单服务员的排队模型

单服务员的排队模型：在某商店有一个售货员，顾客陆续来到，售货员逐个地接待顾客．当到来的顾客较多时，一部分顾客便须排队等待，被接待后的顾客便离开商店．设： 1．顾客到来间隔时间服从参数为 0.1 的指数分布． ２．对顾客的服务时间服从［４，１５］上的均匀分布． ３．排队按先到先服务规则，队长无限制． （1） 模拟 100 个工作日，求出平均每日完成服务的个数及每日顾客的平均等待时间． MATLAB 程序： clear sm=0;%总工作时间，初始为 0 m=0;%服务总个数 for j=1:100 j w(j)=0; i=2; x(i)=exprnd(10); c(i)=x(i); b(i)=x(i); while b(i)<=480 y(i)=unifrnd(4,15); e(i)=b(i)+y(i); w(j)=w(j)+b(i)-c(i); i=i+1; x(i)=exprnd(10); c(i)=c(i-1)+x(i); b(i)=max(c(i),e(i-1)); end i=i-2; t=w(j)/i %每 j 日顾客的平均等待时间 m=m+i; sm=sm+w(j);%总的等待时间 end m ; %100 日服务总个数 am=m/100 %输出平均每日完成服务的个数 at= sm/m %输出平均每日顾客平均等待时间 运行结果：j = 1 t = 7.6488 j = 2 t = 21.5629 j = 3 t = 48.0306 j = 4 t = 15.3583 j = 5 t = 29.0681 j = 6 t = 43.9925 j = 7 t = 9.1838 j = 8 t = 29.3542 j = 9 t = 37.3775 j = 10 t = 36.6198 j = 11 t = 15.1372 j = 12 t = 11.9697 j = 13 t = 46.2765 j = 14 t = 5.0990 j = 15 t = 12.4896 j = 16 t = 19.3674 j = 17 t = 27.7045 j = 18 t = 13.7486 j = 19 t = 24.3442 j = 20 t = 10.8663 j = 21 t = 8.0429 j = 22 t = 10.3723 j = 23 t = 11.8501 j = 24 t = 14.3409 j = 25 t = 46.0177 j = 26 t = 8.8139 j = 27 t = 5.3630 j = 28 t = 12.8179 j = 29 t = 7.2817 j = 30 t = 11.1612 j = 31 t = 9.3863 j = 32 t = 62.4873 j = 33 t = 13.0453 j = 34 t = 21.7910 j = 35 t = 16.5294 j = 36 t = 12.2347 j = 37 t = 24.9796 j = 38 t = 78.2435 j = 39 t = 24.3057 j = 40 t = 15.2035 j = 41 t = 46.8024 j = 42 t = 56.4635 j = 43 t = 37.1819 j = 44 t = 18.2931 j = 45 t = 55.0295 j = 46 t = 35.6992 j = 47 t = 24.6073 j = 48 t = 12.9206 j = 49 t = 15.4886 j = 50 t = 17.0108 j = 51 t = 20.9452 j = 52 t = 21.8094 j = 53 t = 75.8497 j = 54 t = 25.1111 j = 55 t = 34.9260 j = 56 t = 32.5712 j = 57 t = 27.9767 j = 58 t = 29.5067 j = 59 t = 29.4701 j = 60 t = 19.2476 j = 61 t = 16.3576 j = 62 t = 8.8686 j = 63 t = 29.0910 j = 64 t = 14.7117 j = 65 t = 36.7096 j = 66 t = 46.9512 j = 67 t = 7.7582 j = 68 t = 11.8390 j = 69 t = 43.2197 j = 70 t = 97.6024 j = 71 t = 70.4187 j = 72 t = 8.5048 j = 73 t = 4.1632 j = 74 t = 18.7508 j = 75 t = 41.1622 j = 76 t = 28.1712 j = 77 t = 56.6012 j = 78 t = 45.1566 j = 79 t = 12.9582 j = 80 t = 6.6022 j = 81 t = 19.3046 j = 82 t = 26.1914 j = 83 t = 8.4448 j = 84 t = 18.3721 j = 85 t = 18.1843 j = 86 t = 41.0727 j = 87 t = 7.7466 j = 88 t = 54.3138 j = 89 t = 22.9150 j = 90 t = 68.9592 j = 91 t = 11.5373 j = 92 t = 14.4600 j = 93 t = 27.6556 j = 94 t = 41.1297 j = 95 t = 24.8645 j = 96 t = 36.2404 j = 97 t = 5.2884 j = 98 t = 7.2035 j = 99 t = 25.1523 j = 100 t = 24.6979 am = 44.1400 at = 27.1289