单服务排队系统MATLAB仿真程序.docx

1、单服务排队系统MATLAB仿真程序单服务台系统MATLAB仿真学号：* 姓名：缪晨一、引言排队是日常生活中经常遇到的现象。通常 ,当人、物体或是信息的到达速率大于完成服务的速率时 ,即出现排队现象。排队越长 ,意味着浪费的时间越多 ,系统的效率也越低。在日常生活中 ,经常遇到排队现象 ,如开车上班、在超市等待结账、工厂中等待加工的工件以及待修的机器等。总之 ,排队现象是随处可见的。排队理论是运作管理中最重要的领域之一 ,它是计划、工作设计、存货控制及其他一些问题的基础。Matlab是 MathWorks公司开发的科学计算软件 ,它以其强大的计算和绘图功能、大量稳定可靠的算法库、简洁高效的编程语

2、言以及庞大的用户群成为数学计算工具方面的标准 ,几乎所有的工程计算领域 ,Matlab都有相应的软件工具箱。选用 Matlab软件正是基于 Matlab的诸多优点。二、排队模型三仿真算法原理（1）顾客信息初始化根据到达率 和服务率 来确定每个顾客的到达时间间隔和服务时间间隔。服务间隔时间可以用负指数分布函数exprnd()来生成 。由于泊松过程的时间间隔也服从负指数分布, 故亦可由此函数生成顾客到达时间间隔 。需要注意的是exprnd()的输入参数不是到达率 和服务率 而是平均到达时间间隔 1/和平均服务时间1/。根据到达时间间隔 ,确定每个顾客的到达时刻. 学习过C 语言的人习惯于使用 FO

3、R循环来实现数值的累加, 但FOR循环会引起运算复杂度的增加 而在MATLAB 仿真环境中, 提供了一个方便的函数cumsum() 来实现累加功能 读者可以直接引用对当前顾客进行初始化。 第1 个到达系统的顾客不需要等待就可以直接接受服务 其离开时刻等于到达时刻与服务时间之和。（2）进队出队仿真在当前顾客到达时刻， 根据系统内已有的顾客数来确定是否接纳该顾客。 若接纳 则根据前一顾客的离开时刻来确定当前顾客的等待时间 、离开时间和标志位 ；若拒绝， 则标志位置为0.流程图如下：四、程序实现单服务台服务，服务参数M/M/1，=0.1，排队规则为FIFO，以分为单位，仿真时间240分钟。仿真程序代

4、码如下%总仿真时间Total_time = 240;%到达率与服务率lambda = 0.1;mu =0.1;%平均到达时间与平均服务时间arr_mean = 1/lambda;ser_mean = 1/mu;%可能到达的最大顾客数（round：四舍五入求整数）arr_num = round(Total_time*lambda*2);%顾客事件表初始化events = ;%按负指数分布产生各顾客达到时间间隔events(1,:) = exprnd(arr_mean,1,arr_num);%各顾客的到达时刻等于时间间隔的累积和events(1,:) = cumsum(events(1,:);%按

5、负指数分布产生各顾客服务时间events(2,:) = exprnd(ser_mean,1,arr_num);%计算仿真顾客个数，即到达时刻在仿真时间内的顾客数len_sim = sum(events(1,:)Total_timebreak;%如果第i 个顾客的到达时间未超过仿真时间，则计算在其%到达时刻系统中已有的顾客个数else number = sum(events(4,member) events(1,i);%如果系统已满，则系统拒绝第i 个顾客，其标志位置0if number = N+1events(5,i) = 0;%如果系统为空，则第i 个顾客直接接受服务else if numb

6、er = 0%其等待时间为0events(3,i) = 0;%其离开时刻等于到达时刻与服务时间之和events(4,i) = events(1,i)+events(2,i);%其标志位置1events(5,i) = 1;member = member,i;%如果系统有顾客正在接受服务，且系统等待队列未满，则%第i 个顾客进入系统else len_mem = length(member);%其等待时间等于队列中前一个顾客的离开时刻减去其到%达时刻events(3,i)=events(4,member(len_mem)-events(1,i);%其离开时刻等于队列中前一个顾客的离开时刻加上其服%务

