents(1,i)>Total_timebreak;淤口果第i個顧

6、客的到達(dá)時間未超過仿真時間，則計算在其%1U達(dá)時刻系統(tǒng)中已有的顧客個數(shù)elsenumber=sum(events(4,member)>events(1,i);淤口果系統(tǒng)已滿，則系統(tǒng)拒絕第i個顧客，其標(biāo)志位置0ifnumber>=N+1events(5,i)=0;淤口果系統(tǒng)為空，則第i個顧客直接接受服務(wù)elseifnumber=0沮等待時間為0events(3,i)=0;沖離開時刻等于到達(dá)時刻與服務(wù)時間之和events(4,i)=events(1,i)+events(2,i);%其標(biāo)志位置1events(5,i)=1;member=member,i;淤口果系統(tǒng)有顧客正在接受服務(wù)，且系

7、統(tǒng)等待隊列未滿，則9第i個顧客進(jìn)入系統(tǒng)elselen_mem=length(member);沮等待幣問等于隊列中前一個顧客的離開時刻減去其到%4時刻events(3,i)=events(4,member(len_mem)-events(1,i);%其離開時刻等于隊列中前一個顧昴的離開時刻加上其服%務(wù)時間events(4,i)=events(4,member(len_mem)+events(2,i);%S識位表示其進(jìn)入系統(tǒng)后，系統(tǒng)何共有的顧客數(shù)events(5,i)=number+1;member=member,i;endendendend五、仿真結(jié)果events=number=1number=

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