7、时间events(4,i)=events(4,member(len_mem)+events(2,i);%标识位表示其进入系统后，系统内共有的顾客数events(5,i) = number+1;member = member,i;endendendend五、仿真结果events = number = 1 number = 0 events = Columns 1 through 7 5.6418 13.2050 57.5155 68.3886 86.5789 88.8820 100.5548 9.1178 25.7746 14.2747 20.9298 16.9332 14.2731 8.740

8、3 0 0 0 0 0 0 0 14.7597 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 Columns 8 through 14 106.9312 124.9101 129.9854 143.3425 147.5878 151.3098 154.2113 30.0267 1.0235 0.5680 7.1159 7.1488 10.8554 1.0530 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 15 through 21 162.1843 186.9750 201.7163 202.6228 221.4368 2

9、23.3506 229.5432 9.9629 21.9640 2.4814 9.4228 14.2009 9.0656 23.3868 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 22 through 28 229.5819 255.0699 263.2190 285.6008 285.9892 339.7321 342.2822 20.2516 0.5970 0.4486 5.5302 28.1709 14.4911 10.4084 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 2

10、9 through 35 344.2996 345.7073 370.4249 379.5933 393.0690 395.2996 403.7064 1.9700 41.7316 31.4600 17.7792 4.3214 3.1235 4.3426 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 36 through 42 404.6424 421.6883 435.0138 454.2870 474.2329 475.6337 481.0860 7.9646 6.0329 12.1631 2.9478 16.6625 3.7575 1

11、6.9548 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 43 through 48 487.0670 506.3803 507.9699 512.7172 523.1882 529.8581 9.9836 4.6901 2.4817 25.1175 0.7323 2.5397 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 events = Columns 1 through 7 5.6418 13.2050 57.5155 68.3886 86.5789 88.8820 100.5548 9.1178 25.7

12、746 14.2747 20.9298 16.9332 14.2731 8.7403 0 0 0 0 0 0 0 14.7597 0 71.7901 0 0 0 0 1.0000 0 1.0000 0 0 0 0 Columns 8 through 14 106.9312 124.9101 129.9854 143.3425 147.5878 151.3098 154.2113 30.0267 1.0235 0.5680 7.1159 7.1488 10.8554 1.0530 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 15 throu

13、gh 21 162.1843 186.9750 201.7163 202.6228 221.4368 223.3506 229.5432 9.9629 21.9640 2.4814 9.4228 14.2009 9.0656 23.3868 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 22 through 28 229.5819 255.0699 263.2190 285.6008 285.9892 339.7321 342.2822 20.2516 0.5970 0.4486 5.5302 28.1709 14.4911 10.4084

14、 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 29 through 35 344.2996 345.7073 370.4249 379.5933 393.0690 395.2996 403.7064 1.9700 41.7316 31.4600 17.7792 4.3214 3.1235 4.3426 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 36 through 42 404.6424 421.6883 435.0138 454.2870 474.2329 475.6337 48

15、1.0860 7.9646 6.0329 12.1631 2.9478 16.6625 3.7575 16.9548 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 43 through 48 487.0670 506.3803 507.9699 512.7172 523.1882 529.8581 9.9836 4.6901 2.4817 25.1175 0.7323 2.5397 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 number = 1 number = 0 events = Columns 1 thr

16、ough 7 5.6418 13.2050 57.5155 68.3886 86.5789 88.8820 100.5548 9.1178 25.7746 14.2747 20.9298 16.9332 14.2731 8.7403 0 0 0 0 0 0 0 14.7597 0 71.7901 0 0 0 0 1.0000 0 1.0000 0 0 0 0 Columns 8 through 14 106.9312 124.9101 129.9854 143.3425 147.5878 151.3098 154.2113 30.0267 1.0235 0.5680 7.1159 7.1488

17、 10.8554 1.0530 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 15 through 21 162.1843 186.9750 201.7163 202.6228 221.4368 223.3506 229.5432 9.9629 21.9640 2.4814 9.4228 14.2009 9.0656 23.3868 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 22 through 28 229.5819 255.0699 263.2190 285.6008 285.9

18、892 339.7321 342.2822 20.2516 0.5970 0.4486 5.5302 28.1709 14.4911 10.4084 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 29 through 35 344.2996 345.7073 370.4249 379.5933 393.0690 395.2996 403.7064 1.9700 41.7316 31.4600 17.7792 4.3214 3.1235 4.3426 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Colu

19、mns 36 through 42 404.6424 421.6883 435.0138 454.2870 474.2329 475.6337 481.0860 7.9646 6.0329 12.1631 2.9478 16.6625 3.7575 16.9548 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 43 through 48 487.0670 506.3803 507.9699 512.7172 523.1882 529.8581 9.9836 4.6901 2.4817 25.1175 0.7323 2.5397 0 0 0

20、0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 events = Columns 1 through 7 5.6418 13.2050 57.5155 68.3886 86.5789 88.8820 100.5548 9.1178 25.7746 14.2747 20.9298 16.9332 14.2731 8.7403 0 0 0 0 0 0 0 14.7597 0 71.7901 0 103.5121 0 0 1.0000 0 1.0000 0 1.0000 0 0 Columns 8 through 14 106.9312 124.9101 129.9854 143.342

21、5 147.5878 151.3098 154.2113 30.0267 1.0235 0.5680 7.1159 7.1488 10.8554 1.0530 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 15 through 21 162.1843 186.9750 201.7163 202.6228 221.4368 223.3506 229.5432 9.9629 21.9640 2.4814 9.4228 14.2009 9.0656 23.3868 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

22、 Columns 22 through 28 229.5819 255.0699 263.2190 285.6008 285.9892 339.7321 342.2822 20.2516 0.5970 0.4486 5.5302 28.1709 14.4911 10.4084 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 29 through 35 344.2996 345.7073 370.4249 379.5933 393.0690 395.2996 403.7064 1.9700 41.7316 31.4600 17.7792 4.3

23、214 3.1235 4.3426 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 36 through 42 404.6424 421.6883 435.0138 454.2870 474.2329 475.6337 481.0860 7.9646 6.0329 12.1631 2.9478 16.6625 3.7575 16.9548 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 43 through 48 487.0670 506.3803 507.9699 512.7172 523

24、.1882 529.8581 9.9836 4.6901 2.4817 25.1175 0.7323 2.5397 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 number = 1 number = 1 number = 0 events = Columns 1 through 7 5.6418 13.2050 57.5155 68.3886 86.5789 88.8820 100.5548 9.1178 25.7746 14.2747 20.9298 16.9332 14.2731 8.7403 0 0 0 0 0 0 0 14.7597 0 71.7901 0

25、103.5121 0 0 1.0000 0 1.0000 0 1.0000 0 0 Columns 8 through 14 106.9312 124.9101 129.9854 143.3425 147.5878 151.3098 154.2113 30.0267 1.0235 0.5680 7.1159 7.1488 10.8554 1.0530 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 15 through 21 162.1843 186.9750 201.7163 202.6228 221.4368 223.3506 229.5

26、432 9.9629 21.9640 2.4814 9.4228 14.2009 9.0656 23.3868 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 22 through 28 229.5819 255.0699 263.2190 285.6008 285.9892 339.7321 342.2822 20.2516 0.5970 0.4486 5.5302 28.1709 14.4911 10.4084 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 29 through 35

27、344.2996 345.7073 370.4249 379.5933 393.0690 395.2996 403.7064 1.9700 41.7316 31.4600 17.7792 4.3214 3.1235 4.3426 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 36 through 42 404.6424 421.6883 435.0138 454.2870 474.2329 475.6337 481.0860 7.9646 6.0329 12.1631 2.9478 16.6625 3.7575 16.9548 0 0 0

28、0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Columns 43 through 48 487.0670 506.3803 507.9699 512.7172 523.1882 529.8581 9.9836 4.6901 2.4817 25.1175 0.7323 2.5397 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 events = Columns 1 through 7 5.6418 13.2050 57.5155 68.3886 86.5789 88.8820 100.5548 9.1178 25.7746 14.2747 20.9298 16.9332 14.2731 8.7403 0 0 0 0 0 0 0 14.7597 0 71.7901 0 103.5121 0 0 1.0000 0 1.0000 0 1.0000 0 0 Columns 8 through 14 106.9312 124.9101 129.985